Chapter 16 - Managing Bond Portfolios13. a. The duration of the annuity if it were to start in 1 year would be: (1) (2) (3) (4) (5) Time until Cash Flow PV of CF Payment (Discount Weight Column (1) × rate = 10%) Column (4) (years) 0.14795 0.13450 0.14795 1 $10,000 $9,090.909 0.12227 0.26900 2 $10,000 $8,264.463 0.11116 0.36682 3 $10,000 $7,513.148 0.10105 0.44463 4 $10,000 $6,830.135 0.09187 0.50526 5 $10,000 $6,209.213 0.08351 0.55119 6 $10,000 $5,644.739 0.07592 0.58460 7 $10,000 $5,131.581 0.06902 0.60738 8 $10,000 $4,665.074 0.06275 0.62118 9 $10,000 $4,240.976 1.00000 0.62745 10 $10,000 $3,855.433 4.72546 Column Sums $61,445.671 D = 4.7255 years Because the payment stream starts in five years, instead of one year, we add four years to the duration, so the duration is 8.7255 years.b. The present value of the deferred annuity is: 10,000 × Annuity factor (10%,10) = $41,968 1.10 4 Call w the weight of the portfolio invested in the 5-year zero. Then: (w × 5) + [(1 – w) × 20] = 8.7255 ⇒ w = 0.7516 The investment in the 5-year zero is equal to: 0.7516 × $41,968 = $31,543 The investment in the 20-year zeros is equal to: 0.2484 × $41,968 = $10,425 These are the present or market values of each investment. The face values are equal to the respective future values of the investments. The face value of the 5- year zeros is: $31,543 × (1.10)5 = $50,800 Therefore, between 50 and 51 zero-coupon bonds, each of par value $1,000, would be purchased. Similarly, the face value of the 20-year zeros is: $10,425 × (1.10)20 = $70,134 16-6

Chapter 16 - Managing Bond Portfolios14. Using a financial calculator, we find that the actual price of the bond as a function of yield to maturity is:Yield to maturity Price 7% $1,620.45 8% $1,450.31 9% $1,308.21Using the Duration Rule, assuming yield to maturity falls to 7%:Predicted price change = − Duration × ∆y × P0 1+ y = − 11.54 × (−0.01) × $1,450.31 = $154.97 1.08 Therefore: predicted new price = $1,450.31 + $154.97 = $1,605.28The actual price at a 7% yield to maturity is $1,620.45. Therefore:% error = $1,605.28 − $1,620.45 = −0.0094 = −0.94% (approximation is too low) $1,620.45Using the Duration Rule, assuming yield to maturity increases to 9%:Predicted price change = − Duration × ∆y × P0 1+ y = − 11.54 × 0.01× $1,450.31 = −$154.97 1.08 Therefore: predicted new price = $1,450.31 – $154.97= $1,295.34The actual price at a 9% yield to maturity is $1,308.21. Therefore:% error = $1,295.34 − $1,308.21 = −0.0098 = −0.98% (approximation is too low) $1,308.21Using Duration-with-Convexity Rule, assuming yield to maturity falls to 7% − Duration 1+ y ∆y [ ]Predicted price change = × + 0.5 × Convexity × (∆y)2 × P0 11.54 (−0.01) [ ]= 1.08 × $1,450.31 = $168.92 − × + 0.5 ×192.4 × (−0.01)2 Therefore: predicted new price = $1,450.31 + $168.92 = $1,619.23The actual price at a 7% yield to maturity is $1,620.45. Therefore:% error = $1,619.23 − $1,620.45 = −0.00075 = −0.075% (approximation is too low) $1,620.45 16-7

Chapter 16 - Managing Bond PortfoliosUsing Duration-with-Convexity Rule, assuming yield to maturity rises to 9%: − Duration 1+ y ∆y [ ]Predicted price change = × + 0.5 × Convexity × (∆y)2 × P0[ ]= 11.54 − 1.08 × 0.01 + 0.5 ×192.4 × (0.01)2 × $1,450.31 = −$141.02 Therefore: predicted new price = $1,450.31 – $141.02 = $1,309.29The actual price at a 9% yield to maturity is $1,308.21. Therefore:% error = $1,309.29 − $1,308.21 = 0.00083 = 0.083% (approximation is too high) $1,308.21Conclusion: The duration-with-convexity rule provides more accurate approximations tothe true change in price. In this example, the percentage error using convexity withduration is less than one-tenth the error using only duration to estimate the price change.15. The minimum terminal value that the manager is willing to accept is determined by the requirement for a 3% annual return on the initial investment. Therefore, the floor is: $1 million × (1.03)5 = $1.16 million Three years after the initial investment, only two years remain until the horizon date, and the interest rate has risen to 8%. Therefore, at this time, in order to be assured that the target value can be attained, the manager needs a portfolio worth: $1.16 million/(1.08)2 = $0.9945 million This is the trigger point.16. The maturity of the 30-year bond will fall to 25 years, and its yield is forecast to be 8%. Therefore, the price forecast for the bond is: $893.25 [Using a financial calculator, enter the following: n = 25; i = 8; FV = 1000; PMT = 70] At a 6% interest rate, the five coupon payments will accumulate to $394.60 after five years. Therefore, total proceeds will be: $394.60 + $893.25 = $1,287.85 Therefore, the 5-year return is: ($1,287.85/$867.42) – 1 = 0.4847 This is a 48.47% 5-year return, or 8.23% annually. 16-8

Chapter 16 - Managing Bond Portfolios The maturity of the 20-year bond will fall to 15 years, and its yield is forecast to be 7.5%. Therefore, the price forecast for the bond is: $911.73 [Using a financial calculator, enter the following: n = 15; i = 7.5; FV = 1000; PMT = 65] At a 6% interest rate, the five coupon payments will accumulate to $366.41 after five years. Therefore, total proceeds will be: $366.41 + $911.73 = $1,278.14 Therefore, the 5-year return is: ($1,278.14/$879.50) – 1 = 0.4533 This is a 45.33% 5-year return, or 7.76% annually. The 30-year bond offers the higher expected return.17. a. Time PV of CF Discount rate = Period until Cash 6% per period Weight Years × Payment Flow Weight (Years) A. 8% coupon bond 1 0.5 $40 $37.736 0.0405 0.0203 2 1.0 40 35.600 0.0383 0.0383 3 1.5 40 33.585 0.0361 0.0541 4 2.0 1,040 823.777 0.8851 1.7702 Sum: $930.698 1.0000 1.8829 B. Zero-coupon 1 0.5 $0 $0.000 0.0000 0.0000 Sum: 2 1.0 0 0.000 0.0000 0.0000 3 1.5 0 0.000 0.0000 0.0000 4 2.0 1,000 1.0000 2.0000 792.094 1.0000 2.0000 $792.094 For the coupon bond, the weight on the last payment in the table above is less than it is in Spreadsheet 16.1 because the discount rate is higher; the weights for the first three payments are larger than those in Spreadsheet 16.1. Consequently, the duration of the bond falls. The zero coupon bond, by contrast, has a fixed weight of 1.0 for the single payment at maturity. b. Period Time Cash PV of CF Weight Years × A. 8% coupon bond until Flow Discount rate = Weight 1 Payment 5% per period Sum: 2 (Years) 3 4 0.5 $60 $57.143 0.0552 0.0276 54.422 0.0526 0.0526 1.0 60 51.830 0.0501 0.0751 872.065 0.8422 1.6844 1.5 60 $1,035.460 1.0000 1.8396 2.0 1,060 Since the coupon payments are larger in the above table, the weights on the earlier payments are higher than in Spreadsheet 16.1, so duration decreases. 16-9

Chapter 16 - Managing Bond Portfolios18. Time Cash PV(CF) t + t2 (t + t2) × PV(CF) a. (t) Flow Coupon = $80 1 $80 $72.727 2 145.455 YTM = 0.10 Maturity = 5 2 80 66.116 6 396.694 Price = $924.184 3 80 60.105 12 721.262 4 80 54.641 20 1,092.822 5 1,080 670.595 30 20,117.851 Price: $924.184 Sum: 22,474.083 Convexity = Sum/[Price × (1+y)2] = 20.097b. Time Cash PV(CF) t2 + t (t2 + t) × PV(CF) (t) FlowCoupon = $0YTM = 0.10 1 $0 $0.000 2 0.000Maturity = 5Price = $924.184 2 0 0.000 6 0.000 3 0 0.000 12 0.000 4 0 0.000 20 0.000 5 1,000 620.921 30 18,627.640 Price: $620.921 Sum: 18,627.640 Convexity = Sum/[Price × (1+y)2] = 24.79319. a. The price of the zero coupon bond ($1,000 face value) selling at a yield to maturity of 8% is $374.84 and the price of the coupon bond is $774.84 At a YTM of 9% the actual price of the zero coupon bond is $333.28 and the actual price of the coupon bond is $691.79 Zero coupon bond: Actual % loss = $333.28 − $374.84 = −0.1109 = 11.09% loss $374.84 The percentage loss predicted by the duration-with-convexity rule is: [ ]Predicted % loss = [(−11.81) × 0.01]+ 0.5 ×150.3× 0.012 = −0.1106 = 11.06% loss Coupon bond: Actual % loss = $691.79 − $774.84 = −0.1072 = 10.72% loss $774.84 The percentage loss predicted by the duration-with-convexity rule is: [ ]Predicted % loss = [(−11.79) × 0.01]+ 0.5 × 231.2 × 0.012 = −0.1063 = 10.63% loss 16-10

Chapter 16 - Managing Bond Portfolios b. Now assume yield to maturity falls to 7%. The price of the zero increases to $422.04, and the price of the coupon bond increases to $875.91 Zero coupon bond: Actual % gain = $422.04 − $374.84 = 0.1259 = 12.59% gain $374.84 The percentage gain predicted by the duration-with-convexity rule is: [ ]Predicted % gain = [(−11.81) × (−0.01)]+ 0.5 ×150.3× 0.012 = 0.1256 = 12.56% gain Coupon bond Actual % gain = $875.91 − $774.84 = 0.1304 = 13.04% gain $774.84 The percentage gain predicted by the duration-with-convexity rule is: [ ]Predicted % gain = [(−11.79) × (−0.01)]+ 0.5 × 231.2 × 0.012 = 0.1295 = 12.95% gain c. The 6% coupon bond, which has higher convexity, outperforms the zero regardless of whether rates rise or fall. This can be seen to be a general property using the duration-with-convexity formula: the duration effects on the two bonds due to any change in rates are equal (since the respective durations are virtually equal), but the convexity effect, which is always positive, always favors the higher convexity bond. Thus, if the yields on the bonds change by equal amounts, as we assumed in this example, the higher convexity bond outperforms a lower convexity bond with the same duration and initial yield to maturity. d. This situation cannot persist. No one would be willing to buy the lower convexity bond if it always underperforms the other bond. The price of the lower convexity bond will fall and its yield to maturity will rise. Thus, the lower convexity bond will sell at a higher initial yield to maturity. That higher yield is compensation for lower convexity. If rates change only slightly, the higher yield-lower convexity bond will perform better; if rates change by a substantial amount, the lower yield- higher convexity bond will perform better. 16-11

Chapter 16 - Managing Bond Portfolios20. a. The following spreadsheet shows that the convexity of the bond is 64.933. The present value of each cash flow is obtained by discounting at 7%. (Since the bond has a 7% coupon and sells at par, its YTM is 7%.) Convexity equals: the sum of the last column (7,434.175) divided by: [P × (1 + y)2] = 100 × (1.07)2 = 114.49 Time Cash flow PV(CF) t2 + t (t2 + t) × PV(CF) (t) (CF) 2 13.084 1 7 6.542 6 36.684 12 68.569 2 7 6.114 20 106.805 30 149.727 3 7 5.714 42 195.905 56 244.118 4 7 5.340 72 293.333 90 342.678 5 7 4.991 110 5,983.271 6 7 4.664 7,434.175 Convexity: 64.933 7 7 4.359 8 7 4.074 9 7 3.808 10 107 54.393 Sum: 100.000 The duration of the bond is: (1) (2) (3) (4) (5) Time until Cash Flow PV of CF Payment (Discount Weight Column (1) × rate = 7%) Column (4) (years) 0.06542 $6.542 0.06114 0.06542 1 $7 $6.114 0.05714 0.12228 2 $7 $5.714 0.05340 0.17142 3 $7 $5.340 0.04991 0.21361 4 $7 $4.991 0.04664 0.24955 5 $7 $4.664 0.04359 0.27986 6 $7 $4.359 0.04074 0.30515 7 $7 $4.074 0.03808 0.32593 8 $7 $3.808 0.54393 0.34268 9 $7 $54.393 1.00000 5.43934 10 $107 $100.000 7.51523 Column Sums D = 7.515 yearsb. If the yield to maturity increases to 8%, the bond price will fall to 93.29% of par value, a percentage decrease of 6.71%. 16-12

Chapter 16 - Managing Bond Portfoliosc. The duration rule predicts a percentage price change of: − D × 0.01 = − 7.515 × 0.01 = −0.0702 = −7.02% 1.07 1.07 This overstates the actual percentage decrease in price by 0.31%.The price predicted by the duration rule is 7.02% less than face value, or 92.98%of face value.d. The duration-with-convexity rule predicts a percentage price change of:[ ] − 0.01 7.515 × + 0.5 × 64.933× 0.012 = −0.0670 = −6.70% 1.07 The percentage error is 0.01%, which is substantially less than the error using theduration rule.The price predicted by the duration rule is 6.70% less than face value, or 93.30%of face value.CFA PROBLEMS1. a. The call feature provides a valuable option to the issuer, since it can buy back the bond at a specified call price even if the present value of the scheduled remaining payments is greater than the call price. The investor will demand, and the issuer will be willing to pay, a higher yield on the issue as compensation for this feature. b. The call feature reduces both the duration (interest rate sensitivity) and the convexity of the bond. If interest rates fall, the increase in the price of the callable bond will not be as large as it would be if the bond were noncallable. Moreover, the usual curvature that characterizes price changes for a straight bond is reduced by a call feature. The price-yield curve (see Figure 16.6) flattens out as the interest rate falls and the option to call the bond becomes more attractive. In fact, at very low interest rates, the bond exhibits negative convexity. 16-13

Chapter 16 - Managing Bond Portfolios2. a. Bond price decreases by $80.00, calculated as follows: 10 × 0.01 × 800 = 80.00 b. ½ × 120 × (0.015)2 = 0.0135 = 1.35% c. 9/1.10 = 8.18 d. (i) e. (i) f. (iii)3. a. Modified duration = Macaulay duration = 10 = 9.26 years 1 + YTM 1.08b. For option-free coupon bonds, modified duration is a better measure of the bond’s sensitivity to changes in interest rates. Maturity considers only the final cash flow, while modified duration includes other factors, such as the size and timing of coupon payments, and the level of interest rates (yield to maturity). Modified duration, unlike maturity, indicates the approximate percentage change in the bond price for a given change in yield to maturity.c. i. Modified duration increases as the coupon decreases. ii. Modified duration decreases as maturity decreases.d. Convexity measures the curvature of the bond’s price-yield curve. Such curvature means that the duration rule for bond price change (which is based only on the slope of the curve at the original yield) is only an approximation. Adding a term to account for the convexity of the bond increases the accuracy of the approximation. That convexity adjustment is the last term in the following equation:∆P = (−D *×∆y) + 1 × Convexity × (∆y) 2 P 2 4. a. (i) Current yield = Coupon/Price = $70/$960 = 0.0729 = 7.29% (ii) YTM = 3.993% semiannually or 7.986% annual bond equivalent yield. On a financial calculator, enter: n = 10; PV = –960; FV = 1000; PMT = 35 Compute the interest rate. 16-14

Chapter 16 - Managing Bond Portfolios (iii) Horizon yield or realized compound yield is 4.166% (semiannually), or 8.332% annual bond equivalent yield. To obtain this value, first find the future value (FV) of reinvested coupons and principal. There will be six payments of $35 each, reinvested semiannually at 3% per period. On a financial calculator, enter: PV = 0; PMT = $35; n = 6; i = 3%. Compute: FV = $226.39 Three years from now, the bond will be selling at the par value of $1,000 because the yield to maturity is forecast to equal the coupon rate. Therefore, total proceeds in three years will be $1,226.39. Then find the rate (yrealized) that makes the FV of the purchase price equal to $1,226.39: $960 × (1 + yrealized)6 = $1,226.39 ⇒ yrealized = 4.166% (semiannual) b. Shortcomings of each measure: (i) Current yield does not account for capital gains or losses on bonds bought at prices other than par value. It also does not account for reinvestment income on coupon payments. (ii) Yield to maturity assumes the bond is held until maturity and that all coupon income can be reinvested at a rate equal to the yield to maturity. (iii) Horizon yield or realized compound yield is affected by the forecast of reinvestment rates, holding period, and yield of the bond at the end of the investor's holding period. Note: This criticism of horizon yield is a bit unfair: while YTM can be calculated without explicit assumptions regarding future YTM and reinvestment rates, you implicitly assume that these values equal the current YTM if you use YTM as a measure of expected return.5. a. (i) The effective duration of the 4.75% Treasury security is: − ∆P/P = (116.887 − 86.372) /100 = 15.2575 ∆r 0.02 (ii) The duration of the portfolio is the weighted average of the durations of the individual bonds in the portfolio: Portfolio Duration = w1D1 + w2D2 + w3D3 + … + wkDk where wi = market value of bond i/market value of the portfolio Di = duration of bond i k = number of bonds in the portfolio The effective duration of the bond portfolio is calculated as follows: [($48,667,680/$98,667,680) × 2.15] + [($50,000,000/$98,667,680) × 15.26] = 8.79 16-15

Chapter 16 - Managing Bond Portfolios b. VanHusen’s remarks would be correct if there were a small, parallel shift in yields. Duration is a first (linear) approximation only for small changes in yield. For larger changes in yield, the convexity measure is needed in order to approximate the change in price that is not explained by duration. Additionally, portfolio duration assumes that all yields change by the same number of basis points (parallel shift), so any non-parallel shift in yields would result in a difference in the price sensitivity of the portfolio compared to the price sensitivity of a single security having the same duration.6. a. The Aa bond initially has a higher YTM (yield spread of 40 b.p. versus 31 b.p.), but it is expected to have a widening spread relative to Treasuries. This will reduce the rate of return. The Aaa spread is expected to be stable. Calculate comparative returns as follows: Incremental return over Treasuries = Incremental yield spread − (Change in spread × duration) Aaa bond: 31 bp − (0 × 3.1 years) = 31 bp Aa bond: 40 bp − (10 bp × 3.1 years) = 9 bp Therefore, choose the Aaa bond. b. Other variables to be considered: • Potential changes in issue-specific credit quality. If the credit quality of the bonds changes, spreads relative to Treasuries will also change. • Changes in relative yield spreads for a given bond rating. If quality spreads in the general bond market change because of changes in required risk premiums, the yield spreads of the bonds will change even if there is no change in the assessment of the credit quality of these particular bonds. • Maturity effect. As bonds near their maturity, the effect of credit quality on spreads can also change. This can affect bonds of different initial credit quality differently.7. a. % price change = (−Effective duration) × Change in YTM (%) CIC: (−7.35) × (−0.50%) = 3.675% PTR: (−5.40) × (−0.50%) = 2.700% 16-16

Chapter 16 - Managing Bond Portfoliosb. Since we are asked to calculate horizon return over a period of only one coupon period, there is no reinvestment income.Horizon return = Coupon payment +Year-end price − Initial Price Initial priceCIC: $31.25 + $1,055.50 − $1,017.50 = 0.06806 = 6.806% $1,017.50PTR: $36.75 + $1,041.50 − $1,017.50 = 0.05971 = 5.971% $1,017.50c. Notice that CIC is non-callable but PTR is callable. Therefore, CIC has positive convexity, while PTR has negative convexity. Thus, the convexity correction to the duration approximation will be positive for CIC and negative for PTR.8. The economic climate is one of impending interest rate increases. Hence, we will seek to shorten portfolio duration. a. Choose the short maturity (2012) bond. b. The Arizona bond likely has lower duration. The Arizona coupons are lower, but the Arizona yield is higher. c. Choose the 12 3/8 % coupon bond. The maturities are approximately equal, but the 12 3/8 % coupon is much higher, resulting in a lower duration. d. The duration of the Shell bond is lower if the effect of the higher yield to maturity and earlier start of sinking fund redemption dominates its slightly lower coupon rate. e. The floating rate note has a duration that approximates the adjustment period, which is only 6 months.9. a. A manager who believes that the level of interest rates will change should engage in a rate anticipation swap, lengthening duration if rates are expected to fall, and shortening duration if rates are expected to rise. 16-17

Chapter 16 - Managing Bond Portfolios b. A change in yield spreads across sectors would call for an intermarket spread swap, in which the manager buys bonds in the sector for which yields are expected to fall relative to other bonds and sells bonds in the sector for which yields are expected to rise relative to other bonds. c. A belief that the yield spread on a particular instrument will change calls for a substitution swap in which that security is sold if its yield is expected to rise relative to the yield of other similar bonds, or is bought if its yield is expected to fall relative to the yield of other similar bonds.10. a. The advantages of a bond indexing strategy are: • Historically, the majority of active managers underperform benchmark indexes in most periods; indexing reduces the possibility of underperformance at a given level of risk. • Indexed portfolios do not depend on advisor expectations and so have less risk of underperforming the market. • Management advisory fees for indexed portfolios are dramatically less than fees for actively managed portfolios. Fees charged by active managers generally range from 15 to 50 basis points, while fees for indexed portfolios range from 1 to 20 basis points (with the highest of those representing enhanced indexing). Other non-advisory fees (i.e., custodial fees) are also less for indexed portfolios. • Plan sponsors have greater control over indexed portfolios because individual managers do not have as much freedom to vary from the parameters of the benchmark index. Some plan sponsors even decide to manage index portfolios with in-house investment staff. • Indexing is essentially “buying the market.” If markets are efficient, an indexing strategy should reduce unsystematic diversifiable risk, and should generate maximum return for a given level of risk. The disadvantages of a bond indexing strategy are: • Indexed portfolio returns may match the bond index, but do not necessarily reflect optimal performance. In some time periods, many active managers may outperform an indexing strategy at the same level of risk. • The chosen bond index and portfolio returns may not meet the client objectives or the liability stream. • Bond indexing may restrict the fund from participating in sectors or other opportunities that could increase returns. 16-18

Chapter 16 - Managing Bond Portfolios b. The stratified sampling, or cellular, method divides the index into cells, with each cell representing a different characteristic of the index. Common cells used in the cellular method combine (but are not limited to) duration, coupon, maturity, market sectors, credit rating, and call and sinking fund features. The index manager then selects one or more bond issues to represent the entire cell. The total market weight of issues held for each cell is based on the target index’s composition of that characteristic. c. Tracking error is defined as the discrepancy between the performance of an indexed portfolio and the benchmark index. When the amount invested is relatively small and the number of cells to be replicated is large, a significant source of tracking error with the cellular method occurs because of the need to buy odd lots of issues in order to accurately represent the required cells. Odd lots generally must be purchased at higher prices than round lots. On the other hand, reducing the number of cells to limit the required number of odd lots would potentially increase tracking error because of the mismatch with the target.11. a. For an option-free bond, the effective duration and modified duration are approximately the same. Using the data provided, the duration is calculated as follows: − ∆P/P = (100.71 − 99.29) /100 = 7.100 ∆r 0.002b. The total percentage price change for the bond is estimated as follows: Percentage price change using duration = –7.90 × –0.02 × 100 = 15.80% Convexity adjustment = 1.66% Total estimated percentage price change = 15.80% + 1.66% = 17.46%c. The assistant’s argument is incorrect. Because modified convexity does not recognize the fact that cash flows for bonds with an embedded option can change as yields change, modified convexity remains positive as yields move below the callable bond’s stated coupon rate, just as it would for an option-free bond. Effective convexity, however, takes into account the fact that cash flows for a security with an embedded option can change as interest rates change. When yields move significantly below the stated coupon rate, the likelihood that the bond will be called by the issuer increases and the effective convexity turns negative. 16-19

Chapter 16 - Managing Bond Portfolios12. ∆P/P = −D* ∆y ∆P/P = −4.83 × (−0.75%) = 3.6225% For Strategy I: ∆P/P = −23.81 × 0.50% = −11.9050% 5-year maturity: ∆P/P = (0.5 × 3.6225%) + [0.5 × (−11.9050%)] = −4.1413% 25-year maturity: Strategy I: ∆P/P = −14.35 × 0.25% = −3.5875% For Strategy II: 15-year maturity:13. a. i. Strong economic recovery with rising inflation expectations. Interest rates and bond yields will most likely rise, and the prices of both bonds will fall. The probability that the callable bond will be called would decrease, and the callable bond will behave more like the non-callable bond. (Note that they have similar durations when priced to maturity). The slightly lower duration of the callable bond will result in somewhat better performance in the high interest rate scenario. ii. Economic recession with reduced inflation expectations. Interest rates and bond yields will most likely fall. The callable bond is likely to be called. The relevant duration calculation for the callable bond is now modified duration to call. Price appreciation is limited as indicated by the lower duration. The non-callable bond, on the other hand, continues to have the same modified duration and hence has greater price appreciation.b. Projected price change = (modified duration) × (change in YTM) = (–6.80) × (–0.75%) = 5.1% Therefore, the price will increase to approximately $105.10 from its current level of $100.c. For Bond A, the callable bond, bond life and therefore bond cash flows are uncertain. If one ignores the call feature and analyzes the bond on a “to maturity” basis, all calculations for yield and duration are distorted. Durations are too long and yields are too high. On the other hand, if one treats the premium bond selling above the call price on a “to call” basis, the duration is unrealistically short and yields too low. The most effective approach is to use an option valuation approach. The callable bond can be decomposed into two separate securities: a non-callable bond and an option: Price of callable bond = Price of non-callable bond – price of option Since the call option always has some positive value, the price of the callable bond is always less than the price of the non-callable security. 16-20

Chapter 17 - Macroeconomic and Industry Analysis CHAPTER 17: MACROECONOMIC AND INDUSTRY ANALYSISPROBLEM SETS1. Expansionary (looser) monetary policy to lower interest rates would stimulate both investment and expenditures on consumer durables. Expansionary fiscal policy (i.e., lower taxes, increased government spending, increased welfare transfers) would stimulate aggregate demand directly.2. A depreciating dollar makes imported cars more expensive and American cars less expensive to foreign consumers. This should benefit the U.S. auto industry.3. This exercise is left to the student; answers will vary.4. A top-down approach to security valuation begins with an analysis of the global and domestic economy. Analysts who follow a top-down approach then narrow their attention to an industry or sector likely to perform well, given the expected performance of the broader economy. Finally, the analysis focuses on specific companies within an industry or sector that has been identified as likely to perform well. A bottom-up approach typically emphasizes fundamental analysis of individual company stocks, and is largely based on the belief that undervalued stocks will perform well regardless of the prospects for the industry or the broader economy. The major advantage of the top-down approach is that it provides a structured approach to incorporating the impact of economic and financial variables, at every level, in to analysis of a company’s stock. One would expect, for example, that prospects for a particular industry are highly dependent on broader economic variables. Similarly, the performance of an individual company’s stock is likely to be greatly affected by the prospects for the industry in which the company operates.5. Firms with greater sensitivity to business cycles are in industries that produce durable consumer goods or capital goods. Consumers of durable goods (e.g., automobiles, major appliances) are more likely to purchase these products during an economic expansion, but can often postpone purchases during a recession. Business purchases of capital goods (e.g., purchases of manufacturing equipment by firms that produce their own products) decline during a recession because demand for the firms’ end products declines during a recession. 17-1

Chapter 17 - Macroeconomic and Industry Analysis6. a. Gold Mining. Gold traditionally is viewed as a hedge against inflation. Expansionary monetary policy may lead to increased inflation, and thus could enhance the value of gold mining stocks. b. Construction. Expansionary monetary policy will lead to lower interest rates which ought to stimulate housing demand. The construction industry should benefit.7. Supply-side economists believe that a reduction in income tax rates will make workers more willing to work at current or even slightly lower (gross-of-tax) wages. Such an effect ought to mitigate cost pressures on the inflation rate.8. a. The robotics process entails higher fixed costs and lower variable (labor) costs. Therefore, this firm will perform better in a boom and worse in a recession. For example, costs will rise less rapidly than revenue when sales volume expands during a boom. b. Because its profits are more sensitive to the business cycle, the robotics firm will have the higher beta.9. a. Housing construction (cyclical but interest-rate sensitive): (iii) Healthy expansion b. Health care (a non-cyclical industry): (i) Deep recession c. Gold mining (counter-cyclical): (iv) Stagflation d. Steel production (cyclical industry) (ii) Superheated economy10. a. Oil well equipment: Relative decline (Environmental pressures, decline in easily- developed new oil fields) b. c. Computer hardware: Consolidation d. e. Computer software: Consolidation Genetic engineering: Start-up Railroads: Relative decline11. a. General Autos. Pharmaceuticals are less of a discretionary purchase than automobiles. b. Friendly Airlines. Travel expenditure is more sensitive to the business cycle than movie consumption. 17-2

Chapter 17 - Macroeconomic and Industry Analysis12. The index of consumer expectations is a useful leading economic indicator because, if consumers are optimistic about the future, they will be more willing to spend money, especially on consumer durables, which will increase aggregate demand and stimulate the economy.13. Labor cost per unit is a useful lagging indicator because wages typically start rising only well into an economic expansion. At the beginning of an expansion, there is considerable slack in the economy and output can expand without employers bidding up the price of inputs or the wages of employees. By the time wages start increasing due to high demand for labor, the boom period has already progressed considerably.14. The expiration of the patent means that General Weedkillers will soon face considerably greater competition from its competitors. We would expect prices and profit margins to fall, and total industry sales to increase somewhat as prices decline. The industry will probably enter the consolidation stage in which producers are forced to compete more extensively on the basis of price.15. a. Expected profit = Revenues – Fixed costs – Variable costs = $120,000 – $30,000 – [(1/3) × $120,000] = $50,000b. DOL = 1 + fixed cos ts = 1 + $30,000 = 1.60profits $50,000c. If sales are only $108,000, profit will fall to: $108,000 – $30,000 – [(1/3) × $108,000] = $42,000 This is a 16% decline from the forecasted value.d. The decrease in profit is 16%, which is equal to DOL times the 10% drop in sales.e. Profit must drop more than 100% to turn negative. For profit to fall 100%, revenue must fall by: 100% = 100% = 62.5% DOL 1.60 Therefore, revenue would be only 37.5% of the original forecast. At this level, revenue will be: 0.375 × $120,000 = $45,000f. If revenue is $45,000, profit will be: $45,000 – $30,000 – (1/3) × $45,000 = $0 17-3

Chapter 17 - Macroeconomic and Industry AnalysisCFA PROBLEMS1. a. Lowering reserve requirements would allow banks to lend out a higher fraction of deposits and thus increase the money supply. b. The Fed would buy Treasury securities, thereby increasing the money supply. c. The discount rate would be reduced, allowing banks to borrow additional funds at a lower rate.2. a. Expansionary monetary policy is likely to increase the inflation rate, either because it may over stimulate the economy, or ultimately because the end result of more money in the economy is higher prices. b. Real output and employment should increase in response to the expansionary policy, at least in the short run. c. The real interest rate should fall, at least in the short-run, as the supply of funds to the economy has increased. d. The nominal interest rate could either increase or decrease. On the one hand, the real rate might fall [see part (c)], but the inflation premium might rise [see part (a)]. The nominal rate is the sum of these two components.3. a. The concept of an industrial life cycle refers to the tendency of most industries to go through various stages of growth. The rate of growth, the competitive environment, profit margins and pricing strategies tend to shift as an industry moves from one stage to the next, although it is generally difficult to identify precisely when one stage has ended and the next begun. The start-up stage is characterized by perceptions of a large potential market and by a high level of optimism for potential profits. However, this stage usually demonstrates a high rate of failure. In the second stage, often called stable growth or consolidation, growth is high and accelerating, the markets are broadening, unit costs are declining and quality is improving. In this stage, industry leaders begin to emerge. The third stage, usually called slowing growth or maturity, is characterized by decelerating growth caused by factors such as maturing markets and/or competitive inroads by other products. Finally, an industry reaches a stage of relative decline in which sales slow or even decline. 17-4

Chapter 17 - Macroeconomic and Industry Analysis Product pricing, profitability and industry competitive structure often vary by stage. Thus, for example, the first stage usually encompasses high product prices, high costs (R&D, marketing, etc.) and a (temporary) monopolistic industry structure. In stage two (stable growth), new entrants begin to appear and costs fall rapidly due to the learning curve. Prices generally do not fall as rapidly, however, allowing profit margins to increase. In stage three (slowing growth), growth begins to slow as the product or service begins to saturate the market, and margins are eroded by significant price reductions. In the final stage, industry cumulative production is so high that production costs have stopped declining, profit margins are thin (assuming competition exists), and the fate of the industry depends on replacement demand and the existence of substitute products/services. b. The passenger car business in the United States has probably entered the final stage in the industrial life cycle because normalized growth is quite low. The information processing business, on the other hand, is undoubtedly earlier in the cycle. Depending on whether or not growth is still accelerating, it is either in the second or third stage. c. Cars: In the final stages of the life cycle, demand tends to be price sensitive. Thus, Universal can not raise prices without losing volume. Moreover, given the industry’s maturity, cost structures are likely to be similar across all competitors, and any price cuts can be matched immediately. Thus, Universal’s car business is boxed in: Product pricing is determined by the market, and the company is a “price-taker.” Idata: Idata should have much more pricing flexibility given its earlier stage in the industrial life cycle. Demand is growing faster than supply, and, depending on the presence and/or actions of an industry leader, Idata may set prices high to maximize current profits and generate cash for product development, or set prices low in an effort to gain market share.4. a. A basic premise of the business cycle approach to investment timing is that stock prices anticipate fluctuations in the business cycle. For example, there is evidence that stock prices tend to move about six months ahead of the economy. In fact, stock prices are a leading indicator for the economy. Over the course of a business cycle, this approach to investing would work roughly as follows. As the investor perceives that the top of a business cycle is approaching, stocks purchased should not be vulnerable to a recession. When the investor perceives that a downturn is at hand, stock holdings should be lightened with proceeds invested in fixed-income securities. Once the recession has matured to some extent, and interest rates fall, bond prices will rise. As the investor perceives that the recession is about to end, profits should be taken in the bonds and reinvested in stocks, particularly those in cyclical industries with a high beta. 17-5

Chapter 17 - Macroeconomic and Industry Analysis Generally, abnormal returns can be earned only if these asset allocation switches are timed better than those of other investors. Switches made after the turning points may not lead to excess returns. b. Based on the business cycle approach to investment timing, the ideal time to invest in a cyclical stock such as a passenger car company would be just before the end of a recession. If the recovery is already underway, Adam’s recommendation would be too late. The equities market generally anticipates the changes in the economic cycle. Therefore, since the “recovery is underway,” the price of Universal Auto should already reflect the anticipated improvements in the economy.5. a. • The industry-wide ROE is leveling off, indicating that the industry may be approaching a later stage of the life cycle. • Average P/E ratios are declining, suggesting that investors are becoming less optimistic about growth prospects. • Dividend payout is increasing, suggesting that the firm sees less reason to reinvest earnings in the firm. There may be fewer growth opportunities in the industry. • Industry dividend yield is also increasing, even though market dividend yield is decreasing. b. • Industry growth rate is still forecast at 10% to 15%, higher than would be true of a mature industry. • Non-U.S. markets are still untapped, and some firms are now entering these markets. • Mail order sale segment is growing at 40% a year. • Niche markets are continuing to develop. • New manufacturers continue to enter the market.6. a. Relevant data from the table supporting the conclusion that the retail auto parts industry as a whole is in the maturity stage of the industry life cycle are: • The population of 18-29 year olds, a major customer base for the industry, is gradually declining. • The number of households with income less than $35,000, another important consumer base, is not expanding. • The number of cars five to fifteen years old, an important end market, has experienced low annual growth (or actual decline in some years), so the number of units that potentially need parts is not growing. 17-6

Chapter 17 - Macroeconomic and Industry Analysis • Automotive aftermarket industry retail sales have been growing slowly for several years. • Consumer expenditures on automotive parts and accessories have grown slowly for several years. • Average operating margins of all retail autoparts companies have steadily declined. b. (i) Relevant data from the table supporting the conclusion that Wigwam Autoparts Heaven, Inc. (WAH) and its principal competitors are in the consolidation stage of their life cycle are: • Sales growth of retail autoparts companies with 100 or more stores have been growing rapidly and at an increasing rate. • Market share of retail autoparts stores with 100 or more stores has been increasing but is still less than 20 percent, leaving room for much more growth. • Average operating margins for retail autoparts companies with 100 or more stores are high and rising. (ii) Because of industry fragmentation (i.e., most of the market share is distributed among many companies with only a few stores), the retail autoparts industry apparently is undergoing marketing innovation and consolidation. The industry is moving toward the “category killer” format, in which a few major companies control large market shares through proliferation of outlets. The evidence suggests that a new “industry within an industry” is emerging in the form of the “category killer” large chain-store company. This industry subgroup is in its consolidation stage (i.e., rapid growth with high operating profit margins and emerging market leaders) despite the fact that the industry is in the maturity stage of its life cycle.7. i. Substitutes – one year from now: Currently the Carrycom, and other products in their industry segment, have automatic language conversion functionality and geographic region flexibility. This market segment is currently in a strong position. Substitutes – five years from now: White expects that other products in the broader consumer electronics industry, such as PDAs, PCs, and other consumer electronics, will eventually be able to incorporate both functionalities and so therefore diminish the strength of this force for Carrycom and other products in their market segment. ii. Threat of new (or potential) entrants – one year from now: Wade has no threat of entrants into its market for the next three years because: (a) Wade has the exclusive ability to manufacture with ordinary copper, while other potential entrants do not have access to pari-copper, and; (b) Potential entrants do not have access to the exclusive production license for Carrycom technology. 17-7

Chapter 17 - Macroeconomic and Industry Analysis Threat of new (or potential) entrants – five years from now: Beyond the next three years, however, the threat is high. White expects competitors to market copper-based products, eliminating Carrycom’s unique competitive advantage. In addition, the three-year exclusive production license expires. iii. Intensity of rivalry – one year from now: Wade will experience only modest rivalry for three years as it has an exclusive production license for the next three years, which limits the availability of similar products. However, the broader electronics market may be integrating the automatic language conversion feature into its products after one year. Intensity of rivalry – five years from now: After the license expires in three years, White expects other competitors to produce a number of similar products which will limit their pricing power. This demonstrates a high intensity of rivalry.8. a. (iii) b. (iii) c. (iv) d. (iii) 17-8

Chapter 18 - Equity Valuation Models CHAPTER 18: EQUITY VALUATION MODELSPROBLEM SETS1. Theoretically, dividend discount models can be used to value the stock of rapidly growing companies that do not currently pay dividends; in this scenario, we would be valuing expected dividends in the relatively more distant future. However, as a practical matter, such estimates of payments to be made in the more distant future are notoriously inaccurate, rendering dividend discount models problematic for valuation of such companies; free cash flow models are more likely to be appropriate. At the other extreme, one would be more likely to choose a dividend discount model to value a mature firm paying a relatively stable dividend.2. It is most important to use multi-stage dividend discount models when valuing companies with temporarily high growth rates. These companies tend to be companies in the early phases of their life cycles, when they have numerous opportunities for reinvestment, resulting in relatively rapid growth and relatively low dividends (or, in many cases, no dividends at all). As these firms mature, attractive investment opportunities are less numerous so that growth rates slow.3. The intrinsic value of a share of stock is the individual investor’s assessment of the true worth of the stock. The market capitalization rate is the market consensus for the required rate of return for the stock. If the intrinsic value of the stock is equal to its price, then the market capitalization rate is equal to the expected rate of return. On the other hand, if the individual investor believes the stock is underpriced (i.e., intrinsic value < price), then that investor’s expected rate of return is greater than the market capitalization rate.4. a. k = D1/P0 + g 0.16 = $2/$50 + g ⇒ g = 0.12 = 12% b. P0 = D1/(k – g) = $2/(0.16 – 0.05) = $18.18 The price falls in response to the more pessimistic dividend forecast. The forecast for current year earnings, however, is unchanged. Therefore, the P/E ratio falls. The lower P/E ratio is evidence of the diminished optimism concerning the firm's growth prospects. 18-1

Chapter 18 - Equity Valuation Models5. a. g = ROE × b = 16% × 0.5 = 8% D1 = $2(1 – b) = $2(1 – 0.5) = $1 P0 = D1/(k – g) = $1/(0.12 – 0.08) = $25 b. P3 = P0(1 + g)3 = $25(1.08)3 = $31.496. a. k = rf + β[Ε(rM) – rf ] = 6% + 1.25(14% – 6%) = 16% g = 2/3 × 9% = 6% D1 = E0(1 + g) (1 – b) = $3(1.06) (1/3) = $1.06 P0 = D1 = $1.06 = $10.60 k−g 0.16 − 0.06b. Leading P0/E1 = $10.60/$3.18 = 3.33 Trailing P0/E0 = $10.60/$3.00 = 3.53c. PVGO = P0 − E1 = $10.60 − $3.18 = −$9.275 k 0.16 The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is less than the market capitalization rate (16%).d. Now, you revise b to 1/3, g to 1/3 × 9% = 3%, and D1 to: E0 × 1.03 × (2/3) = $2.06 Thus: V0 = $2.06/(0.16 – 0.03) = $15.85 V0 increases because the firm pays out more earnings instead of reinvesting a poor ROE. This information is not yet known to the rest of the market.7. Since beta = 1.0, then k = market return = 15% Therefore: 15% = D1/P0 + g = 4% + g ⇒ g = 11% 18-2

Chapter 18 - Equity Valuation Models8. a. P0 = D1 = $8 = $160 k−g 0.10 − 0.05b. The dividend payout ratio is 8/12 = 2/3, so the plowback ratio is b = 1/3. The implied value of ROE on future investments is found by solving: g = b × ROE with g = 5% and b = 1/3 ⇒ ROE = 15%c. Assuming ROE = k, price is equal to: P0 = E1 = $12 = $120 k 0.10 Therefore, the market is paying $40 per share ($160 – $120) for growth opportunities.9. a. k = D1/P0 + g D1 = 0.5 × $2 = $1 g = b × ROE = 0.5 × 0.20 = 0.10 Therefore: k = ($1/$10) + 0.10 = 0.20 = 20%b. Since k = ROE, the NPV of future investment opportunities is zero: PVGO = P0 − E1 = $10 − $10 = 0 kc. Since k = ROE, the stock price would be unaffected by cutting the dividend and investing the additional earnings.10. a. k = rf + β[E(rM ) – rf ] = 8% + 1.2(15% – 8%) = 16.4% g = b × ROE = 0.6 × 20% = 12% V0 = D0 (1 + g) = $4 ×1.12 = $101.82 k−g 0.164 − 0.12b. P1 = V1 = V0(1 + g) = $101.82 × 1.12 = $114.04 E(r) = D1 + P1 − P0 = $4.48 + $114.04 − $100 = 0.1852 = 18.52% P0 $100 18-3

Chapter 18 - Equity Valuation Models11. 0 1 5 6 Time: $10.000 $12.000 $24.883 $29.860 $0.000 $0.000 $0.000 $11.944 Et Dt 1.00 1.00 1.00 0.60 b 20.0% 20.0% 20.0% 9.0% ga. V5 = D6 = $11.944 = $199.07 k−g 0.15 − 0.09 V0 = V5 = $199.07 = $98.97 (1 + k)5 1.155b. The price should rise by 15% per year until year 6: because there is no dividend, the entire return must be in capital gains.c. The payout ratio would have no effect on intrinsic value because ROE = k.12. a. The solution is shown in the Excel spreadsheet below:Inputs Year Dividend Div growth Term value Investor CFbeta 2008 0.77 0.77mkt_prem .90 2009 0.88 0.1262 0.88rf 0.08 2010 0.99 0.1232 0.99k_equity 0.045 2011 1.10 0.1202 1.10plowback 0.117 2012 1.24 0.1172 1.24roe 0.74 2013 1.39 0.1142 1.39term_gwth 0.13 2014 1.56 0.1112 1.56 0.0962 2015 1.74 0.1082 1.74 2016 1.94 0.1052 1.94Value line 2017 2.16 0.1022 202.65 2.16forecasts of 2018 2.39 0.0992 2.39annual dividends 2019 2.64 0.0962 2.64 2020 2.91 0.0962 2.91Transitional period 2021 3.20 3.20with slowing dividend 2022 3.51 3.51growth 2023 3.85 206.50 Beginning of constant E17 * (1+ F17)/(B5 - F17) growth period 45.71 = PV of CF NPV(B5,H2:H17)b., c. Using the Excel spreadsheet, we find that the intrinsic values are $29.71 and $17.39, respectively. 18-4

Chapter 18 - Equity Valuation Models13. The solutions derived from Spreadsheet 18.2 are as follows: Intrinsic value: Intrinsic value: Intrinsic value Intrinsic value per share: FCFE FCFF FCFE per share: FCFF 37.83a. 81,171 68,470 36.01 27.17b. 59,961 49,185 24.29 32.00c. 69,813 57,913 29.7314. 0 1 2 3 Time: $1.0000 $1.2500 $1.5625 $1.953125 25.0% 25.0% 25.0% Dt 5.0% ga. The dividend to be paid at the end of year 3 is the first installment of a dividend stream that will increase indefinitely at the constant growth rate of 5%. Therefore, we can use the constant growth model as of the end of year 2 in order to calculate intrinsic value by adding the present value of the first two dividends plus the present value of the price of the stock at the end of year 2.The expected price 2 years from now is: P2 = D3/(k – g) = $1.953125/(0.20 – 0.05) = $13.02The PV of this expected price is: $13.02/1.202 = $9.04The PV of expected dividends in years 1 and 2 is: $1.25 + $1.5625 = $2.13 1.20 1.202Thus the current price should be: $9.04 + $2.13 = $11.17b. Expected dividend yield = D1/P0 = $1.25/$11.17 = 0.112 = 11.2%c. The expected price one year from now is the PV at that time of P2 and D2: P1 = (D2 + P2)/1.20 = ($1.5625 + $13.02)/1.20 = $12.15 The implied capital gain is: (P1 – P0)/P0 = ($12.15 – $11.17)/$11.17 = 0.088 = 8.8% The sum of the implied capital gains yield and the expected dividend yield is equal to the market capitalization rate. This is consistent with the DDM. 18-5

Chapter 18 - Equity Valuation Models15. 0 1 4 5 Time: $5.000 $6.000 $10.368 $12.4416 $0.000 $0.000 $0.000 $12.4416 Et DtDividends = 0 for the next four years, so b = 1.0 (100% plowback ratio).a. P4 = D5 = $12.4416 = $82.944 k 0.15 V0 = P4 = $82.944 = $47.42 (1 + k)4 1.154b. Price should increase at a rate of 15% over the next year, so that the HPR will equal k.16. Before-tax cash flow from operations $2,100,000Depreciation 210,000Taxable Income 1,890,000Taxes (@ 35%) 661,500After-tax unleveraged income 1,228,500After-tax cash flow from operations (After-tax unleveraged income + depreciation) 1,438,500New investment (20% of cash flow from operations) 420,000Free cash flow (After-tax cash flow from operations – new investment) $1,018,500The value of the firm (i.e., debt plus equity) is: V0 = C1 = $1,018,500 = $14,550,000 k−g 0.12 − 0.05Since the value of the debt is $4 million, the value of the equity is $10,550,000.17. a. g = ROE × b = 20% × 0.5 = 10% P0 = D1 = D0 (1 + g) = $0.50 ×1.10 = $11 k−g k−g 0.15 − 0.10 18-6

Chapter 18 - Equity Valuation Modelsb. Time EPS Dividend Comment 0 $1.0000 $0.5000 1 $1.1000 $0.5500 g = 10%, plowback = 0.50 2 $1.2100 $0.7260 EPS has grown by 10% based on last year’s earnings plowback and ROE; this year’s earnings plowback ratio now falls to 0.40 and payout ratio = 0.60 3 $1.2826 $0.7696 EPS grows by (0.4) (15%) = 6% and payout ratio = 0.60At time 2: P2 = D3 = $0.7696 = $8.551 k−g 0.15 − 0.06At time 0: V0 = $0.55 + $0.726 + $8.551 = $7.493 1.15 (1.15) 2c. P0 = $11 and P1 = P0(1 + g) = $12.10 (Because the market is unaware of the changed competitive situation, it believes the stock price should grow at 10% per year.)P2 = $8.551 after the market becomes aware of the changed competitive situation.P3 = $8.551 × 1.06 = $9.064 (The new growth rate is 6%.)Year Return 1 ($12.10 − $11) + $0.55 = 0.150 = 15.0% $11 2 ($8.551 − $12.10) + $0.726 = −0.233 = −23.3% $12.10 3 ($9.064 − $8.551) + $0.7696 = 0.150 = 15.0% $8.551Moral: In \"normal periods\" when there is no special information,the stock return = k = 15%. When special information arrives, all the abnormalreturn accrues in that period, as one would expect in an efficient market.CFA PROBLEMS1. P0 = D1/(k – g) = $2.10/(0.11 – 0) = $19.092. I and II 18-7

Chapter 18 - Equity Valuation Models3. a. This director is confused. In the context of the constant growth model [i.e., P0 = D1/(k – g)], it is true that price is higher when dividends are higher holding everything else including dividend growth constant. But everything else will not be constant. If the firm increases the dividend payout rate, the growth rate g will fall, and stock price will not necessarily rise. In fact, if ROE > k, price will fall. b. (i) An increase in dividend payout will reduce the sustainable growth rate as less funds are reinvested in the firm. The sustainable growth rate (i.e., ROE × plowback) will fall as plowback ratio falls. (ii) The increased dividend payout rate will reduce the growth rate of book value for the same reason -- less funds are reinvested in the firm.4. Using a two-stage dividend discount model, the current value of a share of Sundanci is calculated as follows. D3V0 = D1 + D2 + (k − g) (1 + k)1 (1 + k)2 (1 + k)2 $0.5623 = $0.3770 + $0.4976 + (0.14 − 0.13) = $43.98 1.141 1.142 1.14 2where:E0 = $0.952D0 = $0.286E1 = E0 (1.32)1 = $0.952 × 1.32 = $1.2566D1 = E1 × 0.30 = $1.2566 × 0.30 = $0.3770E2 = E0 (1.32)2 = $0.952 × (1.32)2 = $1.6588D2 = E2 × 0.30 = $1.6588 × 0.30 = $0.4976E3 = E0 × (1.32)2 × 1.13 = $0.952 × (1.32)3 × 1.13 = $1.8744D3 = E3 × 0.30 = $1.8743 × 0.30 = $0.5623 18-8

Chapter 18 - Equity Valuation Models5. a. Free cash flow to equity (FCFE) is defined as the cash flow remaining after meeting all financial obligations (including debt payment) and after covering capital expenditure and working capital needs. The FCFE is a measure of how much the firm can afford to pay out as dividends, but in a given year may be more or less than the amount actually paid out. Sundanci's FCFE for the year 2008 is computed as follows: FCFE = Earnings after tax + Depreciation expense − Capital expenditures − Increase in NWC = $80 million + $23 million − $38 million − $41 million = $24 million FCFE per share = FCFE/number of shares outstanding = $24 million/84 million shares = $0.286 At the given dividend payout ratio, Sundanci's FCFE per share equals dividends per share. b. The FCFE model requires forecasts of FCFE for the high growth years (2009 and 2010) plus a forecast for the first year of stable growth (2011) in order to to allow for an estimate of the terminal value in 2010 based on perpetual growth. Because all of the components of FCFE are expected to grow at the same rate, the values can be obtained by projecting the FCFE at the common rate. (Alternatively, the components of FCFE can be projected and aggregated for each year.) The following table shows the process for estimating Sundanci's current value on a per share basis. 18-9

Chapter 18 - Equity Valuation ModelsFree Cash Flow to EquityBase AssumptionsShares outstanding: 84 millionRequired return on equity (r): 14%Growth rate (g) Actual Projected Projected Projected 2008 2009 2010 2011Earnings after taxPlus: Depreciation expense Per share 27% 27% 13%Less: Capital expenditures $0.952Less: Increase in net working capital Total $0.274 $1.2090 $1.5355 $1.7351Equals: FCFE $80 $0.452Terminal value $23 $0.488 $0.3480 $0.4419 $0.4994Total cash flows to equity $0.286Discounted value $38 $0.5740 $0.7290 $0.8238 $41 Current value per share $24 $0.6198 $0.7871 $0.8894 $0.3632 $0.4613 $0.5213 $52.1300* $0.3632 $52.5913** $0.3186*** $40.4673*** $40.7859*****Projected 2010 Terminal value = (Projected 2011 FCFE)/(r − g)**Projected 2010 Total cash flows to equity =Projected 2010 FCFE + Projected 2010 Terminal value***Discounted values obtained using r = 14%****Current value per share =Sum of Discounted Projected 2009 and 2010 Total cash flows to equityc. i. The DDM uses a strict definition of cash flows to equity, i.e. the expected dividends on the common stock. In fact, taken to its extreme, the DDM cannot be used to estimate the value of a stock that pays no dividends. The FCFE model expands the definition of cash flows to include the balance of residual cash flows after all financial obligations and investment needs have been met. Thus the FCFE model explicitly recognizes the firm’s investment and financing policies as well as its dividend policy. In instances of a change of corporate control, and therefore the possibility of changing dividend policy, the FCFE model provides a better estimate of value. The DDM is biased toward finding low P/E ratio stocks with high dividend yields to be undervalued and conversely, high P/E ratio stocks with low dividend yields to be overvalued. It is considered a conservative model in that it tends to identify fewer undervalued firms as market prices rise relative to fundamentals. The DDM does not allow for the potential tax disadvantage of high dividends relative to the capital gains achievable from retention of earnings. 18-10

Chapter 18 - Equity Valuation Models ii. Both two-stage valuation models allow for two distinct phases of growth, an initial finite period where the growth rate is abnormal, followed by a stable growth period that is expected to last indefinitely. These two-stage models share the same limitations with respect to the growth assumptions. First, there is the difficulty of defining the duration of the extraordinary growth period. For example, a longer period of high growth will lead to a higher valuation, and there is the temptation to assume an unrealistically long period of extraordinary growth. Second, the assumption of a sudden shift from high growth to lower, stable growth is unrealistic. The transformation is more likely to occur gradually, over a period of time. Given that the assumed total horizon does not shift (i.e., is infinite), the timing of the shift from high to stable growth is a critical determinant of the valuation estimate. Third, because the value is quite sensitive to the steady-state growth assumption, over- or under-estimating this rate can lead to large errors in value. The two models share other limitations as well, notably difficulties in accurately forecasting required rates of return, in dealing with the distortions that result from substantial and/or volatile debt ratios, and in accurately valuing assets that do not generate any cash flows.6. a. The formula for calculating a price earnings ratio (P/E) for a stable growth firm is the dividend payout ratio divided by the difference between the required rate of return and the growth rate of dividends. If the P/E is calculated based on trailing earnings (year 0), the payout ratio is increased by the growth rate. If the P/E is calculated based on next year’s earnings (year 1), the numerator is the payout ratio. P/E on trailing earnings: P/E = [payout ratio × (1 + g)]/(r − g) = [0.30 × 1.13]/(0.14 − 0.13) = 33.9 P/E on next year's earnings: P/E = payout ratio/(r − g) = 0.30/(0.14 − 0.13) = 30.0 b. The P/E ratio is a decreasing function of riskiness; as risk increases, the P/E ratio decreases. Increases in the riskiness of Sundanci stock would be expected to lower the P/E ratio. The P/E ratio is an increasing function of the growth rate of the firm; the higher the expected growth, the higher the P/E ratio. Sundanci would command a higher P/E if analysts increase the expected growth rate. The P/E ratio is a decreasing function of the market risk premium. An increased market risk premium increases the required rate of return, lowering the price of a stock relative to its earnings. A higher market risk premium would be expected to lower Sundanci's P/E ratio. 18-11

Chapter 18 - Equity Valuation Models7. a. The sustainable growth rate is equal to: plowback ratio × return on equity = b × ROE where b = [Net Income – (Dividend per share × shares outstanding)]/Net Income ROE = Net Income/Beginning of year equity In 2005: b = [208 – (0.80 × 100)]/208 = 0.6154 ROE = 208/1380 = 0.1507 Sustainable growth rate = 0.6154 × 0.1507 = 9.3% In 2008: b = [275 – (0.80 × 100)]/275 = 0.7091 ROE = 275/1836 = 0.1498 Sustainable growth rate = 0.7091 × 0.1498 = 10.6% b. i. The increased retention ratio increased the sustainable growth rate. Retention ratio = [Net Income – (Dividend per share × shares outstanding)]/Net Income Retention ratio increased from 0.6154 in 2005 to 0.7091 in 2008. This increase in the retention ratio directly increased the sustainable growth rate because the retention ratio is one of the two factors determining the sustainable growth rate. ii. The decrease in leverage reduced the sustainable growth rate. Financial leverage = (Total Assets/Beginning of year equity) Financial leverage decreased from 2.34 (= 3230/1380) at the beginning of 2005 to 2.10 at the beginning of 2008 (= 3856/1836) This decrease in leverage directly decreased ROE (and thus the sustainable growth rate) because financial leverage is one of the factors determining ROE (and ROE is one of the two factors determining the sustainable growth rate).8. a. The formula for the Gordon model is: V0 = [D0 × (1 + g)]/(r – g) where: D0 = dividend paid at time of valuation g = annual growth rate of dividends r = required rate of return for equity In the above formula, P0, the market price of the common stock, substitutes for V0 and g becomes the dividend growth rate implied by the market: P0 = [D0 × (1 + g)]/(r – g) Substituting, we have: 58.49 = [0.80 × (1 + g)]/(0.08 – g) ⇒ g = 6.54% 18-12

Chapter 18 - Equity Valuation Models b. Use of the Gordon growth model would be inappropriate to value Dynamic’s common stock, for the following reasons: i. The Gordon growth model assumes a set of relationships about the growth rate for dividends, earnings, and stock values. Specifically, the model assumes that dividends, earnings, and stock values will grow at the same constant rate. In valuing Dynamic’s common stock, the Gordon growth model is inappropriate because management’s dividend policy has held dividends constant in dollar amount although earnings have grown, thus reducing the payout ratio. This policy is inconsistent with the Gordon model assumption that the payout ratio is constant. ii. It could also be argued that use of the Gordon model, given Dynamic’s current dividend policy, violates one of the general conditions for suitability of the model, namely that the company’s dividend policy bears an understandable and consistent relationship with the company’s profitability.9. a. The industry’s estimated P/E can be computed using the following model: P0/E1 = payout ratio/(r − g) However, since r and g are not explicitly given, they must be computed using the following formulas: gind = ROE × retention rate = 0.25 × 0.40 = 0.10 rind = government bond yield + ( industry beta × equity risk premium) = 0.06 + (1.2 × 0.05) = 0.12 Therefore: P0/E1 = 0.60/(0.12 − 0.10) = 30.0 b. i. Forecast growth in real GDP would cause P/E ratios to be generally higher for Country A. Higher expected growth in GDP implies higher earnings growth and a higher P/E. ii. Government bond yield would cause P/E ratios to be generally higher for Country B. A lower government bond yield implies a lower risk-free rate and therefore a higher P/E. iii. Equity risk premium would cause P/E ratios to be generally higher for Country B. A lower equity risk premium implies a lower required return and a higher P/E. 18-13

Chapter 18 - Equity Valuation Models10. a. k = rf + β[Ε(rM) – rf ] = 4.5% + 1.15(14.5% − 4.5%) = 16%b. Year Dividend2009 $1.722010 $1.72 × 1.12 = $1.932011 $1.72 × 1.122 = $2.162012 $1.72 × 1.123 = $2.422013 $1.72 × 1.123 × 1.09 = $2.63Present value of dividends paid in 2010 – 2012:Year PV of Dividend2010 $1.93/1.161 = $1.662011 $2.16/1.162 = $1.612012 $2.42/1.163 = $1.55 Total = $4.82Price at year-end 2012 = D2013 = $2.63 = $37.57 k − g 0.16 − 0.09PV in 2009 of this stock price = $37.57 = $24.07 1.163Intrinsic value of stock = $4.82 + $24.07 = $28.89c. The data in the problem indicate that Quick Brush is selling at a price substantially below its intrinsic value, while the calculations above demonstrate that SmileWhite is selling at a price somewhat above the estimate of its intrinsic value. Based on this analysis, Quick Brush offers the potential for considerable abnormal returns, while SmileWhite offers slightly below-market risk-adjusted returns.d. Strengths of two-stage versus constant growth DDM: • Two-stage model allows for separate valuation of two distinct periods in a company’s future. This can accommodate life cycle effects. It also can avoid the difficulties posed by initial growth that is higher than the discount rate. • Two-stage model allows for initial period of above-sustainable growth. It allows the analyst to make use of her expectations regarding when growth might shift from off-trend to a more sustainable level. A weakness of all DDMs is that they are very sensitive to input values. Small changes in k or g can imply large changes in estimated intrinsic value. These inputs are difficult to measure. 18-14

Chapter 18 - Equity Valuation Models11. a. The value of a share of Rio National equity using the Gordon growth model and the capital asset pricing model is $22.40, as shown below. Calculate the required rate of return using the capital asset pricing model: k = rf + β (kM – rf) = 4% + 1.8(9% – 4%) = 13% Calculate the share value using the Gordon growth model: P0 = Do × (1 + g) = $0.20 × (1 + 0.12) = $22.40 k−g 0.13 − 0.12b. The sustainable growth rate of Rio National is 9.97%, calculated as follows:g = b × ROE = Earnings Retention Rate × ROE = (1 – Payout Ratio) × ROE =1 − Dividends × Net Income = 1 − $3.20 × $30.16 = 0.0997 = 9.97% Net Income Beginning Equity $30.16 $270.3512. a. To obtain free cash flow to equity (FCFE), the two adjustments that Shaar should make to cash flow from operations (CFO) are: 1. Subtract investment in fixed capital: CFO does not take into account the investing activities in long-term assets, particularly plant and equipment. The cash flows corresponding to those necessary expenditures are not available to equity holders and therefore should be subtracted from CFO to obtain FCFE. 2. Add net borrowing: CFO does not take into account the amount of capital supplied to the firm by lenders (e.g., bondholders). The new borrowings, net of debt repayment, are cash flows available to equity holders and should be added to CFO to obtain FCFE.b. Note 1: Rio National had $75 million in capital expenditures during the year. Adjustment: negative $75 million The cash flows required for those capital expenditures (–$75 million) are no longer available to the equity holders and should be subtracted from net income to obtain FCFE. 18-15

Chapter 18 - Equity Valuation Models Note 2: A piece of equipment that was originally purchased for $10 million was sold for $7 million at year-end, when it had a net book value of $3 million. Equipment sales are unusual for Rio National. Adjustment: positive $3 million In calculating FCFE, only cash flow investments in fixed capital should be considered. The $7 million sale price of equipment is a cash inflow now available to equity holders and should be added to net income. However, the gain over book value that was realized when selling the equipment ($4 million) is already included in net income. Because the total sale is cash, not just the gain, the $3 million net book value must be added to net income. Therefore, the adjustment calculation is: $7 million in cash received – $4 million of gain recorded in net income = $3 million additional cash received added to net income to obtain FCFE. Note 3: The decrease in long-term debt represents an unscheduled principal repayment; there was no new borrowing during the year. Adjustment: negative $5 million The unscheduled debt repayment cash flow (–$5 million) is an amount no longer available to equity holders and should be subtracted from net income to determine FCFE. Note 4: On January 1, 2008, the company received cash from issuing 400,000 shares of common equity at a price of $25.00 per share. No adjustment Transactions between the firm and its shareholders do not affect FCFE. To calculate FCFE, therefore, no adjustment to net income is required with respect to the issuance of new shares. Note 5: A new appraisal during the year increased the estimated market value of land held for investment by $2 million, which was not recognized in 2008 income. No adjustment The increased market value of the land did not generate any cash flow and was not reflected in net income. To calculate FCFE, therefore, no adjustment to net income is required. 18-16

Chapter 18 - Equity Valuation Modelsc. Free cash flow to equity (FCFE) is calculated as follows:FCFE = NI + NCC – FCINV – WCINV + Net Borrowingwhere NCC = non-cash charges FCINV = investment in fixed capital WCINV = investment in working capitalNI = Million $ ExplanationNCC = $30.16 From Table 18GFCINV =WCINV = +$67.17 $71.17 (depreciation and amortization from Table 18G) – $4.00* (gain on sale from Note 2)Net Borrowing = –$68.00 $75.00 (capital expenditures from Note 1)FCFE = – $7.00* (cash on sale from Note 2) –$24.00 –$3.00 (increase in accounts receivable from Table 18F) + –$20.00 (increase in inventory from Table 18F) + +(–$5.00) –$1.00 (decrease in accounts payable from Table 18F) $0.33 –$5.00 (decrease in long-term debt from Table 18F)*Supplemental Note 2 in Table 18H affects both NCC and FCINV.13. Rio National’s equity is relatively undervalued compared to the industry on a P/E-to-growth (PEG) basis. Rio National’s PEG ratio of 1.33 is below the industry PEG ratio of 1.66. The lower PEG ratio is attractive because it implies that the growth rate at Rio National is available at a relatively lower price than is the case for the industry. The PEG ratios for Rio National and the industry are calculated below: Rio National Current Price = $25.00 Normalized Earnings per Share = $1.71 Price-to-Earnings Ratio = $25/$1.71 = 14.62 Growth Rate (as a percentage) = 11 PEG Ratio = 14.62/11 = 1.33 Industry Price-to-Earnings Ratio = 19.90 Growth Rate (as a percentage) = 12 PEG Ratio = 19.90/12 = 1.66 18-17

Chapter 19 - Financial Statement Analysis CHAPTER 19: FINANCIAL STATEMENT ANALYSISPROBLEM SETS1. The major difference in approach of international financial reporting standards and U.S. GAAP accounting stems from the difference between ‘principles’ and ‘rules.’ U.S. GAAP accounting is rules-based, with extensive detailed rules to be followed in the preparation of financial statements; many international standards, including those followed in European Union countries, allow much greater flexibility, as long as conformity with general principles is demonstrated. Even though U.S. GAAP is generally more detailed and specific, issues of comparability still arise among U.S. companies. Comparability problems are still greater among companies in foreign countries.2. Earnings management should not matter in a truly efficient market, where all publicly available information is reflected in the price of a share of stock. Investors can see through attempts to manage earnings so that they can determine a company’s true profitability and, hence, the intrinsic value of a share of stock. However, if firms do engage in earnings management, then the clear implication is that managers do not view financial markets as efficient.3. Both credit rating agencies and stock market analysts are likely to be more or less interested in all of the ratios discussed in this chapter (as well as many other ratios and forms of analysis). Since the Moody’s and Standard and Poor’s ratings assess bond default risk, these agencies are most interested in leverage ratios. A stock market analyst would be most interested in profitability and market price ratios.4. ROA = ROS × ATO The only way that Crusty Pie can have an ROS higher than the industry average and an ROA equal to the industry average is for its ATO to be lower than the industry average.5. ABC’s Asset turnover must be above the industry average. 19-1

Chapter 19 - Financial Statement Analysis6. ROE = (1 – Tax rate) × [ROA + (ROA – Interest rate)Debt/Equity] ROEA > ROEB Firms A and B have the same ROA. Assuming the same tax rate and assuming that ROA > interest rate, then Firm A must have either a lower interest rate or a higher debt ratio.CFA PROBLEMS1. ROE = Net profits/Equity = Net profits/Sales × Sales/Assets × Assets/Equity = Net profit margin × Asset turnover × Leverage ratio = 5.5% × 2.0 × 2.2 = 24.2%2. SmileWhite has higher quality of earnings for the following reasons: • SmileWhite amortizes its goodwill over a shorter period than does QuickBrush. SmileWhite therefore presents more conservative earnings because it has greater goodwill amortization expense. • SmileWhite depreciates its property, plant and equipment using an accelerated depreciation method. This results in recognition of depreciation expense sooner and also implies that its income is more conservatively stated. • SmileWhite’s bad debt allowance is greater as a percent of receivables. SmileWhite is recognizing greater bad-debt expense than QuickBrush. If actual collection experience will be comparable, then SmileWhite has the more conservative recognition policy.3. a. ROE = Net profits = Net profits × Sales × Assets Equity Sales Assets Equity = Net profit margin × Total asset turnover × Assets/equity Net profits = 510 = 0.0992 = 9.92% Sales 5,140 Sales = 5,140 = 1.66 Assets 3,100 Assets = 3,100 = 1.41 Equity 2,200 19-2

Chapter 19 - Financial Statement Analysis b. ROE = 510 × 5,140 × 3,100 = 9.92% ×1.66 ×1.41 = 23.2% 5,140 3,100 2,200 c. g = ROE × plowback = 23.2% × 1.96 − 0.60 = 16.1% 1.964. a. Palomba Pizza Stores Statement of Cash Flows For the year ended December 31 Cash Flows from Operating Activities Cash Collections from Customers $250,000 Cash Payments to Suppliers (85,000) Cash Payments for Salaries (45,000) Cash Payments for Interest (10,000) Net Cash Provided by Operating Activities $110,000 Cash Flows from Investing Activities (6,000) Sale of Equipment 38,000 (60,000) Purchase of Equipment (30,000) 44,000 Purchase of Land (14,000) 50,000 Net Cash Used in Investing Activities $94,000 Cash Flows from Financing Activities Retirement of Common Stock (25,000) Payment of Dividends (35,000) Net Cash Used in Financing Activities Net Increase in Cash Cash at Beginning of Year Cash at End of Yearb. Cash flow from operations (CFO) focuses on measuring the cash flow generated by operations and not on measuring profitability. If used as a measure of performance, CFO is less subject to distortion than the net income figure. Analysts use CFO as a check on the quality of earnings. CFO then becomes a check on the reported net earnings figure, but is not a substitute for net earnings. Companies with high net income but low CFO may be using income recognition techniques that are suspect. The ability of a firm to generate cash from operations on a consistent basis is one indication of the financial health of the firm. For most firms, CFO is the “life blood” of the firm. Analysts search for trends in CFO to indicate future cash conditions and the potential for cash flow problems. 19-3

Chapter 19 - Financial Statement Analysis Cash flow from investing activities (CFI) is an indication of how the firm is investing its excess cash. The analyst must consider the ability of the firm to continue to grow and to expand activities, and CFI is a good indication of the attitude of management in this area. Analysis of this component of total cash flow indicates the type of capital expenditures being made by management to either expand or maintain productive activities. CFI is also an indicator of the firm’s financial flexibility and its ability to generate sufficient cash to respond to unanticipated needs and opportunities. A decreasing CFI may be a sign of a slowdown in the firm’s growth. Cash flow from financing activities (CFF) indicates the feasibility of financing, the sources of financing, and the types of sources management supports. Continued debt financing may signal a future cash flow problem. The dependency of a firm on external sources of financing (either borrowing or equity financing) may present problems in the future, such as debt servicing and maintaining dividend policy. Analysts also use CFF as an indication of the quality of earnings. It offers insights into the financial habits of management and potential future policies.5. a. CF from operating activities = $260 – $85 – $12 – $35 = $128 b. CF from investing activities = –$8 + $30 – $40 = –$18 c. CF from financing activities = –$32 – $37 = –$696. a. QuickBrush has had higher sales and earnings growth (per share) than SmileWhite. Margins are also higher. But this does not mean that QuickBrush is necessarily a better investment. SmileWhite has a higher ROE, which has been stable, while QuickBrush’s ROE has been declining. We can see the source of the difference in ROE using DuPont analysis:Component Definition QuickBrush SmileWhiteTax burden (1 – t) Net profits/pretax profits 67.4% 66.0%Interest burden Pretax profits/EBIT 1.000 0.955Profit margin EBIT/Sales 8.5% 6.5%Asset turnover Sales/Assets 1.42 3.55Leverage Assets/Equity 1.47 1.48ROE Net profits/Equity 12.0% 21.4%While tax burden, interest burden, and leverage are similar, profit margin and assetturnover differ. Although SmileWhite has a lower profit margin, it has a far higherasset turnover. 19-4

Chapter 19 - Financial Statement AnalysisSustainable growth = ROE × plowback ratioROE Plowback Sustainable Ludlow’s ratio growth rate estimate of growth rateQuickBrush 12.0% 1.00 12.0%SmileWhite 21.4% 0.34 7.3% 30% 10%Ludlow has overestimated the sustainable growth rate for both companies.QuickBrush has little ability to increase its sustainable growth – plowback alreadyequals 100%. SmileWhite could increase its sustainable growth by increasing itsplowback ratio.b. QuickBrush’s recent EPS growth has been achieved by increasing book value per share, not by achieving greater profits per dollar of equity. A firm can increase EPS even if ROE is declining as is true of QuickBrush. QuickBrush’s book value per share has more than doubled in the last two years. Book value per share can increase either by retaining earnings or by issuing new stock at a market price greater than book value. QuickBrush has been retaining all earnings, but the increase in the number of outstanding shares indicates that it has also issued a substantial amount of stock.7. a. ROE = operating margin × interest burden × asset turnover × leverage × tax burden ROE for Eastover (EO) and for Southampton (SHC) in 2007 are found as follows: EBIT SHC: 145/1,793 = 8.1%profit margin = Sales EO: 795/7,406 = 10.7%interest burden = Pretax profits SHC: 137/145 = 0.95 EBIT EO: 600/795 = 0.75asset turnover = Sales SHC: 1,793/2,104 = 0.85 Assets EO: 7,406/8,265 = 0.90 Assets SHC: 2,140/1,167 = 1.80 leverage = Equity EO: 8,265/3,864 = 2.14 Net profits SHC: 91/137 = 0.66 tax burden = Pretax profits EO: 394/600 = 0.66 ROE SHC: 7.8% EO: 10.2% 19-5

Chapter 19 - Financial Statement Analysisb. The differences in the components of ROE for Eastover and Southampton are:Profit margin EO has a higher marginInterest burden EO has a higher interest burden because its pretax profits are a lower percentage of EBITAsset turnover EO is more efficient at turning over its assetsLeverage EO has higher financial leverageTax Burden No major difference here between the two companiesROE EO has a higher ROE than SHC, but this is only in part due to higher margins and a better asset turnover -- greater financial leverage also plays a part.c. The sustainable growth rate can be calculated as: ROE times plowback ratio. The sustainable growth rates for Eastover and Southampton are as follows:Eastover ROE Plowback SustainableSouthampton ratio* growth rate 10.2% 0.36 7.8% 0.58 3.7% 4.5%*Plowback = (1 – payout ratio)EO: Plowback = (1 – 0.64) = 0.36SHC: Plowback = (1 – 0.42) = 0.58The sustainable growth rates derived in this manner are not likely to berepresentative of future growth because 2007 was probably not a “normal” year.For Eastover, earnings had not yet recovered to 2004-2005 levels; earningsretention of only 0.36 seems low for a company in a capital intensive industry.Southampton’s earnings fell by over 50 percent in 2007 and its earnings retentionwill probably be higher than 0.58 in the future. There is a danger, therefore, inbasing a projection on one year’s results, especially for companies in a cyclicalindustry such as forest products.8. a. The formula for the constant growth discounted dividend model is: P0 = D0 (1 + g) k−gFor Eastover: P0 = $1.20 ×1.08 = $43.20 0.11 − 0.08This compares with the current stock price of $28. On this basis, it appears thatEastover is undervalued. 19-6

Chapter 19 - Financial Statement Analysisb. The formula for the two-stage discounted dividend model is:P0 = D1 + D2 + D3 + P3 (1 + k)1 (1 + k)2 (1 + k)3 (1 + k)3For Eastover: g1 = 0.12 and g2 = 0.08D0 = 1.20D1 = D0 (1.12)1 = $1.34D2 = D0 (1.12)2 = $1.51D3 = D0 (1.12)3 = $1.69D4 = D0 (1.12)3(1.08) = $1.82P3 = D4 = $1.82 = $60.67 k −g2 0.11 − 0.08P0 = $1.34 + $1.51 + $1.69 + $60.67 = $48.03 (1.11)1 (1.11) 2 (1.11)3 (1.11)3This approach makes Eastover appear even more undervalued than was the caseusing the constant growth approach.c. Advantages of the constant growth model include: (1) logical, theoretical basis; (2) simple to compute; (3) inputs can be estimated. Disadvantages include: (1) very sensitive to estimates of growth; (2) g and k difficult to estimate accurately; (3) only valid for g < k; (4) constant growth is an unrealistic assumption; (5) assumes growth will never slow down; (6) dividend payout must remain constant; (7) not applicable for firms not paying dividends. Improvements offered by the two-stage model include: (1) The two-stage model is more realistic. It accounts for low, high, or zero growth in the first stage, followed by constant long-term growth in the second stage. (2) The model can be used to determine stock value when the growth rate in the first stage exceeds the required rate of return.9. a. In order to determine whether a stock is undervalued or overvalued, analysts often compute price-earnings ratios (P/Es) and price-book ratios (P/Bs); then, these ratios are compared to benchmarks for the market, such as the S&P 500 index. The formulas for these calculations are: P/E of specific company Relative P/E = P/E of S&P 500 P/B of specific company Relative P/B = P/B of S&P 500 19-7

Chapter 19 - Financial Statement AnalysisTo evaluate EO and SHC using a relative P/E model, Mulroney can calculate the five-year average P/E for each stock, and divide that number by the 5-year average P/E forthe S&P 500 (shown in the last column of Table 19E). This gives the historicalaverage relative P/E. Mulroney can then compare the average historical relative P/E tothe current relative P/E (i.e., the current P/E on each stock, using the estimate of thisyear’s earnings per share in Table 19F, divided by the current P/E of the market).For the price/book model, Mulroney should make similar calculations, i.e., dividethe five-year average price-book ratio for a stock by the five year averageprice/book for the S&P 500, and compare the result to the current relativeprice/book (using current book value). The results are as follows:P/E model EO SHC S&P5005-year average P/E 16.56 11.94 15.20Relative 5-year P/E 1.09 0.79 20.20Current P/E 17.50 16.00Current relative P/E 0.87 0.79Price/Book model EO SHC S&P5005-year average price/book 1.52 1.10 2.10Relative 5-year price/book 0.72 0.52Current price/book 1.62 1.49 2.60 0.57Current relative price/book 0.62From this analysis, it is evident that EO is trading at a discount to its historical 5-yearrelative P/E ratio, whereas Southampton is trading right at its historical 5-year relativeP/E. With respect to price/book, Eastover is trading at a discount to its historicalrelative price/book ratio, whereas SHC is trading modestly above its 5-year relativeprice/book ratio. As noted in the preamble to the problem (see CFA Problem 7),Eastover’s book value is understated due to the very low historical cost basis for itstimberlands. The fact that Eastover is trading below its 5-year average relative price tobook ratio, even though its book value is understated, makes Eastover seem especiallyattractive on a price/book basis.b. Disadvantages of the relative P/E model include: (1) the relative P/E measures only relative, rather than absolute, value; (2) the accounting earnings estimate for the next year may not equal sustainable earnings; (3) accounting practices may not be standardized; (4) changing accounting standards may make historical comparisons difficult. Disadvantages of relative P/B model include: (1) book value may be understated or overstated, particularly for a company like Eastover, which has valuable assets on its books carried at low historical cost; (2) book value may not be representative of earning power or future growth potential; (3) changing accounting standards make historical comparisons difficult. 19-8

Chapter 19 - Financial Statement Analysis10. The following table summarizes the valuation and ROE for Eastover and Southampton:Stock Price Eastover SouthamptonConstant-growth model $28.00 $48.002-stage growth model $43.20 $29.00 $48.03 $35.50Current P/E 17.50 16.00Current relative P/E 0.87 0.795-year average P/E 16.56 11.94Relative 5 year P/E 1.09 0.79Current P/B 1.62 1.49Current relative P/B 0.62 0.575-year average P/B 1.52 1.10Relative 5 year P/B 0.72 0.52Current ROE 10.2% 7.8%Sustainable growth rate 3.7% 4.5%Eastover seems to be undervalued according to each of the discounted dividend models.Eastover also appears to be cheap on both a relative P/E and a relative P/B basis.Southampton, on the other hand, looks overvalued according to each of the discounteddividend models and is slightly overvalued using the relative price/book model. On arelative P/E basis, SHC appears to be fairly valued. Southampton does have a slightlyhigher sustainable growth rate, but not appreciably so, and its ROE is less thanEastover’s.The current P/E for Eastover is based on relatively depressed current earnings, yet thestock is still attractive on this basis. In addition, the price/book ratio for Eastover isoverstated due to the low historical cost basis used for the timberland assets. This makesEastover seem all the more attractive on a price/book basis. Based on this analysis,Mulroney should select Eastover over Southampton.11. a. Net income can increase even while cash flow from operations decreases. This can b. occur if there is a buildup in net working capital -- for example, increases in accounts receivable or inventories, or reductions in accounts payable. Lower depreciation expense will also increase net income but can reduce cash flow through the impact on taxes owed. Cash flow from operations might be a good indicator of a firm's quality of earnings because it shows whether the firm is actually generating the cash necessary to pay bills and dividends without resorting to new financing. Cash flow is less susceptible to arbitrary accounting rules than net income is.12. $1,200 Cash flow from operations = sales – cash expenses – increase in A/R Ignore depreciation because it is a non-cash item and its impact on taxes is already accounted for. 19-9

Chapter 19 - Financial Statement Analysis13. a Both current assets and current liabilities will decrease by equal amounts. But this is a larger percentage decrease for current liabilities because the initial current ratio is above 1.0. So the current ratio increases. Total assets are lower, so turnover increases.14. a Cost of goods sold is understated so income is higher, and assets (inventory) are valued at most recent cost so they are valued higher.15. a Since goods still in inventory are valued at recent versus historical cost.16. Considering the components of after-tax ROE, there are several possible explanations for a stable after-tax ROE despite declining operating income: 1. Declining operating income could have been offset by an increase in non-operating income (i.e., from discontinued operations, extraordinary gains, gains from changes in accounting policies) because both are components of profit margin (net income/sales). 2. Another offset to declining operating income could have been declining interest rates on any interest rate obligations, which would have decreased interest expense while allowing pre-tax margins to remain stable. 3. Leverage could have increased as a result of a decline in equity from: (a) writing down an equity investment, (b) stock repurchases, (c) losses; or, (d) selling new debt. The effect of the increased leverage could have offset a decline in operating income. 4. An increase in asset turnover could also offset a decline in operating income. Asset turnover could increase as a result of a sales growth rate that exceeds the asset growth rate, or from the sale or write-off of assets. 5. If the effective tax rate declined, the resulting increase in earnings after tax could offset a decline in operating income. The decline in effective tax rates could result from increased tax credits, the use of tax loss carry-forwards, or a decline in the statutory tax rate. 19-10

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