SECTION 10: ANSWERS TO PRACTICE PROBLEMS

Transcription

1 SECTION 10: ANSWERS TO PRACTICE PROBLEMS These practice problems are somewhat advanced material. Some of them approach problems from a different angle than the angle we took in class; and some of them add new complications that we could not tackle in class (due to time constraints). Question 1. a) This is a growing perpetuity, with year 1 cash flow (1+3%)*$1m = $1.03m. With a growth rate of 3% and a required return of 15%, its PV is $1.03m/(.15.03) = $ m. Pay no more than that present value of future cash flows! b) Cash flows in Years 1, 2, and 3 are $1m, (1+20%)*$1m = $1.2m, and (1+20%)*$1.20m = $1.44m, respectively. From that point on, the firm is a growing perpetuity with year 4 cash flow (1+5%)*$1.44m = $1.512m, growth rate 5%, and required return 18%. PV now of Year 1 cash flow = $1.00m/1.18 = $ m PV now of Year 2 cash flow = $1.20m/(1.18) 2 = $ m PV now of Year 3 cash flow = $1.44m/(1.18) 3 = $ m PV at end of Year 3 of all later cash flows: PV at end of Year 3 = $1.512m/(.18.05) = $ m, so PV now of that PV = $ /(1.18) 3 = $ m Present value of all cash flows: $ m Thus, the target is worth at most $ m to your company. Question 2. a) The equipment costs $200,000 in Year 0 (negative cash flow), and is sold for $20,000 in Year 5 (positive cash flow). In the interim, its effect on annual UFCFs is as follows: Wage savings (reduced expense = increased income) 50,000 Depreciation = (200,000 20,000)/5 36,000 EBIT 14,000 Unlev. inc. taxes = 0.21 * 14,000 2,940 NOPLAT 11,060 Depreciation 36,000 CF from changes in NWC 0 CF from changes in FxA 0 UFCF 47,060 Thus, UFCFs by year are: Year 0, $200,000; in each of Years 1 4, $47,060; Year 5, $67,060 (since the firm gets $47,060 from operations plus the $20,000 salvage value). With a WACC of 12.20%, the NPV of the cash flows given above is $19, That s negative, and a fairly large negative number, so don t do the project. b) Under accelerated depreciation, the tax savings from depreciation would come sooner (on average), increasing their present value. Thus, NPV would rise (become less negative). But the firm would have to rely on a very aggressive depreciation schedule to make the NPV positive, and on an extremely aggressive schedule to make the NPV significantly positive P. Povel 10-1

2 Question 3. a) Stock A s required return is rf + (rm rf) = 4.52% * 6.8% = %. For the first five years, it pays $2; the present value of a $2/year, five year annuity at 12% is [ 1 1/(1+12%) 5 ] * $2/12% = $ In year 6 it pays $2 * ( ) = $2.12, then $2 * ( ) 2 in Year 7, etc. We can use a terminal value to discount those later cash flows: viewed from Year 5, the stock is a growing perpetuity starting at $2.12 (in the following year, year 6), growing at g = = 6%/year. The present value of this growing perpetuity in Year 5 is $2.12/(.12.06) = $ ; the present value of this today is $ /(1.12) 5 = $ The value of Stock A is the present value of all cash flows, so it is the sum of the present value of the annuity and the present value of the terminal value. The stock is worth $ $ = $ b) Stock B s required return is 4.52% + 1 * 6.8% = %. Next year s dividend is expected to be $5 * (1 + 4%) = $5.20, which grows thereafter at 4%; thus, this is a growing perpetuity, whose present value is $5.20/( ) = $ Question 4. a) Next year s expected cash flow is $10m * (1+5%) = $10.5m, growing thereafter at 5%. This is a growing perpetuity, whose value at a required return of 13% is $10.5m/(.13.05) = $131.25m. b) Viewed from the end of Year 1, the firm is a growing perpetuity whose next cash flow (in year 2) is $10.5m * (1+5%) = m. The firm s value at the end of year 1 is $11.025m/(.13.05) = $ m, an increase of ($ m $131.25m)/($131.25m) = 5%. [That was obvious: all cash flows are increased by 5% in the second calculation, so the present value must be 5% larger.] c) From your viewpoint, the cash flows are: $5m next year, then $3m in each of Years 2 4, followed by $3m * (1+6%) in Year 5, $3m * (1+6%) 2 in Year 6, etc. Use a terminal value to discount cash flows in years 5 and later to year 4. They form a growing perpetuity starting at $3.18m and growing at 6%; its present value in Year 4 will be $3.18m/(.18.06) = 26.5m, which has a present value today of $26.5m/(1.18) 4 = $ m. PV of cash flows in Years 1 4 is $5m/(1.18) + $3m/(1.18) 2 + $3m/(1.18) 3 +(3m)/(1.18) 4 = $ m. Thus, the total value of the project is $ m + $ m = $ m. Question 5. a) Disagree: in an efficient market, the seasonality of this firm s earnings is public information and will be taken into account in the current share price. Therefore, the stock price can t be expected to show abnormal increases in the spring; if the stock were expected to have abnormally high returns, smart investors would buy it in the fall, hoping for excess profits. The firm should get a fair price for its stock at any time unless management has information which investors do not have. b) Disagree: in an efficient market, investors act intelligently, and price changes reflect changes in publicly available information. Since all the stocks in this industry segment have fallen, it seems likely that some negative information about the industry has just become available. It would be a mistake to completely rule this possibility out by assuming investors are acting irrationally P. Povel

3 Question 6. Immediately after a firm makes a negative announcement, buy its shares; then sell a few weeks later. On average, you ll capture the bounce back. [Of course, if many other investors use this strategy, prices won t fall as far on the announcement more investors will buy and the excess profits will disappear.] Question 7. a) Disagree. If the market is efficient, the NPV of the lucrative contract will have been incorporated into the share price right after the announcement. You shouldn t be able to make excess risk adjusted profits trading on public information. b) Disagree. In an efficient market, current prices reflect the market s perception of share value, and stock prices don t follow predictable cycles. If managers have inside information that the firm itself is undervalued, it might make sense to delay issuing equity, but that is not the reasoning given in the statement. c) Agree (or at worst indifferent). Bicycle manufacturer employees probably don t have any better information about banks than professional investors and analysts. Thus, the investment in bank stocks would have zero NPV at best. In addition, shareholders of the bicycle manufacturer aren t paying the firm to invest in bank stocks; if they want to do it, they can do it themselves. If buying shares is costly, this is probably an unnecessary expenditure. Question 8. a) In this case, there should be no effect on your firm s share price: the market should already be aware of the information from footnotes to the financial reports. b) Here, the change reveals information that the market did not have previously. Investors will have tried to estimate the actual value of your firm s assets, so the answer depends on whether or not the market s earlier estimate was too high, too low, or just right. Question 9. The cash flows include (1) an immediate outflow of $5.0m; (2) fifteen inflows, growing, over 15 years (starting in year 1); (3) an inflow of $5.0m in year 15. The fifteen dividends form a growing annuity. The PV in year zero is [ 1 ((1+g)/(1+r)) T ] * CF1/(r g). We have CF1 = $0.8m, T = 15, and g = 4%. We need r... We can calculate r. We have a beta, and information about the risk-free rate and market returns. Combine those using the CAPM: r = rf + β * MRP. The best estimate for rf is a current treasury rate: 3.88%. The best estimate of MRP is the average return on the market less the corresponding average return on treasuries: MRP = 8.48% % = 5.06%. So r = 3.88% * 5.06% = %. All cash flows can be discounted using this rate. NPV = -$5m + [ 1 (1.04 / ) 15 ] * $0.8m / $5m / = -$5m + $4.8434m + $0.4150m = $0.2584m. Question 10. We can use the WACC. We need unlevered free cash flows and the WACC. 2. We can use the WACC. We need unlevered free cash flows and the WACC. Y1 EBITDA 10 D&A 1 EBIT 9 Unlev. Income Tax 2.25 NOPLAT P. Povel 10-3

4 NOPLAT 6.75 D&A 1 CF from Chg in NWC 0 CF from Chg in FxA -1.3 UFCF 6.45 Since there is no debt, WACC = (1 25%) * 0 * rd + (1 0) * 15% = 15%. (We don t know rd, but with zero leverage that summand is zero for any rd). The UFCFs form a growing perpetuity (the business is growing at a rate of 3%). We can calculate the enterprise value using the growing perpetuity formula. Ent.V. = UFCF1 / (WACC g) = $6.45m / ( ) = $53.75m. Question 11. This changes the valuation by increasing the EBITDA in year 1; in years 2 and later, the original forecasts remain valid (all numbers growing at g = 3%, using the year 1 numbers from the last question.) Y1 Y2 EBITDA D&A EBIT Unlev. Income Tax NOPLAT NOPLAT D&A CF from Chg in NWC 0 0 CF from Chg in FxA UFCF Terminal Value PV(CF) PV(TV) Enterprise Value Question 12. a) The market value of the debt is $100m; that of the equity is m * $16.00 = $350m. So the current leverage ratio is D/(D+E) = The expected returns are rd = rf = 6% and re = 6% + 1.2*8% = 15.6%. With a tax rate of 22%, the WACC is 0.78*0.222*6% *15.6% = %. b) The new rd = 6% + 0.2*8% = 7.6%. We need to calculate the new re, by levering up the equity return. First, we de-lever it (mature, non-growing firm): rua = (0.78*0.222*6% *15.6%)/(0.78* ) = %. So the target re = % *(0.4/0.6)*( % 7.6%) = %. So the target WACC = 0.78*0.4*7.6% + 0.6* % = %. c) We need the unlevered free cash flow. Start with the EBIT of $90, and deduct taxes of 22% to obtain NOPLAT = $70.2m. Add back Depreciation of $10m, CF from Chg in NWC (zero) and CF from Chg in FxA ( $10m) to obtain a UFCF of $70.2m. The UFCFs form a constant perpetuity; enterprise value = $70.2m/ = $ m P. Povel

5 Question 13. a) WACC = 0.25 * (1-0.21) * 7% * 18% = %. b) De-lever re: rua = 0.25* *0.18 = 15.25% (use the growing-firm formula, since the UFCF are growing at a rate of 5%). Then re-lever: re = (0.15/0.85)*( ) = %. So the new WACC will be * 0.15 * 6% * % = %. c) Current value: NOPLAT = 0.79*$10m = $7.9m. Add depreciation and CFs from Chg in NWC and FxA: UFCF = $7m + $2m + ( $2.5m) + ( $0.5m) = $6m. Value of the growing perpetuity: $6.9m/( ) = $ m. Target leverage valuation: Unlev. FCF = same as before, $6.9m. Value of the growing perpetuity: $6.9m/( ) = $ m. The value would decrease because we would lose tax shields. Question 14. a) Use the comparable firms to get an estimate of the industry rua, which you can use as an estimate for Tower Inc. s rua. We have little information about how representative this sample of firms is, or how similar they are to Tower Inc. The fact that the leverage ratios are quite dispersed does not mean that we can exclude firms we need to focus on their operations, not their leverage (an aspect we eliminate, because we delever the returns). It is not clear whether the sales or market cap numbers can be used to exclude firms. If we knew that a firm s products or markets are different, though, that would be a reason to exclude it as a comparable. De-lever each comparable, using its own numbers. Use the formula for growing firms, since all seem to be growing (we only know that their revenues are growing; we are assuming that this means that their UFCFs and enterprise values are growing, too): rua = D/V*rD + (1 D/V)*rE. That gives you rua s of %, %, %, and %. The equally weighted average of the four rua values is %. We can use that industry average as an estimate of Tower Inc. s rua. b) Use the relevering formula for growing firms, and the value of rua estimated in part a), re = rua + (D/V)/(E/V)*(rUA rd) = % /0.75 *(15.638% 9%) = %. Use that to calculate WACC = 0.79*0.25*9% *17.851% = %. Question 15. a) WACC = (1-Tc)*(D/V)*rD+(E/V)*rE = 76%*25%*10%+75%*17% = %. b) The value of the expansion project is the present value of a constant perpetuity: PV = UFCF/WACC = $1.8m/ = $ m. The NPV is $ m, a large positive number, compared with the startup cost, so this is a project worth undertaking. c) The project can be financed in many ways, which lead to different tax shields. For an appraisal of the question whether the project should be undertaken, however, we should only consider the optimal financing strategy (if it is feasible) that would be chosen if the project is a stand-alone firm. It seems that the project is a mini-replica of the firm itself, so we should use the same financing mix in our calculations. Hence, the CEO s suggestion does not change anything as far as part b of this question is concerned. Remember, we are just trying to figure out whether something adds value. If we issue more debt, then this increases our valuation, but we are borrowing against the existing assets and cash flows of the firm, and we could do that without undertaking the project P. Povel 10-5

6 Question 16. a) APV = Unlevered value + IETS. Both projects generate cash flows that are constant perpetuities. Bridge: Unlevered value = $1.2m/.08 = $15m. For the IETS, we need either the yield on the debt or the interest expense. We have neither. However, since the IETS CFs form a constant perpetuity, and (by assumption) the interest tax shields are as risky as the interest payments themselves, we can nevertheless compute the present value of the IETS CF. Under those assumptions, the PV of is Tc*rD*D/rTx = Tc*rD*D/rD = Tc*D. So the bridge project IETS is 0.25*$6m = $1.5m. APV = VU + IETS = $16.5m. Ferry: Unlevered value = $3.34m/.20 = $16.7m; tax shield PV =.25*$5m = $1.25m (the assumptions are all satisfied); APV = $17.95m. b) The bridge NPV is $6.5m. The ferry NPV is $7.95m. Both are large positive numbers, so both projects are attractive. The ferry NPV is somewhat larger, so it is more attractive. c) We do not have enough information to calculate the WACC. Specifically, we need the firm s leverage ratio. However, with some experimenting on a spreadsheet we can put together a WACC valuation anyway. Start with a guess for the firm s leverage ratio. Then value the firm using the WACC that your guess implies, and calculate the leverage ratio implied by your valuation. That is, divide the debt ($50m) by the enterprise value. Compare that leverage ratio with your guess, and adapt your guess until the two ratios are the same (all formulas should recalculate automatically.) Say, we assume that the leverage ratio is 20% (that s just a random guess). The firm is not growing, so use the mature-firm relevering formula to calculate re ( %) and the WACC ( %). The UFCFs form a constant perpetuity, so the enterprise value is $27.375m/ % = $ m. The implied leverage ratio is $50m/$ m = %, higher than the initial guess. A leverage ratio of % yields a consistent valuation: a WACC of %, and an enterprise value of $195m. d) Bayou Freeways should not use its own WACC to evaluate the bridge. (1) The bridge s rua (and thus unlevered asset beta) is lower than that of the firm as a whole (the firm s rua is higher than its WACC, %, so it is much higher than the bridge s rua, 8%). So using the firm s WACC underestimates the bridge s value. (2) The bridge s projected leverage ratio is $6m/$16.5m = %, higher than the firm s ratio of 25%. So using the firm s WACC underestimates the bridge s tax shields. Question 17. a) Let the optimal level of project debt be Dproj, and total project value (i.e., the PV of the future cash flows) be Vproj. Use the APV to value the project. For the Unlevered value, we need to forecast the UFCFs. NOPLAT = (1-Tc)*EBIT = (1- Tc)*(EBITDA D&A) = $1.925m. Add back D&A, CF from Chg in FxA and CF from Chg in NWC (zero) to get UFCF = $1.925m. The UFCFs form a constant perpetuity. Unlevered value = UFCF1/rUA = $1.925m/0.14 = $13.75m. The IETS CFs are = Tc*(rD*Dproj) each year, indefinitely. Since the leverage ratio is 20%, we must have Dproj =.2*APVproj. Since the debt is perpetual and since (by assumption) rtx = rd, the PV of the IETS CF is Tc*rD*Dproj/rD = Tc*Dproj =.23*Dproj. So APVproj = $13.75m +.23*Dproj = $13.75m +.23*.2*APVproj = $13.75m +.046*APVproj. In sum, APVproj = $13.75m +.046*APVproj, which we can solve for APV:.954*APVproj = P. Povel

7 $13.75m APVproj = $ m Dproj =.2*$ m = $ m; Eproj = APVproj Dproj = $ m. The NPV is $ m, positive and probably large for this industry. b) WACC = $80m/$200m * (1.23) *.08 + (1 $80m/$200m) *.13 = = %. Computing the PV of the project s UFCFs with Top Nosh s WACC, PV = $1.925m/ = $ m. The corresponding NPV is $ , higher than the NPV we calculated. That makes the investment look more attractive than it really is. c) Top Nosh s WACC does not correctly value the project. One reason is that the underlying asset risks are not the same. Top Nosh s required return on its levered equity is 13%; its unlevered equity return would be less than 13%. The project s unlevered return is 14%, which means the project s underlying risk is higher than that of Top Nosh. So the WACC is under-estimated, which (wrongly) increases the NPV. Another reason is that Top Nosh s leverage ratio is higher, which again (wrongly) decreases the WACC and increases the NPV. Third, the required return on Top Nosh s debt is lower, which again (wrongly) decreases the WACC and increases the NPV. Question 18. a) In year 1, EBIT = (EBITDA D&A) = (1 0.15)*EBITDA = $17m. NOPLAT = (1 Tc)*EBIT = $13.43m. D&A = CapEx = 15% * $20m = $3m. CF from Chg in FxA = $3m. CF from Chg in NWC = $0. UFCF = $13.43m + $3m $3m + $0 = $13.43m in year 1. The UFCFs form a growing perpetuity. Using rua = 18% and g = 4%, the unlevered value is equal to $13.43m/(18% 4%) = $ m. We need to choose a discount rate for the tax shields; a rate rtx such that rd rtx rua is a priori reasonable. The firm is growing at a rate of 4%, so we should choose rtx = rua = 18%. The PV of the tax shields is (they form a growing perpetuity from the start) Tc*rD*D/(rTx g) = 0.21 * 10% * $15m / (18% - 4%) = $2.25m. The enterprise value (APV) is $ m. b) The NPV is $94m + $ m = $ m. It is positive; not huge, but in this industry, this may be a good project. c) To calculate the WACC, we need a levered equity return, and either E or V (=D+E), so we can calculate D/V. We have neither V nor E nor re, but we can calculate them while performing the WACC valuation. Start with a guess for D/V. Use the re-levering formula for a growing firm to calculate re = rua + (D/V)/(E/V)*(rUA rd). Then compute the WACC and use it to calculate the PV of the growing unlevered FCFs computed in part a). The unlev. FCFs are a growing perpetuity from the start, so PV = UFCF/(WACC g). Divide the value of the debt ($15m) by that calculated value, to get the implied leverage ratio. Now compare that ratio with your initial guess. If they are different, change the guess and compare again (your spreadsheet will recalculate everything after you change your guess). Eventually, you will find the correct guess, i.e., a guess that is consistent with (equal to) the implied value produced by the WACC valuation model. For example, if you guess D/V = 0.2, you get an implied D/V = the guess is too high. An initial guess of D/V = 0.15 gives you an implied D/V = the guess is a little too low. An initial guess of D/V = works, yielding a internally (logically) consistent valuation of $ m based on a WACC of %. The corresponding NPV is then $ m P. Povel 10-7

8 Question 19. The common has more upside potential, since its value will increase if the firm does well. The preferred can never be worth more than the discounted value of its dividend, which is fixed. Because it is senior to the common stock, the preferred stock is paid first if Hicks Cups gets into trouble, giving it better downside protection. Thus, the common stock has both more upside and downside, making it riskier. Question 20. The junior debt should be more risky. Although contractual payments on both classes of debt are the same, if SuperMark Corp. goes into bankruptcy, the senior debtholders get paid first. Thus, the junior debtholders have a greater chance of not being paid in full, and their bonds are more risky. [Note that the junior bonds will have a lower price than the senior bonds. The junior bond s expected payments (factoring in the chance of default) are lower, and their payments are discounted at a higher required rate of return because theye are more risky.] Question 21. The UFCF forecasts are constant indefinitely: Tc = 25% Tc = 0% EBIT Unlev. Inc. Tx. Exp NOPLAT D&A CF from Chg in NWC CF from Chg in FxA UFCF Using the rates and market values, we can calculate the current leverage ratio = 4/45.45 = and WACC = (1-25%) * * 5.7% + ( ) * 12% = %, and confirm the current enterprise value: Ent. V. = $5.625m / ( % 0%) = $49.45m (= D+E ). Note that the tax reduction has two effects: First, the unlevered free cash flows increase, because of the reduced income tax payments; and second, the cost of capital changes, because the interest expense deductibility does not affect the income tax expense, anymore. De-lever, using the formula for mature firms (since the firm is not growing): rua = ( (1-25%) * * 5.7% + ( ) * 12% ) / ( (1-25%) * ( ) ) = %. We need to relever, but we don t know the target leverage ratio or equity value, we know only that the debt level remains unchanged. Use an estimated leverage ratio, say, 8%, to lever up, and after finishing the valuation, calculate the leverage ratio implied by your valuation. Very likely, it will be different from your guess of 8%. Change your estimate, probably several times, until it is consistent with the valuation it produces. (Use a spreadsheet for this.) With a guessed target leverage ratio of 8% (and Tc = 0%), we obtain a return on equity of re = %. So the post-transaction WACC = %. The new enterprise value is $7.5m / ( % 0%) = $64.6m. The implied leverage ratio is $4m/$64.6m = 6.192%, different from our initial guess. So we need to adapt the initial guess, let the spreadsheet recalculate everything, and see whether the guess is closer to the implied leverage ratio. Repeat a few times, and you find that a guessed leverage ratio of 6.192% produces a consistent valuation, with an enterprise value of $64.6m. Note: If Tc = 0, then WACC = rua, which is why the implied leverage is the same for any assumed leverage ratio (the enterprise values are also the same) P. Povel

9 Question 22. a) Yes, it could. This leaves the firm strapped for cash, and the bank and other lenders may be reluctant to put more money into the firm to keep operations afloat especially if the owner is still running the show. Since this is a firm whose going concern value ($900,000) is much greater than the value of its assets in liquidation ($500,000), such delays could cause a lot of damage to total firm value. b) Depending on her salary, it could impose costs on the owner. This is a privately held firm, so she can t sell shares when she needs cash, and the cash distribution restriction prevents her from tapping into her total wealth to meet legitimate expenditures. [She could have the firm pay some of her expenses directly not uncommon for entrepreneurial firms.] Question 23. a) The current value of the firm is D + E = $2m + $0.2m = $2.2m. If the investment is undertaken, the value of the business is ½ * $4m + ½ * $0 = $2m. So the NPV is equal to $2m $2.2m = $0.2m. b) The lenders current claim is worth $2m. If the investment is undertaken, the debt s market value is ½ * $2m + ½ * $0 = $1m, less than $2m. So the lenders would not approve. c) The NPV is negative, so if the forecasts are accurate, the investment does not add value and should not be undertaken. d) The value of the equity, if the investment is undertaken, is ½ * ($4m $2m) + ½ * $0 = $1m, which is higher than $0.2m. This firm is financially distressed, which gives the shareholders an incentive to take on risky projects, even if the NPV is negative they benefit if things work out well, and the lenders suffer if things work out badly. Question 24. a) The (unlevered) FCF is expected to be $12m. Given re = 12%, the Unlevered value is $100m. Without debt, we get APV = Unlevered value + PV(TxSh.) = $100m + 0 = $100m. So Arizona Cream s existing assets are valued at $100m. There is no debt and there are no tax shields; so the value of its equity is equal to the value of the assets. Hence, the current share price is E/10m = $100m/10m = $ b) It issues N new shares at a price P, where P is the price at which shares will be trading after the investment. The net amount needed is equal to the present value of the T-bills, minus the 5% price reduction granted by the seller (there must not have been much buyer competition in this sale). The appropriate discount rate is 4%, since the T-bills are riskfree. (Do not use Arizona Cream s re!) The price is therefore 0.95*$40m/1.04 = $36.538m. Their market value is $40m/1.04 = $38.462m. Arizona Cream s total asset value would be $100m + $38.462m = $ m. As before, this is also the value of the equity (no debt). So (10m+N)*P = $ m. With 3% issuing costs, Arizona Cream must issue shares worth $X, such that (1 3%)*X = $36.538m. That implies X = $36.538m/0.97 = $37.668m. So N*P = $37.668m. Combine the two equations: (10m+N)*P = $ m N*P = $37.668m 10m*P = $ m $37.668m P = $10.08, and N = 3.737m. The share price increased by $0.08, so the investment adds value. (Net value added = $0.08*10m = 2019 P. Povel 10-9

10 $0.8m = $38.462m $36.538m ($37.668m $36.538m) = (Value of T-bills) (price paid) (issuing costs). c) Without the T-bills, EPS = $12m/10m = $1.20. With the T-bills, the interest payment is $40m $38.462m = $1.538m, so we add $1.538m to the earnings. But there are also 3.737m new shares, so the new EPS is $13.538m/13.737m = $0.99. That is considerably less than the earlier EPS, so these investors would conclude that it is a bad deal. Wrongly, since the NPV is positive! Question 25. The value of the new operations is the present value of the expected UFCFs, discounted at the appropriate rate. Because no debt will be used, the valuation is simple: in this case, WACC = rua; if using the APV, there is no IETS to value. The UFCF form a growing perpetuity, so the value is UFCF1 / (r g) = $0.36m / (13% 4%) = $4.000m. The new enterprise value (after the project has been started) would be $75m + $4m = $79m. That would also be the value of the equity, since the debt level will remain zero. If N shares are issued at a price P, then the new equity would be described by (2m + N) * P = $79m. The amount of equity issued would be $2.6m / (1 7%) = $2,795,699. So N * P = $2,795,699. Combine the two equations, (2m + N) * P = $79,000,000 N * P = $2,795,699 Solve to obtain 2m * P = $76.204m and thus P = $38.10 and N = 73,378. The net value added to the company is $4,000,000 $2,795,699 = $1,204,301. Per share of shares outstanding originally, that yields a share price increase of $1,204,301 / 2m = $0.60, consistent with an original share price of $37.50 and a new share price of $ Question 26. a) V = E + D = 30m*$ $40m = $100m. Tax shields: assuming that they are riskless, too, and since the IETS CFs form a constant perpetuity, their PV is Tc*D = 0.23*$40m = $9.2m. So VUA = V PV(TxSh.) = $100m $9.2m = $90.8m. The UFCFs form a constant perpetuity, so PV = UFCF/rUA. Replace, and solve: $90.8m = $12m/rUA rua = $12m/$90.8m = %. Lever up, using the mature firm formula, to get re = rua + (1-Tc)*D/E*(rUA rd) = % * 40/60 * ( % 6.25%) = %. b) Debt reduction by $10m reduces the tax shields by 0.23*$10m = $2.3m. So the value of the firm decreases by $2.3m to $97.7m (assuming that the value of the operating assets is unaffected by this transaction). New value of E = V D = $97.7m $30m = $67.7m. Issue N shares at a price P: (30m + N)*P = $67.7m, and N * P = $10m. Combine to get 30m * P = $57.7m or P = $1.9233, and N = $10m/$ = 5,199,307. Share price decreased by $2.00 $ = $ Total value lost to old shareholders = 30m * $ = $2.3m, equal to the lost tax shields. Question 27. a) Issue N shares at price P so that P * N.05 * P * N = $100m P * N = $105.26m. Afterwards, total firm value V = total equity value E = (value of old assets) + (net cash raised). E = $13.50 * 60m + $100m = $910m = P * (total shares outstanding) = P * (60m+N). Subtracting [P * N = $105.26m] from [P * (60m+N) = $910m] yields P * 60m = $804.74m. So P = $13.41; N = $105.26m/$13.45 = 7.85m shares issued. b) Still issue N shares at price P so that P * N = $105.26m (to cover direct costs of issue) P. Povel

11 However, market now believes value of old assets is.98 * $810m = $793.8m. After issue, total firm value V = E = $793.8m + $100m = $893.8m = P * (60m+N). So P * 60m = $893.8m $105.26m = $788.54m. So P = $13.14 and N = 8.01m. c) Investors were wrong; true value of firm V = E = $910m. Once investors realize this, E = $910m = P * (60m+8.01m) P = $ Total cost of issue = direct issue cost + signaling cost. Direct issue cost = $105.26m $100m = $5.26m. Signaling cost = (amount issued) * [(true value of equity)/(perceived value of equity) 1] = $105.26m * [$910m/$893.8m 1] = $1.91m. [Alternatively, signaling cost = total bargain received by new shareholders = 8.01m * ($13.38 $13.14) $1.91m.] Total cost of issue = $5.26m + $1.91m = $7.17m. d) If investors were right about the signal, the only real cost would be the direct cost of the issue ($5.26m); the signal would only hasten the market s realization that the firm was overvalued. Question 28. In most cases there will be a temptation to build more prestigious headquarters than necessary: the highest high rise in town, by the most fashionable architect, etc. management just likes to consume a very expensive perk. Such news should therefore be taken as a signal that there may be severe agency problems in this firm, and that management destroys shareholder value in many other ways that are harder to observe. (Selling is probably pointless, though: the market probably has incorporated the news into prices already, and the shares are probably trading at their fair price.) Question 29. The public may expect two things, both of which would lead to an increased share price: (1) it could expect the offer to be successful, and that the takeover premium would be around 30% (maybe other bidders may emerge, which would increase the premium above Cutts offer); alternatively, (2) the public could expect the takeover offer to fail, but the increased leverage to discipline management, and to focus it on generating income by reducing waste and inefficiencies. Question 30. a) Quick Shingle is likely to have the higher debt/equity ratio. Its earnings are likely to be less risky for a number of reasons: getting leaking roofs fixed is a consumer expense that is less sensitive to economic conditions and fashions than are luxuries like European sports cars; imports are subject to currency fluctuations and trade disputes. Lower earnings risk means that more debt can be supported without a high chance of losing interest tax shields or facing financial distress. Asset liquidation values may also play a role. Quick Shingle probably owns standard tools, machines and vehicles, that are easy to liquidate. Modena is likely to become financially distressed if it misjudges demand for its stock of cars; by definition, its inventory will be hard to liquidate. b) Tully s Tools is likely to have the higher debt/equity ratio. Its earnings are likely to be less risky than Belgazon Technologies: Belgazon depends on successful R&D (an uncertain activity) for its earnings, while Tully s Tools sells proven products to the retail market. Similarly, Belgazon is more focused on future growth (R&D), so it will be more anxious to avoid the restrictions of debt payments and covenants. Also, Belgazon 2019 P. Povel 10-11

12 Technologies is probably more dependent on its people (researchers) for its value; if Belgazon gets into financial distress, the researchers may leave. Question 31. a) The expected UFCF is 80% * $29m + 20% * $4m = $24m. We can use the APV to value the firm. This is a non-growing firm, so rua = [(1 Tc)(D/V)(rD)+(E/V)(rE)]/[(1 Tc)(D/V)+(E/V)] = ( (1-0%) * 20% * % *.135) / ( (1-0%) * 20% + 80%) =.12. The UFCFs form a constant perpetuity, so VUA = $24m/.12 = $200m. The interest expense is 6% * $40m = $2.4m. Given the assumptions, the debt is risk-free. The firm is not growing, and the firm seems financially healthy (we do not know much about the income statements, admittedly), so a low discount rate for the IETS CF is appropriate use rtx = rd = 6%. The IETS CF are zero, however, since the tax rate is zero. So the value of the firm is $200m. The value of the debt is $40m (the risk-free interest payments of $2.4m, discounted at 6%). So the value of the equity is $160m. Each share is worth $160m/4m = $ b) If it issues 20m more debt at 6%, the total interest expense is (20m+40m)(.06) = 3.6m/yr. Since the UFCFs are never less than 4m/yr, this interest can always be paid, and the debt remains riskless. The new debt can be issued at 6%, which is the rate on the existing debt. c) Issue N shares at P to raise $20m. Retire $20m of debt, so remaining debt D = $20m. There will be 4m+N shares outstanding at price P, and the total value of the shares is the value of equity, E. The firm value will be unchanged, $200m. (That s because we are making the MM assumptions.) V = E + D, so E = V D = $200m $20m = $180m. In addition, PN = $20m. Combine that with P*(4m+N) = E = 180m P*4m = $160m. Thus P = $40. The share price does not change. (As expected, given the MM assumptions.) N = $20m/P = $20m/40 = 500,000 shares issued. The return on equity will be re = rua + (1-0%)*(D/E)*(rUA rd) =.12 + (1 0) * ($20m/$180m) * (.12.06) = = 12.67%. (The original return was higher, re =.12 + (1 0) * ($40m/$160m) * (.12.06) = = 13.5%.) Question 32. a) The new bonds are issued at a fair price (in an efficient market, smart investors won t pay less), which is 150m. The firm uses the $150m to repurchase shares: buy N shares at price P, such that N * P = $150m. Afterwards, there are 15m N shares outstanding at price P; total value P * (15m N ) = Enew The market value balance sheet implies that Vnew = Dnew + Enew, so if we can determine Vnew and Dnew, we can determine the new value of the equity and thus the shares. Before the transaction, firm value Vold = Dold + Eold = $40m + 15m * $18 = $310m. Afterwards, firm value drops by 1%, so Vnew = (1.01) * Vold =.99 * $310m = $306.9m. The old bonds now have value (1.14) * $40m = $34.4m. Thus, total debt value Dnew = $34.4m + $150m = $184.4m, so Enew = Vnew Dnew = $306.9m $184.4m = $122.5m. Thus, P * N = $150m, and P * (15m N ) = Enew = $122.5m. Adding, we have P * 15m = $272.5m, so new share price is $ Since this is up from $18, shareholders are better off. (Even if they sell into the repurchase, they get $18.17 in cash.) b) This would help, but it would not completely prevent the bait and switch. There would still be an increased chance of financial distress because the firm has more total debt outstanding. Old debt would be better protected in distress (by being senior), but P. Povel

13 might still lose some value in distress; because distress is more likely, expected losses to old bondholders would increase, reducing the value of their claims. Question 33. a) Lucy s Greenhouses initial equity (and asset) value = 100m * $16 = $1,600m. It issues N shares at price P to yield $25m, so P * N = $25m. Afterwards, total asset value is (old asset value) + (cash from stock issue) (dividend) = $1,600m + $25m $50m = $1,575m; this equals the total value of equity, so P * (100m + N) = $1,575m. Subtract P * N = $25m from this: P * 100m = $1,550m P = $15.50 and N = $25m/$15.50 = 1.61m shares issued. [From the firm s viewpoint the dividend has an NPV of $50m, so P = $16 + ( $50m/100m) = $15.50.] Total shares outstanding are now m. The share price will not drop until the ex dividend date, since the original shareholders own the dividend until that time, and the planned share issue is a zero NPV transaction. b) Repurchase N shares at price P so that P * N = $25m. Afterwards, there are 100m N shares outstanding, so total equity value = P * (100m N) = total asset value = $1,600m $25m = $1,575m. Adding the two equations yields P * (100m) = $1,600m P = $16 and N = $25m/$16 = 1,562,500 shares repurchased. [The share repurchase is zero NPV in a perfect capital market, so price is unchanged.] Question 34. a) In this case, it s easiest to value the firm focusing on its dividends. With 100% earnings payout, and constant expected EBITs and therefore net incomes, the value of the equity is E = (expected Net Income)/rE = (1.21) * $100m /.1625 = $ m. (This assumes that depreciation equals capital expenditure in each year; reasonable, since the firm does not expect any financing needs.) Share price = $ m/10m = $ b) Issue $100m perpetual debt at rate 10%. Interest expense is $10m; since UFCF is never less than $10m, this debt is riskless, and 10% must be the risk free rate. Firm s total value is now VL = VU + PV(tax shield) = VU + (Tc * IntExp)/rD = $ m +.21*$10m/.10 = $ m E = VL D = $ m $100m = $ m. Cash from debt issue is used to buy back N shares at price P P * N = $100m. Remaining shares have value P * (10m N) = E = $ m. Adding, P * 10m = $ m P = $ N = $100m/$ = 1,971,788 shares repurchased 8,028,212 shares outstanding. Relever rua to obtain re. Using the mature firm formula (no growth), re = 16.25% + (1.21) * $100m / $ m * (16.25% 10%) = %. Alternatively, focusing on the dividends: All NI is paid as dividends re = (Expected Div)/E = 100% * (Expected NI)/E = (EBIT IntExp) * (1 Tc) = ($100m $10m) * (1.21) / $ m = %. Question 35. StuffyNose s asset value V = equity value E + debt value D. E = $50 * 10m = $500m; D = $100m; so V = $600m, which in perfect capital markets is unaffected by changes in capital structure. Share price after announcement = P; 10m + 1m = 11m shares outstanding after issue. Value of debt repurchased = P * 1m; afterwards, debt value D = $100m P * 1m. Value of equity afterwards = E = P * 11m; but E = V D = $600m [$100m P * 1m] = $500m 2019 P. Povel 10-13

14 + P * 1m. So P * 11m = $500m + P * 1m P * 10m = $500m P = $50, unchanged. That had to be the case in a Modigliani-Miller world! Before repurchase, D = $100m, E = $500m, rd = 5%, and re = 5% + 1 * 6% = 11%. Delever that return (both the growing firm and mature firm formulas are identical in a Modigliani Miller world, since Tc = 0): rua = D/V * rd + (1 D/V) * re = $100m/$600m * 5% + $500m/$600m * 11% = 10%. After the repurchase, the debt is still riskless, since the firm is even less leveraged than before. D equals $50m, E equals $50 * 11m = $550m, and we can lever up rua to obtain (both the growing firm and mature firm formulas are identical in a Modigliani Miller world, since Tc = 0) re = rua + D/E * (ra rd) = 10% + $50m/$550m * (10% 5%) = 10.45%. Using the CAPM, the firm s new equity beta satisfies.1045 =.05 + *.06, so = ( )/.06 =.91. Question 36. We have to compare how much money consumers can spend under either payout scheme. That is, if the firm wants to pay out $1.00, how much of that reaches investors pockets, instead of the IRS. The new angle is that we now consider income taxes as paid by investors. Different types of income are taxed at different levels: Let TPI be the personal tax paid on interest income (ordinary income); and let TPE be the effectove personal tax paid on equity income earned in the form of the mix of dividends and capital gains. a) Of every dollar of interest paid, lenders can spend (1 TPI); of every dollar intended for shareholders, only (1 Tc) * (1 TPE) actually reaches their pockets as disposable aftertax income. With TPI =.35, investors called lenders can consume $0.65 of each $1.00 the firm pays out as interest. Next, Tc =.21; and TPE = 2/3 * (dividend tax rate) + 1/3 * (tax rate on repurchases) = 2/3 * /3 *.10 =.200. So compare $0.65 with $(1-0.21)*(1-0.20) = < 0.65 more cash reaches investors if it is paid out as interest. The share price will rise if the firm increases its leverage. In efficient markets, the gain in value will go to the shareholders. b) Now Tc =.12, and TPE =.10. Of $1.00 paid as interest, $0.65 reaches investors pockets. Of $1.00 used to repurchase shares, $(1-0.12)*(1-0.1) = $0.792 reaches investors pockets. So there is a net tax disadvantage to issuing debt; Meyer Squidd should not go through with the increase in leverage. Question 37. a) Expected EBIT =.15 * $10m +.65 * $40m +.20 * $50m = $37.5m; expected NOPLAT = (1.28) * $37.5m = $27.0m. Given the assumptions that depreciation, capital expenditure and changes in net working capital are zero, UFCF = $27m. Since no growth is expected, and there is no debt, unlevered value E = VUA = $27m/.12 = $225m. Share price = $225m/5m = $ b) Maximum annual interest that can be supported risklessly in perpetuity is $10m/year. Since this debt has a return of.08, the firm can support D perpetual risk free debt, where.08*d = $10m. Solve for D to obtain D = $125m. The value of the firm after the debt is issued is V = VUA + IETS. The debt is perpetual and constant, and the firm is not growing. The firm seems financially healthy (the debt is risk-free), so we can assume that rtx = rd. Thus V = VUA + Tc*D. (The formula Tc*D is valid only if the debt is constant and perpetual and the tax shield cash flows are exactly as risky as the interest expense that generates them.) VU = 225m; Tc D =.28 $125m = $35m; so V = $260m. N shares are repurchased at price P so that P N = $125m P. Povel

15 Afterwards, there are (5m N) shares outstanding at price P, so P (5m N) = E = V D = $260m $125m = $135m. Adding the two equations yields P $5m = $260m P = $ N = $125m/$52 2,403,846 shares repurchased, so 5m N = 2,596,154 shares are outstanding. [Alternatively: the share price increases by the amount of the tax shield divided by the original number of shares: new price = $ ($35m/5m) = $52.00.] 2019 P. Povel 10-15