NOTES ON SOLUTIONS

ï The solutions to all the exams are provided. Use it as a holdout exam.

ï In the solutions that follow, I have used the T.Bill rate as the riskfree rate in some problems and the T.Bond rate in others. In those problems, where the risk premium is not given, I have used a risk premium of 8.5% for T.Bills and 5.5% for T.Bonds.

ï There are a few problems in these exams which are from topics that we have not covered (such as option pricing). Ignore them.

PRACTICE FINAL 1: SOLUTION
 PROBLEM 1 a. Cost of equity = 6 + 9 = 15% b. Chg: Debt Incr. BC Incr. tx. Ben. 2500000 0 1000000 Incr BC = Chg in probability * 8 million 2500000 640000 1000000 Incr tx ben. = Chg in debt* Tax rate 2500000 1000000 1000000 STOP HERE 500000 760000 200000 1000000 1200000 400000 1000000 600000 400000 2500000 1400000 1000000 c. Value of the firm at \$7500000 debt = 12,000,000+3000000-1640000 = 13,360,000 PROBLEM 3 Price change/ Dividend = (50 - 46.50)/ 5.00 = 0.70 (1- implied tax rate)/(1-.4*implied tax rate) = 0.7 Implied tax rate = 0.30/0.72 = 0.41666667 PROBLEM 4 Req. Rate of Return = 16% YEAR EPS DPS TERM. PRICE 0 \$1.20 1 \$1.80 \$0.00 2 \$2.70 \$0.00 3 \$3.38 \$0.68 4 \$4.22 \$0.84 5 \$4.64 \$2.32 \$42.54 PRESENT VALUE = \$22.26 PROBLEM 5 PV of Tax Benefits = 30*.46 = 13.8 (This is a perpetuity; Hence the interest rate drops out.) PROBLEM 6 Required rate of return = 7% +0.8(15-7) =13.4% YEAR EPS DPS TERM. PRICE 0 \$2.50 1 \$2.79 \$1.12 2 \$3.12 \$1.25 3 \$3.48 \$1.39 4 \$3.89 \$1.56 5 \$4.35 \$1.74 \$51.27 PRESENT VALUE = \$32.12 Growth rate for first five years = 0.6(15+0.5(15-6))= 11.70% Payout ratio after five years = 1-(8/(15+0.5(15-6)))= 58.97% THE PICKENS VALUATION New Beta = (0.8/(1+0.6*0.5))*(1+0.6*1.5) = 1.17 Required rate of return = 7% + 1.17 (15-7%) = 16.36% YEAR EPS DPS TERM. PRICE 0 \$2.50 1 \$3.09 \$1.24 2 \$3.81 \$1.53 3 \$4.71 \$1.88 4 \$5.82 \$2.33 5 \$7.19 \$2.88 \$71.50 PRESENT VALUE = \$39.52 Growth rate for first five years = 0.6(20+1.5(20-7.2))= 23.52% Payout ratio after five years = 1-8/(20+1.5(20-7.2))= 79.59%

 PRACTICE FINAL 2: Solutions PROBLEM 1 Beta before =1.5 Cost of equity before = 8 + 1.5*8.5 = 20.75 Beta after = (1.5/(1+.54*0.4))*(1+.54*.6) = 1.63 Cost of equity after =8 + 1.63* 8.5 = 21.855 (i) WACC without = 0.2075 (500/700) + 0.11(0.54)(200/700)= 16.52% WACC with=0.2186(500/800)+0.125(0.54)(300/800)= 16.19% (ii) Change in WACC = 0.165 - 0.162 = 0.003 Change in firm value = (500 + 200) * (.003)/0.162 = \$12.96 Change in stock price = Change in firm value / # of shares = =12.96/10= \$ 1.30 per share (iii) NPV = -100 + (50-30)*0.54/0.1619= (\$33.29) (use Cashflows to the firm) (iv) Yes.The present value would be = -100 +(50-30)*0.54/0.08 = 35 ACCEPT PROBLEM 2 IIa. Beta of the company = 1.1*5.9/(5.9+9+12.3+7.8) + 1.3*9/(5.9+9+12.3+7.8) + 0.8* 12.3/(5.9+9+12.3+7.8) + 1.4*7.8/(5.9+9.0+12.3+7.8) = 1.112857143 IIb. 1. Correct answer is (b) 2. True 3. The correct answer is (b) PROBLEM 3 Cost of equity= 8 +1.25*(16-8) = 18% WACC = 18 (1500/2000) + 12 (0.5) (500/2000) = 15 Accept projects A,B and C. Cost = 50 million a. FCFE = \$100 Million - \$50 million = \$50 million .Pay dividend of \$50 million = 50 cents per share b. Price after the ex-dividend date = 15 - (0.6/0.84) (0.5) = \$14.64 PROBLEM 4 YEAR EPS DPS TERM. PRICE 0 \$2.00 1 \$2.29 \$0.57 2 \$2.63 \$0.66 3 \$3.01 \$0.75 4 \$3.45 \$0.86 5 \$3.96 \$0.99 \$29.74 PRESENT VALUE = \$17.26 Growth rate for first five years = 0.75(15+0.5(15-6))= 14.63% Payout ratio after five years = 4/(15+0.5(15-6))= 79.49% YEAR EPS DPS TERM. PRICE 0 \$2.00 1 \$2.50 \$0.62 2 \$3.11 \$0.78 3 \$3.35 \$0.97 4 \$4.84 \$1.21 5 \$6.04 \$1.51 \$42.48 PRESENT VALUE = \$22.42 Growth rate for first five years = 0.75(15+2(15-6))= 24.75% Payout ratio after five years = 4/(15+2.0(15-6))= 87.88% PRESENT VALUE SLIGHTLY HIGHER

 PRACTICE FINAL 3: SOLUTION D/(D+E) Beta Cost of equity Cost of debt WACC Current(20%) 1.15 15.78% 10.00% 13.82% 0.33 1.30 17.01% 10.50% 13.48% 0.428571429 1.45 18.33% 11.50% 13.43% STOP HERE 0.5 1.60 19.60% 13.50% 13.85% 0.555555556 1.75 20.88% 15.00% 14.28% (a) Borrow \$ 1000000 (b) Change in WACC = 13.82% - 13.43% = 0.39% Change in firm value = 2,500,000* 0.0039/0.1343 = 72598.65972 Increase in price per share= (72598/100000) = 72.60 cents Price per share after debt issue = 20.73 (c) See above (d) NPV = -3000000+ 460000/0.1343 = \$425167.54 TAKE PROJECT Note that the WACC is being used as the discount rate. Hence we are adding back debt payments (1- tax rate) to after-tax cash flows to get CF to firm. PROBLEM 2 Price change/ Dividend for firm A = 0.5 for firm B = 0.75 for firm C = 1.00 Firm A's stockholders have the highest tax rates. I would use their stock for dividend arbitrage. 2b. Treasury Bill Rate = 6% Expected Return on Stock = 14.50% Growth rate in perpetuity =0.4 (12+1(12-6)) = 7.20% PV of stock = 2.50 (0.6)(1.072)/(.145-.072)= \$22.03 If payout ratio is changed Growth rate in perpetuity = 0.6(12+1(12-6) = 10.80% PV of stock = 2.50 (0.4) (1.108)/(0.145-0.108) = \$29.95 YES! CUT DIVIDENDS! PROBLEM 3 1 2 3 4 5 6 EBIT \$10,000.00 \$11,500.00 \$13,150.00 \$14,965.00 \$16,961.00 \$18,317.88 Interest \$10,000.00 \$8,000.00 \$6,000.00 \$4,000.00 \$2,000.00 \$0.00 EBT \$0.00 \$3,500.00 \$7,150.00 \$10,965.00 \$14,961.00 \$18,317.88 Taxes \$0.00 \$1,750.00 \$3,575.00 \$5,482.50 \$7,480.50 \$9,158.94 NI \$0.00 \$1,750.00 \$3,575.00 \$5,482.50 \$7,480.50 \$9,158.94 + Deprec'n \$5,000.00 \$5,000.00 \$5,000.00 \$5,000.00 \$5,000.00 \$5,000.00 NCF \$5,000.00 \$6,750.00 \$8,575.00 \$10,482.50 \$12,480.50 \$14,158.94 - Princ. Pmts \$10,000.00 \$10,000.00 \$10,000.00 \$10,000.00 \$10,000.00 \$0.00 CF to Equity (\$5,000.00) (\$3,250.00) (\$1,425.00) \$482.50 \$2,480.50 \$14,158.94 Terminal value = 14158/(0.145-0.08) = \$217,815.38 Debt \$50,000.00 \$40,000.00 \$30,000.00 \$20,000.00 \$10,000.00 Equity \$15,000.00 \$15,000.00 \$16,750.00 \$20,325.00 \$25,807.50 D/E Ratio 3.333333333 2.666666667 1.791044776 0.98400984 0.387484258 Beta 2.666666667 2.333333333 1.895522388 1.49200492 1.193742129 Cost of Equity 0.286666667 0.258333333 0.221119403 0.186820418 0.161468081 PV of CF to Equity = \$74,425.54 YES! take the deal PV of Interest tax savings = \$9,093.29 The Deal would make sense even without the interest tax savings

FINAL: SPRING 1989 (SOLUTION)
 PROBLEM 1 1 2 3 4 5 Term. year Oper. Income \$9.60 \$11.52 \$13.82 \$16.59 \$19.91 \$21.50 Interest Exp \$7.70 \$6.34 \$4.98 \$3.62 \$2.26 \$0.90 Taxable Inc. \$1.90 \$5.18 \$8.84 \$12.97 \$17.65 \$20.60 Tax \$0.76 \$2.07 \$3.54 \$5.19 \$7.06 \$8.24 Net Income \$1.14 \$3.11 \$5.31 \$7.78 \$10.59 \$12.36 +Deprec'n \$5.00 \$5.00 \$5.00 \$5.00 \$5.00 \$5.00 - Princ. Rep. \$8.00 \$8.00 \$8.00 \$8.00 \$8.00 \$0.00 CF to Equity (\$1.86) \$0.11 \$2.31 \$4.78 \$7.59 \$17.36 + Int(1-t) \$4.62 \$3.80 \$2.99 \$2.17 \$1.36 \$0.54 + Princ. Rep \$8.00 \$8.00 \$8.00 \$8.00 \$8.00 \$0.00 Cf to firm \$10.76 \$11.91 \$13.29 \$14.95 \$16.94 \$17.90 -Bk Int(1-t) \$1.20 \$0.96 \$0.72 \$0.48 \$0.24 \$0.00 - Bk princ. \$2.00 \$2.00 \$2.00 \$2.00 \$2.00 \$0.00 CF to LB_ \$7.56 \$8.95 \$10.57 \$12.47 \$14.70 \$17.90 Term Val Equ. \$174.58 Term. Val. Firm \$179.58 Bank Borrow. \$10.00 \$8.00 \$6.00 \$4.00 \$2.00 \$0.00 Senior Debt \$30.00 \$24.00 \$18.00 \$12.00 \$6.00 \$0.00 Sub. Debt \$5.00 \$5.00 \$5.00 \$5.00 \$5.00 \$5.00 Equity \$5.00 \$6.14 \$9.25 \$14.55 \$22.34 \$32.92 Beta 6.171428571 4.450791066 2.778577608 1.799084813 1.301030715 1.052151432 Cost of Equity 61.46% 46.83% 32.62% 24.29% 20.06% 17.94% WACC 15.39% 15.48% 15.70% 16.05% 16.52% 17.00% LB_WACC 16.23% 16.28% 16.39% 16.57% 16.79% 17.00% NPV of CF to Equity= 39.70105234 Makes sense from viewpoint of eq. investors! NPV of CF to firm= 129.5171243 Makes sense from viewpoint of all capital NPV of CF to LB.= 117.3837358 Makes sense from viewpoint of LBO participants PROBLEM 2 Debt Equity Beta Cost of Eq. Cost of Debt WACC 0 1 1.50 21.75% 0.1 21.75% 0.1 0.9 1.60 22.60% 0.105 20.97% 0.2 0.8 1.73 23.66% 0.11 20.25% 0.3 0.7 1.89 25.03% 0.12 19.68% 0.4 0.6 2.10 26.85% 0.13 19.23% 0.5 0.5 2.40 29.40% 0.14 18.90% OPTIMAL 0.6 0.4 2.85 33.23% 0.16 19.05% 0.7 0.3 3.60 39.60% 0.18 19.44% 0.8 0.2 5.10 52.35% 0.2 20.07% 0.9 0.1 9.60 90.60% 0.25 22.56% PROBLEM 3 S =40 K=40 R=0.10 STD DEV=0.3 t=1 Value of one call = 6.69 The executive is getting 20000 calls (\$200 for every cent) Total value of compensation package= 150000 + 6.69*20000 = 283800 PROBLEM 4 3. FALSE (It makes them worse off) 1. TRUE 4. FALSE (It depends on why takeover fails) 2. FALSE. (They go down) 5. FALSE ( you really cannot tell)

 FINAL EXAM: SPRING 1990: SOLUTIONS 1a. Current WACC: Current beta= 1.06 Cost of Equity= 17.01% WACC = .1701 (250/275)+6 (25/275)= 16.01% 1b. New Beta = 1.06/(1+.6*.1) *(1+.6*125/150) = 1.5 New cost of equity = 8 +1.5*8.5 = 20.75% New WACC = 20.75(150/275) + 7.8 (125/275) = 14.86% 2. (10-9.20)/1.00 = (1-.5)/(1-capital gains rate) Capital gains rate = 0.375 (0.5) = 0.375*(1.1)^n (10% is the discount rate) Solving for n, n = 3.02 years 3a. Fundamental growth rate = 0.6 (15% + 1 (15 -6)) = 14.40% 3b. Payout ratio after year 5 = 1 - (8/(15+1(15-6)) = 0.666666667 3c. Year EPS DPS Term. Value 0 \$2.00 1 \$2.29 \$0.92 2 \$2.62 \$1.05 3 \$2.99 \$1.20 4 \$3.43 \$1.37 5 \$3.92 \$1.57 \$43.41 Value of the stock = \$26.05 3d. Year EPS Deprec/Sh CS/Share WC/share FCFE/share Term. value 0 \$2.00 \$3.00 \$2.50 \$0.00 1 \$2.29 \$3.43 \$2.86 \$0.29 \$2.57 2 \$2.62 \$3.93 \$3.27 \$0.33 \$2.94 3 \$2.99 \$4.49 \$3.74 \$0.38 \$3.37 4 \$3.43 \$5.14 \$4.28 \$0.43 \$3.85 5 \$3.92 \$5.88 \$4.90 \$0.49 \$4.41 \$77.08 Term. Year \$4.23 \$6.35 \$5.29 \$0.28 \$5.01 Value of the stock = \$50.38 Note: I am not multiplying the net cap ex by (1-Debt Ratio) because the depreciation exceeds the cap expenditure, leading to a positive cash flow from this item. There is no need for new debt.. 4a. WACC in the first year = 0.12*(500/600) + 0.42 (100/600) = 0.1687 (Beta in first year = 1.00*(1+0.6*5) = 4) Cost of Equity= 42.00% 4b. Terminal value of equity = 300/(0.165-0.08) = \$3,529.41 Terminal value of the firm =3529 4c. PV of interest tax savings = 40/1.1687 = \$34.23 5a. Value of a call option (S=20, K=25,t=10,r=10%,Std. dev=0.1,Div. Yld=5%) = 5.41 Value of the conversion option = 5.41*40 = 216.39 5b. Value of the straight portion of bond = PV of 80 at 12% for 20 years + PV of 1000 in 20 years= 774

 FINAL EXAM: FALL 1990 (SOLUTIONS) 1a. Current cost of equity = 7 + 1.12 * 8.5 = 16.52% 1b. Current cost of debt = (10/100) * ( 1- 16/40) = 6% 1c. Current WACC = 16.52 * ( 500/ 600) + 6 * (100/600) = 14.77% 1d. Unlevered beta = 1.12/ (1+0.6*0.2) = 1.00 New levered beta = 1.00 *(1+0.6*450/150) = 2.80 New cost of equity = 7% + 2.8*8.5 = 30.8% 1e. Effective tax rate : Interest payment = 67.5 Available EBIT = 50 Tax rate = 40% Effective tax rate = 40% * (50/67.5) = 29.63% 1f. New WACC = 30.8 *(150/600) + 15*(1-0.2963)*(450/600) = 15.6% 2a. A short cut you can use here is to calculate the Return on capital of each project approximately: Project ROC = (EBIT*(1-t)+Depreciation)/Investment Project 1 = (1 *(1-0.4) + 0.5)/10 = 11% (I am assuming no cap ex is needed in future years) Project 2 = (5 *(1-0.4)+1)/40 = 10% Project 3 = (5*(1-0.4)+1)/50 = 8% Reject all three projects since they make less than the WACC. (WACC = 22*(500/600) + 10*0.6*(100/600)) 2b. Pay out 100 million in dividend. 3a. Growth rate in first five years = .6 (20+0.75*(20-7.2)) = 0.1776 3b. Payout ratio after year 5 = 1- 8/(16% +0.75*(16-7.2)) = 64.60% 3c. PV from DDM =(5 years of growth at 17.76%, 8% thereafter) = \$55.82 Add Intrinsic value of firm = \$10 per shares Value per share = \$65.82 4a. ABC value = 500*1.08*0.5/(0.146-0.08) = \$4,090.91 4b. DEF value= 400* 1.06*0.5/(0.135-0.06) = \$2,826.67 4c. Growth rate of combined firm = 8%*(4091/(4091+2827)) + 6%*(2827/(4091+2827)) + 1% = 8.18% d. Beta of combined firm = 1.20*(4091/(4091+2827)) + 1.00*(2827/(4091+2827)) = 1.12 e. Estimated value of synergy: Value of combined firm with synergy = 900 * 1.0818 *0.50/(.08+1.12*.055-0.0818)) = \$8,140.64 Value of synergy = 8151 - 4091 - 2827 = \$1,233.00 5a. Yield on straight bond = 12.694 % (from price and coupon) Straight bond portion of convertible bond value = 80(PVA,20,12.64%) + 1000(PF,20,12.64%) = 664.24 Option Value =1035 - 664 = 371 5b. S = 148.22 (PV of cashflows of \$25 at 16% over 20 years) K = 300 t= 10 r = 12% Variance = 0.04

 SPRING 1991: SOLUTION 1a. Current Cost of Equity = 6 + 1.25 * 8.5 = 16.63% b. Current after-tax cost of debt =11% (1- 0.5) = 5.50% c. Current WACC = (1800/ 2700) (0.1663) + (900/2700) (0.055) = 12.92% d. New beta for the firm = [1.25/(1+(1-0.5)(900/1800))]*(1+(1-0.5)*(700/2000) = 1.175 New cost of equity = 6 + 1.175*8.5 = 15.9875 e. New WACC = .159875 (2000/2700) + .05 (700/2700) = 13.14% f. Change in value of the firm = (0.1291 - 0.1315)* 2700 /0.1315 = (\$49.28) ! Firm value drops Problem 2 Available CF before capital expenditure = Net Income + Deprec'n - Chg in WC = 1000 + 500 - 100 =1400 Working Capital Change = Change in Revenues * 0.25 = 5000 * .08 *.25 = 100 Project IRR Cost of Equity A 21% 0.23 ! Use beta of 2.0 B 20% 0.1875 ! Use beta of 1.5 C 12% 0.145 ! Use beta of 1.0 Accept only project B, with initial investment of \$ 600 a. Available FCFE = 1000-(600-500)*0.8-100*0.8 = 840 ! Available for dividends b. Effective tax rate on dividends = 0.40 * (1 - 0.85) = 0.06 ! 85% of dividends are exempt from tax Tax rate on capital gains = 28% (1 - Tax rate on dividends) / (1 - tax rate on capital gains) = (1-0.06)/(1-0.28) = 1.305555556 (Pb - Pa)/ Dividend = (10 - Pa)/(0.84) = 1.31 Solving for P after = \$8.90 Problem 3 Year EPS Payout ratio DPS 0 \$4.00 1 \$4.80 \$0.00 \$0.00 ! Payout ratio = 1 - g/(ROA + D/E (ROA -i)) 2 \$5.52 \$0.25 \$1.38 3 \$6.07 \$0.50 \$3.04 Terminal Value = 6.072 * 1.08 * 0.5 /(0.14 -0.08 ) = 54.67 ! Payout ratio = 1 - 0.08/0.16 Present Value = 1.38/1.14^2 + (3.04 + 54.67)/1.14^3 = \$40.01 b. If debt/equity ratio increases to 1, new beta = 1.6; new cost of equity = 8.5+1.6*5.5 = 17.30% Year EPS Payout ratio DPS 0 \$4.00 1 \$4.80 41% \$1.98 2 \$5.52 56% \$3.08 3 \$6.07 71% \$4.29 Terminal Value = 6.072 * 1.08 * (1-(8/(16+1(16-6)))/(.173-.08)= \$48.82 Present Value = 1.98/1.173 + 3.08/1.173^2 +(4.29+48.82)/1.173^3 = \$36.83 Problem 4 Use put call parity Value of call with K = 50; C-P = S - K exp (-rt); C = \$11.76 Value of call with K =75; C= 31 + 45 - 75 exp(-.10) = \$8.14 Value of the compensation package = Straight salary 500000 Value of bonus package 117581 ! 10000 calls with K =50 -Effect of cap on bonus 81372 ! 10000 calls with K =75 Net package value = 536209

 FINAL FALL: 1992 1a. Current Cost of Equity = 8% + 1.15 (8.5%) = 17.78% Current after-tax Cost of Debt = 10% (1- 0.4) = 6.00% Current Weighted Average Cost of Capital = 17.78% (0.8) + 6.00% (0.2) = 15.42% 1b. New Debt Ratio = (200+200)/1000 = 40.00% Unlevered Beta = 1.15/(1+0.6*.25) = 1.00 New levered beta = 1.00 (1+0.6*0.67) = 1.40 New Cost of Equity = 8%+1.40 (8.5%) = 19.90% New Cost of Capital = 19.90% (0.6) + 6.60% (0.4) = 14.58% 1c. Change in Firm Value = 1000 (.1542-.1458)/.1458 = \$ 57.61 millions Increase in Stock Price = \$57.61 million/ 40 million = \$ 1.44 1d. Debt next year = \$ 200 + \$150 = \$350 million Expected Price Appreciation in Equity = Expected Return - Dividend Yield = 17.78%-10% = 7.78% Expected Value of Equity = 800 (1.0778) = \$ 862.24 Expected Debt/Equity Ratio at end of next year = \$350/\$862 = 40.60% 2a. - 1 2 3 Net Income \$ 100.00 \$ 110.00 \$ 121.00 \$ 133.10 + Deprec'n \$ 50.00 \$ 54.00 \$ 58.32 \$ 62.99 - Cap. Ex. \$ 60.00 \$ 60.00 \$ 60.00 \$ 60.00 - Chg. WC \$ 10.00 \$ 10.00 \$ 10.00 \$ 10.00 = FCFE \$ 94.00 \$ 109.32 \$ 126.09 Dividends \$ 66.00 \$ 72.60 \$ 79.86 (Assuming that net capital investment and working capital is financed with equity) Cash Balance \$50.00 \$78.00 \$114.72 \$160.95 If the firm had financed its net capital investment and working capital with 20% debt (current debt ratio) Net Income \$ 100.00 \$ 110.00 \$ 121.00 \$ 133.10 - (CE-Dep) (1-_) \$ 8.00 \$ 4.80 \$ 1.34 \$ (2.39) - (Ch WC) (1-_) \$ 8.00 \$ 8.00 \$ 8.00 \$ 8.00 = FCFE \$ 97.20 \$ 111.66 \$ 127.49 Dividends \$ 66.00 \$ 72.60 \$ 79.86 Cash Balance \$ 50.00 \$ 81.20 \$ 120.26 \$ 167.88 2b. Ordinary Tax Rate = (0.3)(0.15) = 4.50% Capital Gains Tax Rate = 20.00% Dividends Per Share = \$2.00 Price Change per share on Ex-Dividend Day = [(1-.045)/(1-.20)](\$2.00) = \$ 2.39 Problem 3 1 2 3 4 EPS \$ 2.40 \$ 2.78 \$ 3.12 \$ 3.37 Payout Ratio 0.00% 25.65% 36.17% 48.72% DPS \$ - \$ 0.71 \$ 1.13 \$ 1.64 Beta 1 1.06 1.15 1.3 Cost of Equity 0.12 0.1233 0.12825 0.1365 Note: The alternative to estimating a levered beta in year 4 is to assume a beta of 1. Terminal Price = \$1.64/(.1365 - .08) = \$ 29.03 DDM Value = \$0.71/1.12*1.1233+(1.13+29.03)/1.12*1.1233*1.12825 = \$ 21.81

FINAL: FALL 1993 - SOLUTIONS
Debt3,000,0002,700,0002,400,000 1,800,0001,500,000Debt/Equity Ratio3.00
 Year 1 2 3 4 5 Term. Year Revenues \$1,100,000 \$1,210,000 \$1,331,000 \$1,464,100 \$1,610,510 \$1,707,141 - Expenses \$440,000 \$484,000 \$532,400 \$585,640 \$644,204 \$682,856 - Depreciation \$100,000 \$110,000 \$121,000 \$133,100 \$146,410 \$155,195 EBIT \$560,000 \$616,000 \$677,600 \$745,360 \$819,896 \$869,090 - Interest Exp. \$360,000 \$324,000 \$288,000 \$252,000 \$216,000 \$180,000 Taxable Income \$200,000 \$292,000 \$389,600 \$493,360 \$603,896 \$689,090 - Tax \$80,000 \$116,800 \$155,840 \$197,344 \$241,558 \$275,636 Net Income \$120,000 \$175,200 \$233,760 \$296,016 \$362,338 \$413,454 + Depreciation \$100,000 \$110,000 \$121,000 \$133,100 \$146,410 \$155,195 - Cap. Exp. \$120,000 \$132,000 \$145,200 \$159,720 \$175,692 \$186,234 - _ WC \$20,000 \$22,000 \$24,200 \$26,620 \$29,282 \$19,326 - Princ. Repaid \$300,000 \$300,000 \$300,000 \$300,000 \$300,000 \$0 FCFE (\$220,000) (\$168,800) (\$114,640) (\$57,224) \$3,774 \$363,089 + Int (1-t) \$216,000 \$194,400 \$172,800 \$151,200 \$129,600 \$108,000 + Princ. Rep. \$300,000 \$300,000 \$300,000 \$300,000 \$300,000 \$0 FCFF \$296,000 \$325,600 \$358,160 \$393,976 \$433,374 \$471,089 1 2 3 4 5 Term. Year Equity 1,000,000 1,120,000 1,295,200 1,528,960 1,824,976 2,187,314 Debt 3,000,000 2,700,000 2,400,000 2,100,000 1,800,000 1,500,000 D/E Ratio 3.00 2.41071429 1.85299568 1.37348263 0.986314341 0.68577272 Beta 2.58 2.25071429 1.94285361 1.67816241 1.464445516 1.29854654 Cost of Equity 24.90% 22.13% 19.51% 17.26% 15.45% 14.04% Kentucky Fried Chicken 1.05 0.2 Hardee's 1.2 50% Popeye's Fried Chicken 0.9 10% Roy Rogers 1.35 70% AVERAGE 1.125 0.375 0.91836735 1a. First calculate the beta based upon comparable firms: Average Beta = 1.125 Average D/E Ratio = 0.375 Unlevered beta = 0.91836735 Beta for Boston Turkey = 1.2627551 Use this beta to calculate the cost of equity Cost of Equity = 3% + 1.26*8.5% = 13.71% (Alternatively the long bond rate could have been used as the riskfree rate, with a 5.5% premium) 1b. After-tax Cost of Debt : First compute the interest coverage ratio = EBIT / Interest Expense = 5 This yields a bond rating of A, and a pre-tax rate of 7.50% After-tax cost of debt = 7.5% (1-0.4) = 0.045 1c. Cost of Capital = 13.71% (2/3.25) + 4.5% (1.25/3.25) = 10.17% 1d. New Debt Equity ratio after repurchase = 1.16666667 New beta after repurchase = 1.56122449 New cost of equity = 3% + 1.56*8.5% = 16.26% 1e. New after-tax cost of debt = 7.75% (1-0.4) = 0.0465 New cost of capital = 16.26% (1.5/3.25) + 4.65% (1.75/3.25) = 10.01% Change in Firm Value = 3,250,000(.1001-.1017)/1.001 = \$51,948.05 Change in stock price per share = \$0.52 2a. First decide which projects you will accept Project ROE Cost of Equity A 12.50% 11.50% Accept B 14.00% 15.75% Reject C 16.00% 18.30% Reject D 24.00% 20.00% Accept Next calculate working capital as % of Revenues Working Capital = Current Assets - Current Liabilities = \$500,000 Working Capital as % of Revenues = 50% Income Statement Next year Revenues 1100000 - Expenses 440000 - Depreciation 100000 = EBIT 560000 - Interest Exp 100000 = Taxable Inc. 460000 - Tax 184000 = Net Income 276000 -(CapEx- Deprec)(1-_) 30000 (150000-100000)(1-0.4) - _ WC (1-_) 30000 (50% of increase in revenues (\$100000))*(1-0.4) = FCFE 216000 2b. Cash Balance next year = Current Balance + FCFE - Dividends = 150000+216000-100000 = 266000 2c. Ordinary tax rate = 40% Capital Gains tax rate = 28% (Price before - Price after) / Dividend = (1-0.4)/(1-0.28) = 0.833 Change in price = \$0.833 3a. Retention Ratio = 1 -(1/2.4) = 0.58333333 ROA = (Net Income + Interest Expense(1-t)) / (BV of Debt + BV of Equity ) = 12.00% Debt/Equity Ratio = 1.25/2 = 0.625 Interest rate = Interest Expense / MV of Debt = 8.00% Expected Growth Rate = 0.5833 ( 0.12 + 0.625 (0.12 - 0.048) = 9.63% 3b. Terminal price = Price at the end of year 3 Payout Ratio at the end of year 3 = 1 - (0.06/(0.12+0.625(0.12-0.048))) = 0.63636364 Terminal price = (\$2.40*1.0963^3*1.06*0.6364)/(0.1371-0.06) = \$27.66 3c. Year DPS 1 \$1.10 2 \$1.20 3 \$1.32 \$27.66 Present Value of Dividends and Terminal Price = \$21.60 Problem 4 Year 1 2 3 4 5 Term. Year Revenues \$1,100,000 \$1,210,000 \$1,331,000 \$1,464,100 \$1,610,510 \$1,707,141 - Expenses \$440,000 \$484,000 \$532,400 \$585,640 \$644,204 \$682,856 - Depreciation \$100,000 \$110,000 \$121,000 \$133,100 \$146,410 \$155,195 EBIT \$560,000 \$616,000 \$677,600 \$745,360 \$819,896 \$869,090 - Interest Exp. \$360,000 \$324,000 \$288,000 \$252,000 \$216,000 \$180,000 Taxable Income \$200,000 \$292,000 \$389,600 \$493,360 \$603,896 \$689,090 - Tax \$80,000 \$116,800 \$155,840 \$197,344 \$241,558 \$275,636 Net Income \$120,000 \$175,200 \$233,760 \$296,016 \$362,338 \$413,454 + Depreciation \$100,000 \$110,000 \$121,000 \$133,100 \$146,410 \$155,195 - Cap. Exp. \$120,000 \$132,000 \$145,200 \$159,720 \$175,692 \$186,234 - _ WC \$20,000 \$22,000 \$24,200 \$26,620 \$29,282 \$19,326 - Princ. Repaid \$300,000 \$300,000 \$300,000 \$300,000 \$300,000 \$0 FCFE (\$220,000) (\$168,800) (\$114,640) (\$57,224) \$3,774 \$363,089 + Int (1-t) \$216,000 \$194,400 \$172,800 \$151,200 \$129,600 \$108,000 + Princ. Rep. \$300,000 \$300,000 \$300,000 \$300,000 \$300,000 \$0 FCFF \$296,000 \$325,600 \$358,160 \$393,976 \$433,374 \$471,089 Problem 4b. 1 2 3 4 5 Term. Year Equity 1,000,000 1,120,000 1,295,200 1,528,960 1,824,976 2,187,314 2,100,000