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.

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% | |||||||||

PRESENT VALUE = | $22.26 | ||||||||

PROBLEM 5 | |||||||||

PV of Tax Benefits = 30*.46 = | (This is a perpetuity; Hence the interest rate drops out.) | ||||||||

PROBLEM 6 | |||||||||

Required rate of return = 7% +0.8(15-7) =13.4% | |||||||||

TERM. PRICE | |||||||||

PRESENT VALUE = | |||||||||

Growth rate for first five years = 0.6(15+0.5(15-6))= | |||||||||

Payout ratio after five years = 1-(8/(15+0.5(15-6)))= | |||||||||

THE PICKENS VALUATION | |||||||||

New Beta = (0.8/(1+0.6*0.5))*(1+0.6*1.5) = | |||||||||

Required rate of return = 7% + 1.17 (15-7%) = | |||||||||

PRESENT VALUE = | |||||||||

Growth rate for first five years = 0.6(20+1.5(20-7.2))= | |||||||||

Payout ratio after five years = 1-8/(20+1.5(20-7.2))= | |||||||||

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) = | |||||||||

Cost of equity after =8 + 1.63* 8.5 = | |||||||||

(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 = | |||||||||

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= | (use Cashflows to the firm) | ||||||||

(iv) | |||||||||

Yes.The present value would be = -100 +(50-30)*0.54/0.08 = | 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) = | |||||||||

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 | |||||||||

$29.74 | |||||||||

PRESENT VALUE = | $17.26 | ||||||||

Growth rate for first five years = 0.75(15+0.5(15-6))= | |||||||||

Payout ratio after five years = 4/(15+0.5(15-6))= | |||||||||

$42.48 | |||||||||

PRESENT VALUE = | $22.42 | ||||||||

Growth rate for first five years = 0.75(15+2(15-6))= | |||||||||

Payout ratio after five years = 4/(15+2.0(15-6))= | |||||||||

PRESENT VALUE SLIGHTLY HIGHER |

PRACTICE FINAL 3: SOLUTION | ||||||

Current(20%) | ||||||

0.33 | ||||||

0.428571429 | STOP HERE | |||||

0.5 | ||||||

0.555555556 | ||||||

(a) Borrow $ 1000000 | ||||||

(b) Change in WACC = 13.82% - 13.43% = 0.39% | ||||||

Change in firm value = 2,500,000* 0.0039/0.1343 = | ||||||

Increase in price per share= (72598/100000) = | ||||||

Price per share after debt issue = 20.73 | ||||||

(c) See above | ||||||

(d) NPV = -3000000+ 460000/0.1343 = | 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 = | Expected Return on Stock = | |||||

Growth rate in perpetuity =0.4 (12+1(12-6)) = | ||||||

PV of stock = | 2.50 (0.6)(1.072)/(.145-.072)= | |||||

If payout ratio is changed | ||||||

Growth rate in perpetuity = | 0.6(12+1(12-6) = | |||||

PV of stock = 2.50 (0.4) (1.108)/(0.145-0.108) = | ||||||

YES! CUT DIVIDENDS! | ||||||

PROBLEM 3 | ||||||

1 |
2 | 3 | 4 | 5 | 6 | |

EBIT | ||||||

Interest | ||||||

EBT | ||||||

Taxes | ||||||

NI | ||||||

+ Deprec'n | ||||||

NCF | ||||||

- Princ. Pmts | ||||||

CF to Equity | ||||||

Terminal value = 14158/(0.145-0.08) = | ||||||

Debt | ||||||

Equity | ||||||

D/E Ratio | ||||||

Beta | ||||||

Cost of Equity | ||||||

PV of CF to Equity = | YES! take the deal | |||||

PV of Interest tax savings = | The Deal would make sense even without the interest tax savings |

PROBLEM 1 | ||||||||

1 | 2 | 3 | 4 | 5 | Term. year | |||

Oper. Income | ||||||||

Interest Exp | ||||||||

Taxable Inc. | ||||||||

Tax | ||||||||

Net Income | ||||||||

+Deprec'n | ||||||||

- Princ. Rep. | ||||||||

CF to Equity | ||||||||

+ Int(1-t) | ||||||||

+ Princ. Rep | ||||||||

Cf to firm | ||||||||

-Bk Int(1-t) | ||||||||

- Bk princ. | ||||||||

CF to LB_ | ||||||||

Term Val Equ. | ||||||||

Term. Val. Firm | ||||||||

Bank Borrow. | ||||||||

Senior Debt | ||||||||

Sub. Debt | ||||||||

Equity | ||||||||

Beta | 6.171428571 | 4.450791066 | 2.778577608 | 1.799084813 | 1.301030715 | 1.052151432 | ||

Cost of Equity | ||||||||

WACC | ||||||||

LB_WACC | ||||||||

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 | ||||||||

OPTIMAL | ||||||||

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= | Cost of Equity= | ||||||||

WACC = .1701 (250/275)+6 (25/275)= | |||||||||

1b. New Beta = 1.06/(1+.6*.1) *(1+.6*125/150) = 1.5 | |||||||||

New cost of equity = 8 +1.5*8.5 = | |||||||||

New WACC = 20.75(150/275) + 7.8 (125/275) = | |||||||||

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)) = | |||||||||

3b. Payout ratio after year 5 = 1 - (8/(15+1(15-6)) = | 0.666666667 | ||||||||

3c. | |||||||||

Value of the stock = | |||||||||

3d. | |||||||||

Value of the stock = | |||||||||

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= | ||||||||

4b. Terminal value of equity = 300/(0.165-0.08) = | |||||||||

Terminal value of the firm =3529 | |||||||||

4c. PV of interest tax savings = 40/1.1687 = | |||||||||

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)) = | |||||||||

3b. Payout ratio after year 5 = 1- 8/(16% +0.75*(16-7.2)) = | |||||||||

3c. PV from DDM =(5 years of growth at 17.76%, 8% thereafter) = | |||||||||

Add Intrinsic value of firm = $10 per shares | |||||||||

Value per share = | |||||||||

4a. ABC value = 500*1.08*0.5/(0.146-0.08) = | |||||||||

4b. DEF value= 400* 1.06*0.5/(0.135-0.06) = | |||||||||

4c. Growth rate of combined firm = | |||||||||

8%*(4091/(4091+2827)) + 6%*(2827/(4091+2827)) + 1% = | |||||||||

d. Beta of combined firm = | |||||||||

1.20*(4091/(4091+2827)) + 1.00*(2827/(4091+2827)) = | |||||||||

e. Estimated value of synergy: | |||||||||

Value of combined firm with synergy = 900 * 1.0818 *0.50/(.08+1.12*.055-0.0818)) = | |||||||||

Value of synergy = 8151 - 4091 - 2827 = | |||||||||

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) = | ||||||||||

New cost of equity = | 6 + 1.175*8.5 = | |||||||||

e. New WACC = .159875 (2000/2700) + .05 (700/2700) = | ||||||||||

f. Change in value of the firm = (0.1291 - 0.1315)* 2700 /0.1315 = | ! 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 = | ||||||||||

! Use beta of 2.0 | ||||||||||

! Use beta of 1.5 | ||||||||||

! 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 = | ! Available for dividends | |||||||||

b. Effective tax rate on dividends = 0.40 * (1 - 0.85) = | ! 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 = | ||||||||||

Problem 3 | ||||||||||

! Payout ratio = 1 - g/(ROA + D/E (ROA -i)) | ||||||||||

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 = | ||||||||||

b. If debt/equity ratio increases to 1, new beta = 1.6; new cost of equity = 8.5+1.6*5.5 = | 17.30% | |||||||||

Terminal Value = 6.072 * 1.08 * (1-(8/(16+1(16-6)))/(.173-.08)= | ||||||||||

Present Value = 1.98/1.173 + 3.08/1.173^2 +(4.29+48.82)/1.173^3 = | ||||||||||

Problem 4 | ||||||||||

Use put call parity | ||||||||||

Value of call with K = 50; | C-P = S - K exp (-rt); C = | |||||||||

Value of call with K =75; | C= | 31 + 45 - 75 exp(-.10) = | ||||||||

Value of the compensation package = | Straight salary | |||||||||

Value of bonus package | ! 10000 calls with K =50 | |||||||||

-Effect of cap on bonus | ! 10000 calls with K =75 | |||||||||

Net package value = |

FINAL FALL: 1992 | |||||||||

1a. Current Cost of Equity = 8% + 1.15 (8.5%) = | |||||||||

Current after-tax Cost of Debt = 10% (1- 0.4) = | |||||||||

Current Weighted Average Cost of Capital = 17.78% (0.8) + 6.00% (0.2) = | |||||||||

1b. New Debt Ratio = (200+200)/1000 = | |||||||||

Unlevered Beta = 1.15/(1+0.6*.25) = | |||||||||

New levered beta = 1.00 (1+0.6*0.67) = | |||||||||

New Cost of Equity = 8%+1.40 (8.5%) = | |||||||||

New Cost of Capital = 19.90% (0.6) + 6.60% (0.4) = | |||||||||

1c. Change in Firm Value = 1000 (.1542-.1458)/.1458 = | millions | ||||||||

Increase in Stock Price = $57.61 million/ 40 million = | |||||||||

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. | |||||||||

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 |

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 | |||||||

Hardee's | |||||||

Popeye's Fried Chicken | |||||||

Roy Rogers | |||||||

AVERAGE | |||||||

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 = | |||||||

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 = | |||||||

2a. First decide which projects you will accept | |||||||

Project | ROE | Cost of Equity | |||||

A | Accept | ||||||

B | Reject | ||||||

C | Reject | ||||||

D | 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) = | |||||||

3c. | |||||||

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 |