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: DebtIncr. BC Incr. tx. Ben.
250000001000000 Incr BC = Chg in probability * 8 million
25000006400001000000 Incr tx ben. = Chg in debt* Tax rate
250000010000001000000 STOP HERE
500000760000200000
10000001200000400000
1000000600000400000
250000014000001000000
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 =1.5Cost 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 = 0.75for 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
123 45Term. 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
Beta6.1714285714.450791066 2.7785776081.799084813 1.3010307151.052151432
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 12 34
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
Beta1 1.061.15 1.3
Cost of Equity 0.120.1233 0.128250.1365
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
Equity1,000,0001,120,000 1,295,2001,528,9601,824,976 2,187,314
Debt3,000,0002,700,000 2,400,0002,100,0001,800,000 1,500,000
D/E Ratio3.002.41071429 1.852995681.37348263 0.9863143410.68577272
Beta2.582.25071429 1.942853611.67816241 1.4644455161.29854654
Cost of Equity24.90%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
ProjectROECost 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
Revenues1100000
- Expenses440000
- Depreciation100000
= EBIT560000
- Interest Exp100000
= Taxable Inc.460000
- Tax184000
= Net Income276000
-(CapEx- Deprec)(1-_)30000 (150000-100000)(1-0.4)
- _ WC (1-_)30000 (50% of increase in revenues ($100000))*(1-0.4)
= FCFE216000
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
Equity1,000,0001,120,000 1,295,2001,528,9601,824,976 2,187,314
2,100,000