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SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND
PROBLEMS – Chapters 3 through 11,15-25
Corrections:
*Problem 7-2; problem should read investment is depreciated over 5 years to $400,000.
*Problem 10-16; NPVs are too high. For example, the calculation for NPV in the first case
should be: =-10,000,000-50,000,000+500,000*12*0.6*1.03*(1-1.03^20/1.1^20)/(0.1-0.03)-
1,000,000*.6*(1-1.1^(-20))/0.1+1,200,000*(1-1.1^(-20))/0.1
*Problem 15-14; problem (b.) should read semi-annual coupon rate of 6%, 10 years to
maturity, and trading at par.
*Problem 25-14; total values don’t match numbers calculated; since revenue increases,
working capital for part d should be greater than sum of individual wc.
*Problem 21-12; missing 1991
3-6
Value of 15-year corporate bond; 9% coupon rate; 8% market interest rate
Assuming coupons are paid semi-annually,
Value of Bond = 45* (1-1.04^ (-30))/ .04+ 1,000/ 1.04^30= $1,086.46
If market interest rates increase to 10%,
Value of Bond = 45* (1-1.05^( -30))/ .05+ 1,000/ 1.05^30= $923.14
The bonds will trade at par only if the market interest rate = coupon rate.
3-8
Value of Dividends during high growth period = $ 1.00 (1.15)(1-1.15^5/1.125^5)/(.125-.15)
= $5.34
Expected Dividends in year 6= $1.00 (1.15)^5*1.06*2=$4.26
Expected Terminal Price= $4.26/(.125-.06)= $65.54
Value of Stock= $5.34 + $65.54/1.125^5= $41.70
3-16
a. Chatham South Orange
Mortgage: $300,000 $200,000
Monthly Payment: $2,201 $1,468
Annual Payments $26,416 $17,610
Property Tax $6,000 $12,000
Total Payment $32,416 $29,610
b. Mortgage payments will end after 30 years. Property taxes are not only a perpetuity; they
are a growing perpetuity. Therefore, they are likely to be more onerous.
c. If property taxes are expected to grow at 3% annually forever,
PV of property taxes= Property tax* (1+g) / (r-g)
For Chatham, PV of property tax = $6,000 *1.03/(.08-.03) = $123,600
For South Orange, PV of property tax = $12,000 *1.03/(.08-.03)= $247,200
To make the comparison, add these to the house prices,
Cost of the Chatham house= $400,000 + $123,600 = $523,600
Cost of the South Orange house= $300,000+ $247,200= $547,200
The Chatham house is cheaper.
3-20
a. Amount needed in the bank to withdraw $80,000 each year for 25 years= $1,127,516
b. Future Value of Existing Savings in the Bank= $407,224
Shortfall in Savings= $1,127,516 - $407,224= $720,292
Annual Savings needed to get FV of $720,292 = $57,267
c. If interest rates drop to 4% after the 10th year,
Annuity based upon interest rate of 4% and PV of $1,127,516= $72,175
The decline in the amount of withdrawal = $80,000 - $72,175
3-22
a. Value of Store= $100,000 (1.05)/(.10-.05) = $2,100,000
b. Growth rate needed to justify a value of $2.5 million,
Solving for g, 100,000(1+g)/(.10-g) =2,500,000
g=5.77%
4-8
cash from operations= net earnings+ depreciation= 30+2= $32 million
increase in non-cash assets= 10+20+15= $45 million
the need for financing= 45-32= $13 million
4-10
total assets= debt+ equity= 100+ 42.5= 142.5
interest expense= coupon rate* debt= 10% * 100=10
then from the equation:
return on assets= (net income + interest expenses (1-tax rate))/ total assets
we can solve for tax rate:
tax rate=1- (return on assets* total assets- net income)/ interest expenses
=1- (20%*142.5-25)/ 10= 65%
4-12
increase in the operating profits= operating leverage* increase in sales= 4.0*3.5%=14%
operating profits in 1995= $20.5 millions *(1+14%)= $23.37 million
4-18
(420,000+ Long term debt)/ (420,000+ Long-term debt+ equity)=0.4
and Long-term debt) / equity = .5
Solving both equations, we get
Long-term debt= 1,260,000 and Equity= 2,520,000
5-2
a. average annual return= 10.91% and standard deviation= 22.72%
b. Price in 1986= 25.6 (1-2.2%) (1+ 10.2%) (1+11.4%)(1-30.5%)*
(1+45.8%)(1+10.3%)(1+ 12.5%)(1+20.4%)(1-10.9%)(1+42.1%)
=$58.91
c. annual compounding growth rate= (58.91/ 25.6)^0.1-1=8.69%
the annual compounding growth rate is always smaller than the average return.
5-6
the expected return= 0.3*15%+0.4*20%+0.3*35%=23%
the standard deviation= square root of (0.3^2*0.2^2+0.4^2*0.4^2+0.3^2*0.7^2
+2*0.3*0.4*0.5*0.2*0.4+2*0.3*0.3*0.7*0.2*0.7
+2*0.4*0.3*0.9*0.4*0.7=40.13%
5-10
Beta= (15%-5%)/ (12%-5%)=1.43
5-12
the portfolio’s beta= 0.4*1.2+0.3*0.9+0.3*1.8=1.29
the expected return of this portfolio= 5%+ 1.29* (12%-5%)= 14.03%
6-2 a. Unlevered Beta= 0.95/ ( 1+ ( 1- 0.36)( 1700/1500)) = 0.55
b. The beta of 0.95 can be broken down into business risk (0.55) and financial risk (0.40).
6-6 Unlevered Beta= 1.20 / (1+(1-0.4)(50/100))= 0.923
New Beta= 0.923 (1 + (1-0.4)(8))= 5.35
6-8 a. Beta for Hewlett Packard= 1.10(2/8) + 1.50(2/8) + 2.00(1/8) + 1.00(3/8)=1.275
This beta may not be equal to the regression estimate of beta, because both of these are
estimated with error.
b. Cost of Equity= 7.5% + 1.275 (5.5%) = 14.51%
Mainframes Cost of Equity= 7.5% + 1.10(5.5%) = 13.55%
Personal Computers Cost of Equity= 7.5% + 1.5(5.5%)= 15.75%
Software Cost of Equity= 7.5% + 2(5.5%)= 18.50%
Printer Division’s Cost of Equity= 7.5% + 1(5.5%)= 13.00%
To value the printer division, I would use a 13.00% cost of equity.
c. Assuming that the leverage is equally distributed across the divisions,
Unlevered Value of Ascribed Firm
Division Beta Beta Equity Debt Value
Mainframes 1.10 1.019 2.00 0.25 2.25
Pcs 1.50 1.389 2.00 0.25 2.25
Software 2.00 1.852 1.00 0.125 1.13
Printers 1.00 0.926 3.00 0.375 3.38
Unlevered Beta=1.389(2.25/6.75)+1.852(1.125/6.75)+0.926 (3.375/ 6.75)=1.235
New Debt/ Equity Ratio= 1/7
New Levered Beta = 1.235 ( 1+ (1-4)(1/7))=1.34
6-12
a. Regression Results
Returns on AD = -0.00147 + 0.735 (NYSE)
The intercept is -0.147%; the beta is 0.735.
b. Expected Return over next year = 6% + 0.735(8.5%) = 12.25%
c. Intercept = -0.147%
Risk-free Rate (1-Beta) = 5% (1-0.735) = 1.325%
Intercept - Risk-free Rate ( 1- Beta) = -0.147% - 1.325%= -1.32647%
On an annual basis, the stock did -1.32647% worse than expected.
d. If you were an undiversified investor, you would be exposed to all risk in AD; this
can be measured in terms of the standard deviation in AD returns (10.61%).
The R-squared of this regression is 29%; this suggests that 71% is diversifiable risk.
e. Beta for divested division = 2 (0.735) = 1.47
1.47 (.2) + X (0.8) = 0.6
Solve for X,
X= 0.306/ .8 = 0.3825
This is the beta after the divestiture, assuming that the cash is paid out and that the
leverage is unaffected.
6-16
a.Intercept - Risk-free Rate (1- Beta) = -0.05% - 0.49% ( 1-1.20) = 0.05%
Monthly Risk-free Rate = 1.06(1/12) - 1= 0.49%
The stock did 0.05% better than expected during the period of the regression.
b. Debt before restructuring= $40 million - $20 million = $ 20 million
Equity before restructuring = $120 million + $40 million = $160 million
Debt / Equity Ration before restructuring= 20/160= 12.50%
Unlevered Beta before restructuring= 1.20 / (1+ (1-.4)(.125))= 1.12
Unlevered Beta after the divisional sale,
0.6(20/180) + X (160/180) = 1.12
Solving for X,
Unlevered Beta after divisional sale= 1.19
New Debt/ Equity Ratio after restructuring = 40/120 = 0.33
New Beta = 1.19 ( 1+ (1-.4)( 0.33)) = 1.43
6-20
a. Unlevered Beta for Food Business = 0.95/ ( 1+ (1-.36)(.35)) = 0.78
Beta for Food Division = 0.78 ( 1+ (1-.36)(.25)) = 0.90
b. Yes. The higher fixed cost structure would lead me to use a higher unlevered
beta for Nabisco
7-2
a. We have to assume for the purpose of calculating ROC that the depreciation
would not fo down to zero:
Year EBIT(1-t) Depreciation Net book Average ROC
Value Investment
0 0 0 $1200000
1 $132000 $160000 $1040000 $1120000 11.79%
2 $132000 $160000 $880000 $960000 13.75%
3 $132000 $160000 $720000 $800000 16.5%
4 $132000 $160000 $560000 $640000 20.63%
5 $132000 $160000 $400000 $480000 27.5%
b. The geometrical mean return=
[(1+11.79%)(1+13.75%)(1+16.5%)(1+20.63%)(1+27.5%)]1/5 -1
c. The project should be rejected since the cost of capital is higher than the return.
7-8
(1) Since the initial cost = $ 1 million and
the annual after-tax cash inflow =$300000*(1-34%)+ 1000000/10=$298000
then the payback period for the project = 1000000 / 298000 = 3.36 years
(2) The project should be accepted.
7-12
The NPV = 350000/ (1+12%)(1+10%) + 300000(1+10%) - 500000= $56818.18
7-14
a. The IRR for Project A= 8.04%
b. The IRR for Project B= 7.32%
c. Project A is accepted based on the IRR rule since it has higher IRR.
d. Since the NPV of Project A = $141.95 and the NPV of Project B =$424.35
when the cost of capital is 5%, it is obvious that the Project B should be accepted.
e. Since the NPV of Project A= $21.50 and the NPV of Project B= -$27.73 when
the cost of capital is 7.5%, then the Project A should be accepted.
f. In this example, the IRR rule finds the Project A superior to the Project B.
However, the NPV rule may give different conclusions when the cost of capital
changes. The NPV rule is more consistent with the objective of financial
management to maximize the shareholder’s wealth.
8-6
a.Unlevered beta (Nuk-Nuk) = 1.3/(1+(1-0.6)0.5) = 1
unlevered beta (Gerber) = 1.5/(1+(1-0.5)1.00) = 1
(note: if there are more than 2 companies, I would use the average leverage and the average
equity beta)
This project has no debt. So the appropriate beta = 1.00
Appropriate discount rate =11.5 + 1.0(5.5) = 17.0%
b.Revenues 30,000
Expenses 12,000
Garage cost 2,000
BTCF 16,000
Taxes 4,400 =(16,000-5,000)*0.4
If you considered working capital increase in Year 1,the ATCF in year 1 alone =4,100
(Note that since working capital stays at 7,500, there are no working capital changes after the
initial year)
c.NPV=-57,500 + 11,600 (PVA,17%,10 years) + 6,000(PF,17%,10years) = $(2,212)
8-10
Initial Investment=-500,000-50,000+50,000=-500,000
ATCF per year=1,000,000-500,000-200,000-.5(300,000-100,000)=$200,000
NPV of this project=-500,000+200,000*(AF,10%,5 years)= $258,157
NPV of investment banking job=75,000*.5*(Af,10%,5 years)=$142,155
Take the investment! Alternatively, you can show the investment banking job as an opportunity
cost in the analysis.
Remember that the interest you could have made on the CD should not be considered as an
explicit opporunity cost. It is already taken into account through discounting.
8-14
a.Initial investment= 10 million(Distribution system) = 1 million(WC)= 11 million
b.
Incremental Revenues 10,000,000
-Variable Costs (40%) 4,000,000
-Advertising Costs 1,000,000
-Depreciation 1,000,000
EBIT 4,000,000
-Taxes 1,600,000
+Depreciation 1,000,000
ATCF 3,400,000
c. NPV=-11,000,000 + 3,400,000(PVA,10 years,8%) + 1,000,000(PF,10 years,8%)
=$12,277,470
8-16
a.Working capital without computer: 0.5*5,000,000= $2,500,000
Working capital with computer: 0.25*8,000,000=$2,000,000
Decrease in working capital with computer=$500,000
Cash flow in year 0= -10,000,000 = 50,000= $9,500,000
(the initial investment is $10 million)
b.After-tax cash flows Each Year
w/o computer w/computer Incremental CF
Revenues 5,000,000 8,000,000 3,000,000
COGS 2,500,000 4,000,000 1,500,000
Selling expenses 1,500,000 500,000 -1,000,000
Gross Profit 1,000,000 3,500,000 2,500,000
Depreciation 0 1,000,000 1,000,000
Taxable Income 1,000,000 2,500,000 1,500,000
Tax 400,000 1,000,000 600,000
Net Income 600,000 1,500,000 900,000
+Depreciation 0 1,000,000 1,000,000
ATCF 600,000 2,500,000 1,900,000
c. NPV = -9,500,000 + 1,900,00(PVA,8%,10 years) - 500,000/1.08^10
=$3,017,558
9-6
a. Initial investment = 10 million (Distribution system) + 1 million (WC) = 11 million
b.
Incremental Revenues 10,000,000
Variable Costs (40%) 4,000,000
Advertising Costs 1,000,000
BTCF 5,000,000
Taxes 1,600,000 =(5,000,000-1,000,000)*0.4
ATCF $3,400,000
c. NPV= -11,000,000 + 3,400,000 (PVA,10 years,8%) +1,000,000 (PF, 10 years, 8%)=
$12,277,470
d. Precise Breakeven:
(-10,000,000-.1x)+(.6x-1,000,000-(.6x-1,000,000-1,000,000)*.4)(PVA,10yrs,8%)+ .1x/ 1.08^ 10
=0
(-10,000,000-.1x)+(.6x-1,000,000-(.6x-1,000,000-1,000,000)*.4)(6.71)+.1x*0.4632=0
-.1x+2.4156x+.04632x= 10,000,000+200,000*6.71
2.36192x= 11,342,000
x= 4,802,025.47 or Increase4.80% from initial level of 10%
9-12
Equivalent Annual Cost of inexpensive machines=-2,000(APV,12%,3)-150= $(983)
Equivalent Annual Cost of expensive machines= -4,000 (APV,12%,5)- 50=$(1,160)
I would pick the more expensive machines. They are cheaper on an annual basis.
9-16
___________________ Years 1-10
ATCF: Store 10,000
-CF from Lost Sales -1,200
Net ATCF 8,800
NPV=-50,000 + 8,800 (PVA,14%,10 years)=$(4,098)
I would not open the store
9-18
Total Cost of Buying Computers= $2,500*5,000
-PV of Salvage= $2,500,000/1.12^3
-PV of Depreciation= $3,333,333*.4*(PVA,12%,3)
=Net Cost of Buying Computers= $7,518108
(APV,12%,3) = $3,023,143
Annualized Cost of Leasing= $5,000,000 (1-.4)= $3,000,000
It is cheaper to lease the computers rather than buy them.
10-2
Initial Investment = $(10,000,000)
Annual Operating Cash Flows
Year 1 2 3 4 5
Revenues= $5,000,000 $5,250,000 $5,512,500 $5,788,125 $6,077,531
-VariableCost $2,000,000 $2,100,000 $2,205,000 $2315,250 $2,431,013
-Fixed Costs $500,000 $500,000 $500,000 $500,000 $500,000
-Depreciation $2,000,000 $2,000,00 $2,000,000 $2,000,000 $2,000,000
EBIT $500,000 $650,000 $807,500 $972,875 $1,146,519
EBIT(1-t) $300,000 $390,000 $484,500 $583,725 $687,911
+Depreciation $2,000,000 $2,000,000 $2,000,000 $2,000,000 $2,000,000
ATCF $2,300,000 $2,390,000 $2,484,500 $2,583,725 $2,687,911
PV at 15% $2,000,000 $1,807,183 $1,633,599 $1,477,253 $1,336,367
A. Total PV of Cash Inflows = $8,254,403
NPV = -$10,000,000 + $8,254,403 = $(1,745,597)
IRR of Project = 7.55%
B.
Year CF
0 -10,000,000
1 $2,300,000
2 $2,390,000
3 $2,484,500
4 $2,583,725
5 $2,687,911
Sensitivity of Measures to Change in Assumptions
# units sold NPV IRR
15,000 ($3,390,179) -0.13%
20,000 ($1,745,597) 7.55%
25,000 ($101,016) 14.58%
30,000 $1,543,565 21.15%
sale price/unit NPV IRR
200 ($3,061,262) 1.47%
250 ($1,745,597) 7.55%
300 ($429,932) 13.22%
350 $885,733 18.57%
400 $2,201,398 23.68%
C. Breakeven number of units (NPV = 0) = 25307 units
Breakeven number of of units (EBIT = 0) = 16667 units
10-10
Initial investement = $100 million (1-.4) = $60,000,000
A. Accounting Breakeven = Fixed Costs/Contribution Margin per Units
=$10 million / $0.30 = 33,333,333
B.
Annual Operating Cash Flows
Revenues $37,595,940
-Variable cost $15,038,376 # OF UNITS= 75,191,880
-Fixed cost $10,000,000
EBIT $12,557,564
EBIT (1-t) $7,534,538
NPV of Project = $1.49
Approximately 75,191,880 cans have to be sold to break even financially.
10-16
Mega Well NPV Probability
500,000 barrels $10,833,568 0.2
for 20 years:
Full Rig Typical Well
($50,000,000) 250,000 barrels $(2,083,216) 0.2
for 20 years
Initial Cost Bust Well
($10,000,000) 50,000 barrels $(12,416,64) 0.2
for 20 years
$(10,000,000) 0.4
Expected NPV without abandonment option = $(4,733,258)
b. The company should not spend any money for the option to explore, since the expected NPV
is negative.
c. If you can abandon the project, you would under the 50,000 barrels scenario.
Expected NPV with the abandonment option = $(3,684,090)
Value of the abandonment option = $1,049,168
11-6
a. Unlevered Beta for Automobile Component Business = 0.90/(1+(1-.36)(.40)) = 0.72
Beta for Automobile Component Business = 0.72 (1+(1-.36)(30/70)) = 0.92
b. Cost of Equity for Auto Component Business = 7% + 0.92 (5.5%) = 12.06%
Cost of Capital for Auto Component Business = 12.06% (.70) + 7.5%(1-.36)(.3) = 9.88%
c. If Intel uses its current cost of equity and capital on this project, it will make it more likely to
reject the project - the current cost of equity and capital are very high.
11-12
a. Unlevered Beta for Workstation Business = 1.20/(1+(1-.36)(.20)) = 1.06
Beta for Workstation Business = 1.06 (1+(1-.36)(10/90)) = 0.99
Cost of Equity for Workstation Business = 7% + 0.99 (5.5%) = 12.45%
Cost of Capital for Workstation Business = 12.45% (.9) + 7.5% (1-.36)(.1) = 11.69%
b. No. I would not. The fact that the business is intensely competitive will be reflected in my
estimates of profit margins and cash flows for the project, but not in the discount rate. This risk is
industry risk and should not be reflected in the beta.
11-14
The risk associated with the tobacco lawsuits is firm-specific risk and should be diversifiable in a
portfolio concept. It will not affect the cost of equity. The effect that these suits have on default
risk do affect the cost of debt and thus do affect the cost of capital, at least on the margin.
23-4
a. Expected Earnings Per Share in 1999= $2.10*1.155*1.06= $4.48
Expected Dividends Per Share in 1999= $4.48*0.65=$2.91
Cost of Equity After 1999= 6.25%+ 1.1*5.5%= 12.30%
Expected Price at the End of 1998= Expected DPS in 1999/ (ke, at 1999- g) = $2.91/(.1230-
.06)= $46.19
b.
Year EPS DPS
1994 $2.42 $0.79
1995 $2.78 $0.91
1996 $3.19 $1.05
1997 $3.67 $1.21
1998 $4.22 $1.39 $46.19
Cost of Equity= 6.25%+ 1.40*5.5%= 13.95%
PV of Dividends and Terminal Price (@ 13.95%)= $27.59
23-8
a.
Year EPS Cap Exp Depr DWC FCFE Term Price
1 $2.71 $2.60 $1.30 $0.05 $1.64
2 $3.13 $3.00 $1.50 $0.05 $1.89
3 $3.62 $3.47 $1.73 $0.05 $2.19
4 $4.18 $4.00 $2.00 $0.06 $2.54
5 $4.83 $4.62 $2.31 $0,06 $2.93 $84.74
6 $5.12 $4.90 $4.90 $0.04 $5.08
Net capital expenditures (Cap Ex-Depreciation) and working capital change is offset partially by debt
(20%). The balance comes from equity. For instance, in year 1:
FCFE=$2.71- ($2.60- $1.30)*(1-0.20)- $0.05* (1-0.20) = $1.64)
Cost of Equity= 6.5%+ 1*5.5%= 12%
Terminal Value Per Share= $5.08/(.12-.06)= $84.74
Present Value Per Share=
1.64/1.12+1.89/1.122+2.19/1.123+2.54/1.124+(2.93+84.74)/1.125=$55.89
b.
Year EPS Cap Exp Depr DWC FCFE Term Price
1 $2.71 $2.60 $1.30 $0.05 $1.64
2 $3.13 $3.00 $1.50 $0.05 $1.89
3 $3.62 $3.47 $1.73 $0.05 $2.19
4 $4.18 $4.00 $2.00 $0.06 $2.54
5 $4.83 $4.62 $2.31 $0,06 $2.93 $52.09
6 $5.12 $4.90 $2.45 $0.04 $5.08
Terminal Value Per Share= $3.13/(.12-.6)=$52.09
Present Value Per Share=
1.64/1.12+1.89/1.122+2.19/1.123+2.54/1.124+(2.93+52.09)/1.125=$37.36
c.
Year EPS Cap Exp Depr DWC FCFE Term Price
1 $2.71 $2.60 $1.30 $0.05 $1.43
2 $3.13 $3.00 $1.50 $0.05 $1.66
3 $3.62 $3.47 $1.73 $0.05 $1.92
4 $4.18 $4.00 $2.00 $0.06 $2.23
5 $4.83 $4.62 $2.31 $0,06 $2.58 $45.85
6 $5.12 $4.90 $2.45 $0.04 $2.75
Terminal Value Per Share= $2.75/(.12-.06)=$45.85
Present Value Per Share=
1.43/1.12+1.66/1.122+1.92/1.123+2.23/1.124+(2.58+45.85)/1.125=$32.87
The Beta will probably be lower because of lower leverage.
23-10
a.
Year 1 2 3 4 5
Earnings $0.66 $0.77 $0.90 $1.05 $1.23
(CapEx- $0.05 $0.06 $0.07 $0.08 $0.10
Deprec’n)*(1-D)
D Working $0.27 $0.31 $0.37 $0.43 $0.50
Capital* (1-D)
FCFE $0.34 $0.39 $0.46 $0.54 $0.63
Present Value $0.29 $0.30 $0.30 $0.31 $0.31
Year 6 7 8 9 10
Growth Rate 14.60% 12.20% 9.80% 7.40% 5.00%
Cumulated Growth 14.60% 28.58% 41.18% 51.63% 59.21%
Earnings $1.41 $1.58 $1.73 $1.86 $1.95
(CapEx-Deprec’n) $0.11 $0.13 $0.14 $0.15 $0.16
* (1-D)
Working Capital $0.45 $0.39 $0.30 $0.22 $0.13
* (1-D)
FCFE $0.84 $1.07 $1.29 $1.50 $1.67
Beta 1.38 1.31 1.24 1.17 1.1
Cost of Equity 14.59% 14.21% 13.82% 13.44% 13.05%
Present Value $0.37 $0.41 $0.43 $0.44 $0.43
End-of-Life Index 1
Stable Growth Phase
Growth Rate: Stable Phase=5.00%
FCFE in Terminal Year= $1.92
Cost of Equity in Stable Phase= 13.05%
Price at the End of Growth Phase= $23.79
PV of FCFE in High Growth Phase= $1.51
Present Value of FCFE in Transition Phase= $2.08
Present Value of Terminal Price= $6.20
Value of the Stock= $9.79
b.
Year 1 2 3 4 5
Earnings $0.66 $0.77 $0.90 $1.05 $1.23
(CapEx- $0.05 $0.06 $0.07 $0.08 $0.10
Deprec’n)*(1-D)
D Working $0.27 $0.31 $0.37 $0.43 $0.50
Capital* (1-D)
FCFE $0.34 $0.39 $0.46 $0.54 $0.63
Present Value $0.29 $0.30 $0.30 $0.31 $0.31
Transition Period (up to ten years)
Year 6 7 8 9 10
Growth Rate 14.60% 12.20% 9.80% 7.40% 5.00%
Cumulated Growth 14.60% 28.58% 41.18% 51.63% 59.21%
Earnings $1.41 $1.58 $1.73 $1.86 $1.95
(CapEx-Deprec’n) $0.11 $0.13 $0.14 $0.15 $0.16
* (1-D)
Working Capital $0.50 $0.48 $0.43 $0.36 $0.26
* (1-D)
FCFE $0.79 $0.97 $1.16 $1.35 $1.54
Beta 1.38 1.31 1.24 1.17 1.1
Cost of Equity 14.59% 14.21% 13.82% 13.44% 13.05%
Present Value $0.34 $0.37 $0.39 $0.40 $0.40
End-of-Life Index 1
Stable Growth Phase
Growth Rate: Stable Phase=5.00%
FCFE in Terminal Year= $1.78
Cost of Equity in Stable Phase= 13.05%
Price at the End of Growth Phase= $22.09
PV of FCFE in High Growth Phase= $1.51
Present Value of FCFE in Transition Phase= $1.90
Present Value of Terminal Price= $5.76
Value of the Stock= $9.17
c.
Year 1 2 3 4 5
Earnings $0.66 $0.77 $0.90 $1.05 $1.23
(CapEx- $0.05 $0.06 $0.07 $0.08 $0.10
Deprec’n)*(1-D)
D Working $0.27 $0.31 $0.37 $0.43 $0.50
Capital* (1-D)
FCFE $0.34 $0.39 $0.46 $0.54 $0.63
Present Value $0.29 $0.30 $0.30 $0.31 $0.31
Transition Period (up to ten years)
Year 6 7 8 9 10
Growth Rate 14.60% 12.20% 9.80% 7.40% 5.00%
Cumulated Growth 14.60% 28.58% 41.18% 51.63% 59.21%
Earnings $1.41 $1.58 $1.73 $1.86 $1.95
(CapEx-Deprec’n) $0.11 $0.13 $0.14 $0.15 $0.16
* (1-D)
Working Capital $0.45 $0.39 $0.30 $0.22 $0.13
* (1-D)
FCFE $0.84 $1.07 $1.29 $1.50 $1.67
Beta 1.45 1.45 1.45 1.45 1.45
Cost of Equity 14.98% 14.98% 14.98% 14.98% 14.98%
Present Value $0.36 $0.40 $0.42 $0.43 $0.41
End-of-Life Index 1
Stable Growth Phase
Growth Rate in Stable Phase= 5.00%
FCFE in Terminal Year= $1.92
Cost of Equity in Stable Phase= 14.98%
Price at the End of Growth Phase= $19.19
PV of FCFE in High Growth Phase= $1.51
Present Value of FCFE in Transition Phase= $2.03
Present Value of Terminal Price= $4.75
Value of the Stock= $8.29
23-15
a. Beta for the Health Division=1.15
Cost of Equity= 7%+1.15*5.5%=13.33%
Cost of Capital= 13.33%* 0.80+ (7.5%*0.6)*0.2=11.56%
b.
Year Deprec’n EBIT EBIT(1-t) Cap Ex FCFF Term Value
0 $350 $560 $336 $420 $266
1 $364 $594 $356 $437 $283
2 $379 $629 $378 $454 $302
3 $394 $667 $400 $472 $321
4 $409 $707 $424 $491 $342
5 $426 $749 $450 $511 $364 $5,014
Now after 5 years:
Cost of Equity= 13.33%
Cost of Debt= 4.50%
Cost of Capital= 11.56%
Value of the Division=
283/1.1156+302/1.11562+321/1.11563+342/1.11564+(364+5,014)/1.11565=$4,062 millions
c. There might be potential for synergy, with an acquirer with related businesses. The health division at
Kodak might also be mismanaged, creating the potential for additional value from better management.
23-20
a. Dividend Payout Ratio=$1.12/$2.45=0.46
Expected Growth Rate= 6%
Cost of Equity=7%+0.9(5.5%)=11.95%
Profit Margin= 2.45/122=2%
P/S Ratio= .02* 0.4571* (1.06)/(.1195-.06)=0.16
Price Based on this Multiple = 0.16288* 122=$19.87
b. P/S Ratio Needed for a price of $34=$34/122=0.28
Profit Margin Needed for this P/S Ratio= 0.0342 or 3.42%
15-4
Value of Straight Preferred Stock portion of Convertible= 6/ .09= $66.67!
Perpetual Life Value of Conversion Portion= $105 - $66.67 = $38.33
15-8
A. Number of shares you would need to sell in rights offering= $100mil/$25= 4 million
Number of shares outstanding = 10 million
You would need 5 rights to buy two shares.
B. Ex-rights price = (50* 10+25 * 4)/ 14 = $42.86
C. Value per right = Pre-right price- Ex-rights price = $50 - $42.86 = $7.14
D. If the price of the right were higher than $7.14, I would sell my rights at the higher price and
keep the difference as excess return. The stock price after the rights issue and the cash will yield
me more than what I paid for the stock which was $50.
15-14
Value of Common Stock = $1 million * 50= $50 million
Value of Warrants = 200,000 * $12= $2.4 million
Value of Straight Debt = $250 million
Value of Straight Debt portion of Convertible Debt
= 10,000 * (30 *( PVA,4.5%,20) + 1000/1.045^20) = $8.049 million
Value of Conversion Option(Equity)=10,000*1000-$8.049=$1.951 million
Value of Debt= $250 + $8.049 = $258.049 million
Value of Equity = $50 +$2.4 + $1.951 million = $54.351 million
Debt Ratio= 258.049/(258.049+54.531) = 82.6%
16-10
The positive stock price reaction is not surprising. Financial markets had for the long
known that the Fokker division was losing substantial amounts of money for Daimler Benz. The
write-off was viewed by markets as closure on a bad investment. The stock price reaction would
have been negative if the markets had not realized the extent of the problems and had been
surprised by the write-off.
16-12
While the underpricing is always a transfer of wealth from me to the new stockholders, I
would be more inclined to support it if only 10% of the stock is being offered at the initial
offering - the loss is smaller and the price increase following the offering may serve as a
promotional for the future offerings.
16-14
Yes. The market reaction might be less negative if the information is revealed early
rather than if it is a total surprise.
Chapter 17 Solutions
17-6
a. Cost of Equity= 9%+6%=15%
Since it is an all-equity financed firm, the cost of capital is equal to the cost of equity.
b.
Marginal Marginal
Value of Debt Increase in Debt Tax Benefits Exp. Bankrup. Cost
2500,000 2,500,000 1,000,000 0
5000,000 2,500,000 1,000,000 640,000
7500,000 2,500,000 1,000,000 1,000,000
8000,000 500,000 200,000 760,000
9000,000 1000,000 400,000 1,200,000
10,000,000 1000,000 400,000 600,000
12,500,000 2,500,000 1,000,000 1,400,000
Every marginal increment past $7.5 million has expected cost > expected tax benefits!
Optimal debt is between $5 million and $7.5 million.
c. Value of Firm at Optimal Capital Structure
= Current Firm Value+ Sum of Marginal Tax Benefits- Sum of marginal costs= $13,360,000
17-8
The second firm should borrow more because
1. It has lower bankruptcy costs due to more predictable cash flows.
2. It does not have much of a need for flexibility because its future needs are known.
17-10
a. In the Miller-Modigliani world with no taxes, the value of the firm will be $100 million no matter
what the debt ratio.
b. The cost of capital will always be 11%.
c. With taxes, the value of the firm will increase as the debt is increased (because of the tax benefits
of debt) and the cost of capital will go down (due to the interest tax savings again).
17-16
I would expect a decline in the optimal debt ratios of firms because the tax benefit of borrowing is
significantly lower. If the tax deductibility of interest were removed, I would expect a similar effect.
17-24
This is not true. While debt is always cheaper than equity, taking on more debt will make you a
riskier firm- this, in turn, will push up the cost of both debt and equity. This negative effect may
offset the positive effect of replacing more expensive equity with less expensive debt.
Chapter 18 Solutions
18-4
a) Intuitively, I would expect Rubbermaid to have a higher debt ratio than its competitiors
because: (1) its earnings are less volatile than those of ite competitors
(2) it has higher cash flows as a percent of firm value than its competitors.
(3) it has a higher tax rate than its competitors
(4) it has a lower need for flexibility; it has lower R&D expenses
b) Plugging in the values into the regression,
Predicted Debt/ Equity Ratio= .10-.5 (.2)+2.0(.25)+.4(.4)+2.5(.02)=71.00%
18-6
1)First we calculate the cost of capital at different levels of debt
Add Debt Beta Cost of Equity Rating Debt Cost Cost of Capital
Current 1.15 12.33% BBB 6.00% 11.06%
500,000 1.30 13.15% BB 6.30% 10.87% Optimal
1,000,000 1.45 13.98% B 6.90% 10.94%
1,500,000 1.60 14.80% B- 8.10% 11.45%
2,000,000 1.75 15.63% C 9.00% 11.94%
Unlevered Beta= 1.15/ (1+.6*(500/2000)=1.00
This assumes that the new debt will not be used to buy back stock.
2) Effect of moving to the optimal on the Stock Price
Increase in Firm Value= 2500000 (.1106-.1087)/.1087= $43,698
Increase in Stock Price= $43,698/100000= $0.44
3)See above
After-tax Cash Flow to Firm from Project= EBIT (1-t)+ Depreciation
=$600,000 (1-.4)+$100,000= $460,000
NPV of Project= 460000/.1087-$3,000,000= $1,231,831
18-10
a) Current Cost of Equity =6%+1.25(5.5%)=12.88%
b)Current After-tax Cost of Debt = 11%(1-.5)=6.60%
c)Current Cost of Capital= 12.88% (1800/2700)+6.60% (900/2700)=10.79%
[Market Value of Equity=PE*Net Income=9*200=1,800;
Market Value of Debt=0.9*1,000=900]
d)After the action,
New Equity=2000
New Debt=700
Unlevered Beta=1.25/(1+0.6*(900/1800)=0.96
New Levered Beta= 1.00 (1+.6*(700/2000))=1.163
New Cost of Equity=6%+1.163(5.5%)=12.4%
e)New WACC= 12.4%(2000/2700)+10%(1-.4)(700/2700)=10.74%
f)Change in Value of Firm= 2700 (.1079-.1074)/.1074= $12.57
New Firm Value= $2700+$12.57=$2,712.57
18-20
a. Optimal with WACC Approach
Debt Ratio D/E Ratio Beta Cost of Equity Debt Cost Cost of Capital
0% 0% 0.75 12.01% 5.15% 12.01%
10% 11% 0.80 12.29% 5.15% 11.58%
20% 25% 0.87 12.65% 5.54% 11.23%
30% 43% 0.95 13.12% 5.75% 10.91%
40% 67% 1.07 13.74% 5.91% 10.61%
50% 100% 1.22 14.60% 6.54% 10.57%
60% 150% 1.46 15.90% 6.54% 10.28% Optimal
70% 233% 1.85 18.07% 7.48% 10.66%
80% 400% 2.64 22.40% 8.11% 10.97%
90% 900% 5.00 35.39% 8.74% 11.41%
Unlevered Beta= 1.26/((1+(1-.37)(237/11*19.88))=0.75
b. Optimal with Return Differential Approach
Debt Ratio Cost of ROE Differential
Equity
0% 12.01% 11.09% -0.92%
10% 12.29% 11.75% -0.55%
20% 12.65% 12.47% -0.18%
30% 13.12% 13.37% 0.26%
40% 13.74% 14.54% 0.80%
50% 14.60% 15.64% 1.03%
60% 15.90% 17.91% 2.01%
70% 18.07% 19.50% 1.43%
80% 22.40% 22.98% 0.58%
90% 35.39% 32.18% -3.21%
Return on Assets = 44 (1-.37)/250 = 11.09%
c. Differences in Optimal
The two approaches provide different optimal debt ratios, since they are based upon different analyses.
The WACC approach attempts to maximize firm value, given its assets. The return differential approach
attempts to maximize the return differential to equity investors.
18-24
a. Estimated Market Value of Debt:
Calculate present value of $80,000 for 5 years and $1 million at end of fifth years at 8.25%
PV of Debt = $990,084
Debt/Equity Ratio= 990,084/6,000,000=16.50%
Unlevered Beta for comparable firms= 1.05/(1+0.6*.25)=0.91
Beta based upon D/E ratio of 16.50%= 0.91(1+0.6*.165)=1.00
Cost of Equity= 7%+5.5%=12.5%
Cost of Capital= 12.5%(6000/6990)+8.25%(1-.4)(1990/6990)=11.43%
b. New D/E ratio = 1,990,084/6000000 = 0.331666667! Assumes debt is used to take projects
New beta = 0.91(1+.6*.33) = 1.09
New cost of equity = 7% + 1.09*5.5% = 13.00%
New cost of capital = 13%(6000/7990) + 9%(1-.4)(1990/7990) = 11.11%
Change in Firm Value= (0.1143-0.1111)(6990)/0.1111=$201
New Firm Value= 6990+ 1000+201=$8,191
c. Estimated Debt Ratio= 0.15+1.05(500/6990)-0.10(1.00)=12.51%
d. These analyses are based upon the assumption that the only risk is market risk. For a private firm, all
risk matters, since the owners of these firms may not be well diversified.
Chapter 19 Solutions
19-6
a. Given that the projects are long-term and require large initial investments, I would suggest
long-term debt.
b. Since the cash flows are the local currencies, I would suggest that the debt also be in local
currencies.
c. Since future cash flows will depend upon the growth of the emerging markets, I would be
more likely to use convertible debt.
19-12
I would expect steel companies in emerging countries to use far less debt than their mature U.S.
counterparts. In addition, I would expect these companies to use convertible debt rather than
straight debt.
19-18
I would expect these companies to use floating-rate dollar debt, since their cash flows tend to
move with inflation. The external restrictions on investment policy will also reduce any concerns
bondholders might have about expropriation and allow them to borrow long-term.
19-22
I would concur with the use of convertible debt for the following reasons:
a. Borrowing fixed-rate, long-term debt would be expensive, given that the market perceives
them to be riskier than they are.
b. The conversion option will be priced based upon perceived volatility; to the extent that the
market is perceiving that the firm is volatile, this allows the firm to take advantage of this
perception.
Chapter 20 solutions
20-2
Firms usually do not change their dividends very frequently. This is what is meant by sticky
dividends. Part of the reason for sticky dividends is that firms are reluctant to cut dividends,
because of the fear that markets will punish them. Consequently, they do not increase dividends
unless they believe that they an maintain these higher dividends.
20-10
If the marginal investor (which is a corporation) sells the stock before the ex-dividend day,
CFB=PB - (PB-P)tcg
If the marginal investor sells the stock after the ex-dividend day,
CFA= PA - (PA - P) tcg + D(1 - 0.15to)
If no arbitrage is allowed to occur,
CFB=CFA
Then we find (PB - PA)/D= (1 - 0.15to)/ (1-tcg)
20-12
Assume that the true capital gains tax rate = State Rate/ (1=Rf)/n
(Pb - Pa) = (1- to) / (1 - tcg) or ($10 - 9.20) = (1-.5)/ (1-.5/1.1n)
Solving for n, n= approximately 3 years
20-22
Firms’ dividend policy would be affected in different ways because the clientele of each firm
may be in different tax bracket today.
Chapter 21 solutions.
21-4
a. Estimate the FCFE.
Investable funds $100.00
- (Cap Ex)(1-) $37.50
- Change in WC (1-) -
=FCFE $62.50
Capital Expenditures:
Cost of Equity = 18%
After-tax Cost of Debt = 6%
Debt Ratio= 500/ (500+1500) = 25%
Cost of Capital= (.18)(.75) + .06(.25) = 15%
Accept projects A, B, C: They have returns on capital that exceed the cost of capital.
Total Capital Expenditures = $50 million
b. The company should return $62.5 million to its stockholders.
21-12
Year Net Income (Capx-Depr) Ch WC (1- FCFE Dividends
)
(1-)
1992 $282.00 $102.60 $(87.00) $266.40 $80.00
1993 $320.00 $169.20 $195.00 $(44.20) $95.00
1994 $375.00 $127.20 $(24.00) $271.80 $110.00
1995 $441.00 $120.60 $45.00 $275.40 $124.00
Average $198.04 $95.80
a. Conrail could have paid out $198 million in dividends. It paid out only 495.8 million a year.
b.
Return on Equity = 13.50%
Cost of Equity = 7% + 1.25(5.5%) = 13.88%
Conrail’s projects did not do as well as they should have. I would recommend that if conrail ‘s
project choice is not expected to improve, they return more cash to their stockholders.
21-16
a.
Estimated Net Income next year $140.80
- (Cap Ex -Depreciation)(1-.10) $25.74
- Change in Working Capital(1-.10) $45.00
= FCFE $70.06
This is what the company can afford to pay in dividends.
21-18
Company Divs Vs. FCFE ROE Cost of Equity Action
Alexander < 8% 11.00% Pressure to pay
more dividends
American Press < 14.50% 13.50% Allow to cont.
ROE>COE
OMI > 4% 13.25% Evaluate invst;
FCFE<dividend
OverseaS < 1.50% 11.50% Pressure to pay
more dividends
Sea Containers > 14% 12.25% Pressure to pay
less dividends
a. Alexander and Brown and Overseas Shipholding
b. Sea Containers
c. If I thought that the returns on projects for this entire sector were going to improve, it would
make me more cautious about raising dividends in the first place. If, on the other hand, I thought
that returns for this entire sector were going to drop, I would push for more dividends more
aggressively.
Chapter 22 solutions
22-6
A. Current market value of debt = current market value of stock = $42 * 1 million = $42 million
After $5million of debt is retired, total debt becomes $37 million
EPS = (15,000,000 - 37,000,000*10%)(1-40%) / (1,000,000-100,000)=$7.53
b. Current EPS = (15,000,000 -42,000,000*10%) (1-40%) / 1,000,000= $6.48
Current P/E ratio= $42/$6.48=$6.48
The new price would be $7.53*6 or $48.79 per share. It is lower than the tendering price of $50.
The management would provably argue that the P/E ratio would be higher, leading to a higher
price.
c. If the stocks are brought back at the ongoing market price, it is less likely that the market
could believe that argument made by the management that the stock is underpriced.
d. The answer to (b) and (c) may differ if the management is allowed to tender shares. The
prices would go down because the market may conclude that the management is trying to unload
its shares.
22-10
I would recommend a split up of the firm into tobacco and food companies. A major barrier to
such an action might be covenants in bond agreements protecting bondholders who might be hurt
by such an action.
22-18
The positive reaction can be explained by several factors. First, the action suggested that the
management of the firm was aware they had a problem and were willing to deal with it. Second,
the split up units had more independence and were no longer burdened by the policies and
practices of the other units. Third, it allowed each of the split up units to reveal their assets and
earning power separately making it easier to value the component parts.
Chapter 24
24-4
a. Value of Novell Prior to Acquisition Announcement= 308 million*$23.75= $7.315 Billion
b. Value of the Novell After the Acquisition Announcement= 308*20= $6.160 Billion
Drop in Value of Novell= $7.315 Billion- $6.160 Billion= $1.155 Billion
If the entire drop is attributed to the decision to buy WordPerfect, the
Value assigned to WordPerfect= $1.4 Billion- $1.155 Billion= $245 million
c. Given the size of the drop in market value, it seems likely that market participants are reacting
not only to Novell’s acquisition of WordPerfect, but also to the implicit message sent by that
action on Novell’s own projects, i.e., that it does not have very many. It may also affect the
trepidation that markets feel about Novell’s plans to grow by acquiring other firms.
24-14
a. 0 1 2 3 4 5
1993 1994 1995 1996 1997 1998 1999
Revenues 450.00 477.00 505.62 535.96 568.11 602.20 632.31
(COGS %) 0.94 0.93 0.92 0.91 0.90 0.89 0.89
COGS 423.00 443.61 465.17 487.72 511.30 535.96 562.76
Deprec 26.00 27.56 29.21 30.97 32.82 34.79 36.53
EBIT 1.00 5.83 11.24 17.27 23.99 31.45 33.02
tax 0.40 2.33 4.49 6.91 9.59 12.58 13.21
EBIT(1-t) 0.60 3.50 6.74 10.36 14.39 18.87 19.81
Cap 38.00 40.28 42.70 45.26 47.97 50.85
Deprecn 26.00 27.56 29.21 30.97 32.82 34.79
WC 2.03 2.15 2.28 2.41 2.56 2.26
FCFF -11.25 -8.89 -6.21 -3.17 0.25 17.55
Terminal 300.95
value
FCFF+t.v. -11.25 -8.89 -6.21 -3.17 301.20
PV@11.02 $154.63
share price 2.745047
b. 0 1 2 3 4 5
1993 1994 1995 1996 1997 1998 1999
Revenues 450.00 477.00 505.62 535.96 568.11 602.20 632.31
(COGS %) 0.940 0.934 0.928 0.922 0.916 0.910 0.910
COGS 423.00 445.52 469.22 494.15 520.39 548.00 575.40
Deprec 26.00 27.56 29.21 30.97 32.82 34.79 36.53
EBIT 1.00 3.92 7.19 10.84 14.90 19.40 20.37
tax 0.40 1.57 2.88 4.34 5.96 7.76 8.15
EBIT(1-t) 0.60 2.35 4.31 6.50 8.94 11.64 12.22
Cap 38.00 40.28 42.70 45.26 47.97 50.85
Deprecn 26.00 27.56 29.21 30.97 32.82 34.79
WC 2.03 2.15 2.28 2.41 2.56 2.26
FCFF -12.39 -11.32 -10.06 -8.62 -6.97 9.97
Terminal 170.87
value
FCFF+t.v. -12.39 -11.32 -10.06 -8.62 163.89
PV@11.02 $63.80
share price 0
current cost of capital:
cost of 0.136
equity
after tax 0.054
cost of debt
WACC 0.1102
cost of capital after 98:
cost of 0.136
equity
after tax 0.048
cost of debt
WACC 0.1083
24-15
$Return on Capital $Cost of Capital EVA
AMR $1,080 $1,313 $(233)
Alaska Air $60 $56 $4
UAL $550 $615 $(65)
b. The firms with positive EVA would be considered healthy. To the extent that EVA is
negative for AMR and UAL, they are not creating value for their stockholders. Alaska Air, on
the other hand, created for their stockholders.
c. The EVA provides a measure of the efficiency of use of existing assets. To the extent that
Alaska Air has more growth expected, I would need to consider the quality of these projects as
well.
Chapter 25
25-10
Since there is disadvantage of receiving cash for the shareholders of the target firm, the acquiring
firm would naturally try to offer stock if possible.
25-14
Novell WordPerfect No Synergy w/ Synergy
Cost of Equity (Initial) 14.98% 13.88% 14.85%
Cost of Equity (Stable) 13.05% 13.05% 13.05%
The cost of equity is also the weighted average cost of capital because neither firm has any debt.
The weights are based upon the estimate values.
(The free cash flow to the firm under synergy in year 1 is greater than the sum of the FCFF of the two
individual firms because of the higher growth rate in cash flows. All the estimated numbers under
synergy are based upon the expected growth rate which is 24%.)
a.
Novell
0 1 2 3 4 5 6 7 8 9 10 11
rev 1200.00 1500.00 1875.00 2343.75 2929.69 3662.11 4577.64 5722.05 7152.56 8940.70 11175.87 11846.42
cogs 684.00 855.00 1068.75 1335.94 1669.92 2087.40 2609.25 3261.57 4076.96 5096.20 6370.25 6752.46
depr 42.00 52.50 65.63 82.03 102.54 128.17 160.22 200.27 250.34 312.92 391.16 414.62
ebit 474.00 592.50 740.63 925.78 1157.23 1446.53 1808.17 2260.21 2825.26 3531.58 4414.47 4679.34
ebit(1-t) 308.10 385.13 481.41 601.76 752.20 940.25 1175.31 1469.14 1836.42 2295.52 2869.40 3041.57
-capex 75.00 93.75 117.19 146.48 183.11 228.88 286.10 357.63 447.03 558.79 698.49
+depr 42.00 52.50 65.63 82.03 102.54 128.17 160.22 200.27 250.34 312.92 391.16
-wc 120.00 150.00 187.50 234.38 292.97 366.21 457.76 572.20 715.26 894.07 268.22
fcff 223.88 279.84 349.80 437.26 546.57 683.21 854.02 1067.52 1334.40 1668.00 2773.35
tv 39338.27
fcff + tv 223.88 279.84 349.80 437.26 546.57 683.21 854.02 1067.52 1334.40 41006.27
value 12658.93
WP
0 1 2 3 4 5 6 7 8 9 10 11
rev 600.00 690.00 793.50 912.53 1049.40 1206.81 1387.84 1596.01 1835.41 2110.73 2427.33 2572.97
cogs 450.00 517.50 595.13 684.39 787.05 905.11 1040.88 1197.01 1376.56 1583.04 1820.50 1929.73
depr 25.00 28.75 33.06 38.02 43.73 50.28 57.83 66.50 76.48 87.95 101.14 107.21
ebit 125.00 143.75 165.31 190.11 218.63 251.42 289.13 332.50 382.38 439.73 505.69 536.04
ebit(1-t) 81.25 93.44 107.45 123.57 142.11 163.42 187.94 216.13 248.55 285.83 328.70 348.42
-capex 40.00 46.00 52.90 60.84 69.96 80.45 92.52 106.40 122.36 140.72 161.82
+depr 25.00 28.75 33.06 38.02 43.73 50.28 57.83 66.50 76.48 87.95 101.14
-wc 27.00 31.05 35.71 41.06 47.22 54.31 62.45 71.82 82.59 94.98 43.69
fcff 49.19 56.57 65.05 74.81 86.03 98.93 113.77 130.84 150.47 173.04 304.73
tv 4322.43
fcff + tv 49.19 56.57 65.05 74.81 86.03 98.93 113.77 130.84 150.47 4495.47
b. value 1629.84
c. $14,288.77
d. combined; synergy
0 1 2 3 4 5 6 7 8 9 10 11
rev 1800.00 2232.00 2767.68 3431.92 4255.58 5276.93 6543.39 8113.80 10061.11 12475.78 15469.97 16398.16
cogs 1134.00 1406.16 1743.64 2162.11 2681.02 3324.46 4122.33 5111.69 6338.50 7859.74 9746.08 10330.84
depr 67.00 83.08 103.02 127.74 158.40 196.42 243.56 302.01 374.50 464.38 575.83 610.38
ebit 599.00 742.76 921.02 1142.07 1416.16 1756.04 2177.49 2700.09 3348.11 4151.66 5148.06 5456.94
ebit(1-t) 389.35 482.79 598.66 742.34 920.51 1141.43 1415.37 1755.06 2176.27 2698.58 3346.24 3547.01
-capex 115.00 142.60 176.82 219.26 271.88 337.14 418.05 518.38 642.79 797.06 988.36
+depr 67.00 83.08 103.02 127.74 158.40 196.42 243.56 302.01 374.50 464.38 575.83
-wc 158.4 196.42 243.56 302.01 374.49 464.37 575.82 714.01 885.38 1097.87 340.3
fcff 264.87 328.44 407.27 505.02 626.22 776.51 962.87 1193.96 1480.51 1835.84 3206.67
tv 45484.75
fcff + tv 264.87 328.44 407.27 505.02 626.22 776.51 962.87 1193.96 1480.51 47320.59
value 14726.57
e. $437.80
25-16
a. Value of Synergy Pre-merger Post-merger
Value of Aetna 22,800 21,800
Value of U.S. Healthcare 1,550 1,875
Total 24,350 23,675
The total market value of the two firms declined by $675 million after the merger was announced. This
would suggest that the market does not believe that there is synergy.
b. Managers may be over optimistic about the potential for synergy, while markets might be much too
pessimistic. I would tend to believe the markets.
25-22
a. No. The stockholders could do it themselves at far lower costs.
b. Yes. Diversification may provide a benefit to the owner of a private firm, since much of his or her
wealth is probably concentrated in the firm.
c. If by doing this acquisition, the publicly traded firm was able to increase its debt capacity
substantially and take better projects, it might make sense to do the acquisition.
