Chapter 8 Problem 12 Suggested Answers
a).
Facts and Assumptions
Initial cost ($000 omitted) 28,000$
Unit sales (000 0mitted) 400
Selling price per unit, this year 60$
Variable cost per unit, this year 42$
Life expectancy (years) 8
Salvage value $0
Depreciation Straight line
Tax rate 37%
Nominal discount rate 10.0%
Real discount rate 10.0%
Inflation rate 0.0%
Year 0 1 2 3 4 5 6 7 8
Initial cost 28,000$
Annual sales (units) 400 400 400 400 400 400 400 400
Price per unit 60 60 60 60 60 60 60 60
Variable cost per unit 42 42 42 42 42 42 42 42
Revenue 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000
Variable cost 16,800 16,800 16,800 16,800 16,800 16,800 16,800 16,800
Depreciation 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500
Income before tax 3,700 3,700 3,700 3,700 3,700 3,700 3,700 3,700
Tax 1,369 1,369 1,369 1,369 1,369 1,369 1,369 1,369
Income after tax 2,331 2,331 2,331 2,331 2,331 2,331 2,331 2,331
Free Cash Flow (28,000)$ 5,831 5,831 5,831 5,831 5,831 5,831 5,831 5,831
b).
IRR 13.0%
NPV @ nominal rate $3,108
In “Facts and assumptions” above, change the inflation rate to 8%.
IRR 20.2%
NPV @ nominal rate $1,351
d).
The IRR increases because inflation causes nominal future cash flows to rise.
The NPV falls because the real value of depreciation tax shields falls in the presence of inflation.
e).
The investment is less attractive in the presence of inflation. The NPV falls. In addition, the difference between the IRR and the nominal discount rate also falls.
Absent inflation the spread is 3.0% (13.0% – 10%). With inflation, the spread falls to 1.4% (20.2% – 18.8%). Alternatively, note that the present value of income
taxes paid, discounted at the nominal discount rate rises from $7,303.51 in the absence of inflation to $9,060.07 with inflation. Not coincidentally, the increase
in the present value of taxes paid precisely equals the decline in the investment’s NPV. Inflation is a silent tax on corporate investment.
Chapter 8 Problem 17 Suggested Answers
Assumptions
Discount Rate 0.15
Cost 425 PV(cost) 321
Stage 2: Option to Expand, Probability of Success (Assuming Stage 1 Successful) = 90%
Invest $425 million in year 2 if Stage 1 is successful (present value at 15% = $321)
Present
Value
1 2 3 4 5 67
Success $634 0 0 250 250 250 250 250
Failure $63 0 0 (50) (50) 250 0 0
NPV_Stage 2 $27 =(.5 x $634 + .5 x $63 – 321) (before knowing outcome of stage 1)
NPV_Stage 2 $255 =(.9 x $634 + .1 x $63 – 321) (conditional on knowing stage 1 is successful)
Total Project NPV $135 =($7 + $128) (conditional on knowing stage 1 is successful)
Expected After-Tax Cash Flows
Chapter 8 Problem 19 Suggested Answers
Assumptions
Discount Rate (Stage 1) 0.15
Discount Rate (Stage 2) 0.1
Cost (at time 2) 425
Stage 2: Option to Expand, Probability of Success (Assuming Stage 1 Successful) = 90%
Lower discount rate of 10% for Stage 2
Invest $425 million in year 2 if Stage 1 is successful
1234567
Success 0 0 250 250 250 250 250
Failure 0 0 (50) (50) 250 0 0
NPV (today) Stage 1 $7 From Table 8.6(b)
Calculations as of Time 2
NPV(Success) $948
NPV (Failure) $101
Expected payoff time 2 $863 =(0.9 x $948 + 0.1 x $101)
NPV time 2 $438 =(0.9 x $948 + 0.1 x $101 – $425)
Calculations as of Time 0
NPV (today) of stage 2 $331 =($438/(1+.15)^2)
Expected NPV(today) of stage 2 $166 =(0.5 x $331)
NPV(today) of .5 stage 2 and stage 1 $173 =($166 + $7)
Chapter 8 Problem 20
Facts and Assumptions
Yield to maturity on long-term government bonds
4.54%
Yield to maturity on company long-term bonds 6.32%
Coupon rate on company long-term bonds 7.50%
Market price of risk, or risk premium 6.30%
Estimated company equity beta 1.05
Stock price per share 25.97$
Number of shares outstanding 681.2 million
Book value of equity 4,965$ million
Book value of interest-bearing debt 6,674$ million
Tax rate 35.0%
a. Estimate Kroger’s cost of equity capital.
b.
Estimate Kroger’s weighted-average cost of capital. Prepare a spreadsheet or table showing the relevant
variables.
Key facts and assumptions concerning Kroger Company, at December 12, 2007, appear below. Using this
information, answer the questions following.
Chapter 8 Problem 20 Suggested Answers
Facts and Assumptions
Yield to maturity on long-term government bonds 4.54%
Yield to maturity on company long-term bonds 6.32%
Coupon rate on company long-term bonds 7.50%
Market price of risk, or excess return 6.30%
Estimated company equity beta 1.05
Stock price per share 25.97$
Number of shares outstanding 681.2 million
Book value of equity 4,965$ million
Book value of interest-bearing debt 6,674$ million
Tax rate 35.0%
a.
KE = gov’t borrowing rate + equity beta*market risk premium
KE = 11.2%
b. Calculation of Kroger’s Cost of Capital
Source
Amount ($
millions)
Percentage
of Total
Cost after
tax
Weighted
Cost
Debt 6,674.00$ 27.4% 4.1% 1.1%
Equity 17,690.76$ 72.6% 11.2% 8.1%
Cost of Capital = 9.2%
Chapter 8 Problem 21
Company
Equity
beta
Interest-
Bearing
Debt
Market
value equity
Kroger Company 1.05 6,674.0$ 17,690.8$
Safeway Inc. 0.49 5,897.9 15,236.3
Supervalu Inc. 1.17 8,936.0 8,054.3
Whole Foods Markets 1.16 760.9 5,762.1
Winn Dixie Stores Inc. 2.56 160.1 916.8 .
a.
b.
Relever the industry asset beta to reflect Kroger’s capital structure, and to
make another (industry-informed) estimate of Kroger’s equity beta.
Information regarding Kroger Company, and four industry competitors is shown
below, on December 12, 2007.
Estimate the industry asset beta, weighting each company by its proportion
of total market value of equity.
Chapter 8 Problem 21 Suggested Answers
a.
Company Equity beta
Interest-
Bearing
Debt
Market value
equity
Equity/firm
value
Asset beta
% Total
Market value
equity
Weighted
asset beta
Kroger Company 1.05 6,674.0$ 17,690.8$ 72.6% 0.76 37.1% 0.28
Safeway Inc. 0.49 5,897.9 15,236.3 72.1% 0.35 32.0% 0.11
Supervalu Inc. 1.17 8,936.0 8,054.3 47.4% 0.55 16.9% 0.09
Whole Foods Markets 1.16 760.9 5,762.1 88.3% 1.02 12.1% 0.12
Winn Dixie Stores Inc. 2.56 160.1 916.8 85.1% 2.18 1.9% 0.04
Industry asset beta 0.66
b.
Equity beta =
Value /
Equity
x
Industry asset
beta
Equity beta = 1.38 x 0.66
Equity beta = 0.90
The table below estimates the industry asset beta, with each company weighted by
its proportion of total market value of equity.
To relever the industry asset beta: