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Unformatted text preview: Chapter 18
Capital Budgeting and Valuation with Leverage 18.1 Overview
1) Which of the following is not one of the simplifying assumptions made for the three main methods of
capital budgeting?
A) The firm pays out all earnings as dividends.
B) The project has average risk.
C) Corporate taxes are the only market imperfection.
D) The firm’s debt equity ratio is constant.
Answer: A
Diff: 1
Skill: Conceptual 18.2 The Weighted Average Cost of Capital Method
1) Which of the following statements is false?
A) Because the WACC incorporates the tax savings from debt, we can compute the levered value of
an investment, which is its value including the benefit of interest tax shields given the firmʹs
leverage policy, by discounting its future free cash flow using the WACC.
B) The WACC incorporates the benefit of the interest tax shield by using the firmʹs before  tax cost
of capital for debt.
C) When the market risk of the project is similar to the average market risk of the firmʹs
investments, then its cost of capital is equivalent to the cost of capital for a portfolio of all of the
firmʹs securities; that is, the projectʹs cost of capital is equal to the firm’s weighted average cost of
capital (WACC).
D) A projectʹs cost of capital depends on its risk.
Answer: B
Diff: 1
Skill: Conceptual Chapter 18 Capital Budgeting and Valuation with Leverage 499 2) Which of the following statements is false?
A) The WACC can be used throughout the firm as the company wide cost of capital for new
investments that are of comparable risk to the rest of the firm and that will not alter the firm’s
debt  equity ratio.
B) A disadvantage of the WACC method is that you need to know how the firmʹs leverage policy is
implemented to make the capital budgeting decision.
C) The intuition for the WACC method is that the firmʹs weighted average cost of capital represents
the average return the firm must pay to its investors (both debt and equity holders) on an
after tax basis.
D) To be profitable, a project should generate an expected return of at least the firmʹs weighted
average cost of capital.
Answer: B
Diff: 1
Skill: Conceptual 3) Which of the following is not a step in the WACC valuation method?
A) Compute the value of the investment, including the tax benefit of leverage, by discounting the
free cash flow of the investment using the WACC.
B) Compute the weighted average cost of capital.
C) Determine the free cash flow of the investment.
D) Adjust the WACC for the firmʹs current debt/equity ratio.
Answer: D
Diff: 1
Skill: Conceptual 4) Consider the following equation:
E
D
rwacc = r + r (1  τc)
E + D E E + D D
the term E in this equation is?
A) the dollar amount of equity.
B) the dollar amount of debt
C) the required rate of return on debt
D) the required rate of return on equity
Answer: A
Diff: 1
Skill: Conceptual 500 Berk/DeMarzo · Corporate Finance 5) Consider the following equation:
D
E
r + r (1  τc)
rwacc = E + D E E + D D
the term D in this equation is?
A) the dollar amount of debt
B) the required rate of return on equity
C) the required rate of return on debt
D) the dollar amount of equity.
Answer: A
Diff: 1
Skill: Conceptual 6) Consider the following equation:
E
D
rwacc = r + r (1  τc)
E + D E E + D D
the term rE in this equation is?
A) the after tax required rate of return on debt
B) the required rate of return on debt
C) the required rate of return on equity
D) the dollar amount of equity.
Answer: C
Diff: 1
Skill: Conceptual 7) Consider the following equation:
E
D
rwacc = r + r (1  τc)
E + D E E + D D
the term rD(1  τc) in this equation is?
A) the required rate of return on debt
B) the dollar amount of equity.
C) the after tax required rate of return on debt
D) the required rate of return on equity
Answer: C
Diff: 1
Skill: Conceptual Chapter 18 Capital Budgeting and Valuation with Leverage 501 8) Consider the following equation:
L
Dt = d × V t
the term Dt in this equation is?
A) the firms target debt to value ratio.
B) the firms target debt to equity ratio.
C) the investmentʹs debt capacity.
D) the dollar amount of debt outstanding at time t.
Answer: C
Diff: 2
Skill: Conceptual 9) Consider the following equation:
L
Dt = d × V t
the term d in this equation is?
A) the firms target debt to value ratio.
B) the dollar amount of debt outstanding at time t.
C) the firms target debt to equity ratio.
D) the investmentʹs debt capacity.
Answer: A
Diff: 2
Skill: Conceptual 502 Berk/DeMarzo · Corporate Finance Use the table for the question(s) below.
Consider the information for the following four firms:
Firm Cash Eenie
Meenie
Minie
Moe Debt Equity 0
0
25
50 150
250
175
350 150
750
325
150 rD
5%
6%
6%
7.50% rE
10%
12%
11%
15% τc
40%
35%
35%
30% 10) The weighted average cost of capital for ʺEenieʺ is closest to:
A) 6.0%
B) 6.5%
C) 7.5%
D) 5.5%
Answer: B
Explanation: B) rwacc = Firm
Eenie
Meenie
Minie
Moe E
D rE + r (1  τc), where D = net debt = Debt  Cash
E + D
E + D D Cash Debt Equity
0
0
25
50 150
250
175
350 150
750
325
150 rD
5%
6%
6%
7.50% rE
10%
12%
11%
15% τc
40%
35%
35%
30% Wacc
6.50%
9.98%
8.76%
8.50% Diff: 1
Skill: Analytical 11) The weighted average cost of capital for ʺMeenieʺ is closest to:
A) 10.5%
B) 7.4%
C) 10.0%
D) 8.8%
Answer: C
Explanation: E
D
C) rwacc = r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D Firm
Eenie
Meenie
Minie
Moe Diff: 1
Skill: Analytical Cash Debt Equity
0
0
25
50 150
250
175
350 150
750
325
150 rD
5%
6%
6%
7.50% rE
10%
12%
11%
15% τc
40%
35%
35%
30% Wacc
6.50%
9.98%
8.76%
8.50% Chapter 18 Capital Budgeting and Valuation with Leverage 503 12) The weighted average cost of capital for ʺMinieʺ is closest to:
A) 9.50%
B) 8.75%
C) 6.75%
D) 8.25%
Answer: B
Explanation: B) rwacc = Firm
Eenie
Meenie
Minie
Moe E
D r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D Cash Debt Equity
0
0
25
50 150
250
175
350 150
750
325
150 rD
5%
6%
6%
7.50% rE
10%
12%
11%
15% τc
40%
35%
35%
30% Wacc
6.50%
9.98%
8.76%
8.50% Diff: 2
Skill: Analytical 13) The weighted average cost of capital for ʺMoeʺ is closest to:
A) 10.00%
B) 7.75%
C) 8.25%
D) 8.50%
Answer: D
Explanation: D) rwacc = Firm
Eenie
Meenie
Minie
Moe Diff: 2
Skill: Analytical E
D rE + r (1  τc), where D = net debt = Debt  Cash
E + D
E + D D Cash Debt Equity
0
0
25
50 150
250
175
350 150
750
325
150 rD
5%
6%
6%
7.50% rE
10%
12%
11%
15% τc
40%
35%
35%
30% Wacc
6.50%
9.98%
8.76%
8.50% 504 Berk/DeMarzo · Corporate Finance Use the information for the question(s) below.
Omicron Industriesʹ Market Value Balance Sheet ($ Millions) and Cost of Capital
Assets
Liabilities
Cost of Capital
Cash
0
Debt
200
Debt
Other Assets
500
Equity
300
Equity
τc
Omicron Industries New Project Free Cash Flows
Year
0
1
2
Free Cash Flows
($100)
$40
$50 6%
12%
35% 3
$60 Assume that this new project is of average risk for Omicron and that the firm wants to hold constant its debt to
equity ratio.
14) Omicronʹs weighted average cost of capital is closest to:
A) 7.10%
B) 7.50%
C) 9.60%
D) 8.75%
Answer: D
Explanation: D) rwacc = E
D r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D 300
200
rwacc = (.12) + (.06)(1  .35) = .0876
300 + 200
300 + 200
Diff: 1
Skill: Analytical 15) The NPV for Omicronʹs new project is closest to:
A) $23.75
B) $27.50
C) $28.75
D) $25.75
Answer: D
Explanation: D) rwacc = E
D r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D 300
200
rwacc = (.12) + (.06)(1  .35) = .0876
300 + 200
300 + 200
NPV =  100 + Diff: 2
Skill: Analytical 40
(1.0876) 1 + 50
(1.0876) 2 + 60
(1.0876) 3 = $25.69 Chapter 18 Capital Budgeting and Valuation with Leverage 505 16) The Debt Capacity for Omicronʹs new project in year 0 is closest to:
A) $38.75
B) $75.50
C) $50.25
D) $10.25
Answer: C
Explanation: E
D
C) rwacc = r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D 300
200
rwacc = (.12) + (.06)(1  .35) = .0876
300 + 200
300 + 200
L
V 0 = 40
(1.0876) 1 + 50
(1.0876) 2 + 60
(1.0876) 3 = $125.69 L
D0 = d × V 0
200 ($125.69) = $50.28
D0 = 300 + 200
Diff: 3
Skill: Analytical 17) The Debt Capacity for Omicronʹs new project in year 1 is closest to:
A) $38.75
B) $48.25
C) $50.25
D) $58.00
Answer: A
Explanation: A) rwacc = E
D r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D 300
200
rwacc = (.12) + (.06)(1  .35) = .0876
300 + 200
300 + 200
L
V 1 = 50
(1.0876) 1 + 60
(1.0876) 2 = $96.70 L
D1 = d × V 1
200 ($96.70) = $38.68
D1 = 300 + 200
Diff: 3
Skill: Analytical 506 Berk/DeMarzo · Corporate Finance 18) The Debt Capacity for Omicronʹs new project in year 2 is closest to:
A) $55.25
B) $38.75
C) $22.00
D) $33.00
Answer: C
Explanation: E
D
C) rwacc = r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D
300
200
rwacc = (.12) + (.06)(1  .35) = .0876
300 + 200
300 + 200
L
V 2 = 60
(1.0876) 1 = $55.17 L
D2 = d × V 2
200 ($55.17) = $22.06
D2 = 300 + 200
Diff: 2
Skill: Analytical Chapter 18 Capital Budgeting and Valuation with Leverage 507 Use the information for the question(s) below.
Iota Industries Market Value Balance Sheet ($ Millions) and Cost of Capital
Assets
Liabilities
Cost of Capital
Cash
250
Debt
650
Debt
7%
Other Assets
1200
Equity
800
Equity
14%
τc
35%
Iota Industries New Project Free Cash Flows
Year
0
1
2
Free Cash Flows
($250)
$75
$150 3
$100 Assume that this new project is of average risk for Iota and that the firm wants to hold constant its debt to equity
ratio.
19) Iotaʹs weighted average cost of capital is closest to:
A) 8.40%
B) 9.75%
C) 10.85%
D) 11.70%
Answer: C
Explanation: D
E r + r (1  τc), where D = net debt = Debt  Cash
C) rwacc = E + D E E + D D 800
400
rwacc = (.14) + (.07)(1  .35) = .1085
800 + 400
800 + 400 Diff: 3
Skill: Analytical 20) The NPV for Iotaʹs new project is closest to:
A) $25.25
B) $13.25
C) $9.00
D) $18.50
Answer: B
Explanation: B) rwacc = E
D rE + r (1  τc), where D = net debt = Debt  Cash
E + D
E + D D 800
400
rwacc = (.14) + (.07)(1  .35) = .1085
800 + 400
800 + 400
NPV =  250 + Diff: 2
Skill: Analytical 75
(1.1085) 1 + 150
(1.1085) 2 + 100
(1.1085) 3 = $13.14 508 Berk/DeMarzo · Corporate Finance 21) The Debt Capacity for Iotaʹs new project in year 0 is closest to:
A) $263.25
B) 87.75
C) $50.25
D) $118.00
Answer: B
Explanation: B) rwacc = E
D r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D 800
400
rwacc = (.14) + (.07)(1  .35) = .1085
800 + 400
800 + 400
V 0 L = 75
(1.1085) 1 + 150
(1.1085) 2 + 100
(1.1085) 3 = $263.14 L
D0 = d × V 0
400 ($263.14) = $87.71
D0 = 800 + 400
Diff: 3
Skill: Analytical 22) Calculate the NPV for Iotaʹs new project.
D
E r + r (1  τc), where D = net debt = Debt  Cash
Answer: rwacc = E + D E E + D D 800
400
rwacc = (.14) + (.07)(1  .35) = .1085
800 + 400
800 + 400
NPV =  250 + 75
(1.1085) 1 + 150
(1.1085) 2 + 100
(1.1085) 3 = $13.14 Diff: 3
Skill: Analytical Use the information for the question(s) below.
Omicron Industriesʹ Market Value Balance Sheet ($ Millions) and Cost of Capital
Assets
Liabilities
Cost of Capital
Cash
0
Debt
200
Debt
Other Assets
500
Equity
300
Equity
τc
Omicron Industries New Project Free Cash Flows
Year
0
1
2
Free Cash Flows
($100)
$40
$50 6%
12%
35% 3
$60 Assume that this new project is of average risk for Omicron and that the firm wants to hold constant its debt to
equity ratio.
23) Calculate the debt capacity of Omicronʹs new project for years 0, 1, and 2. Chapter 18 Capital Budgeting and Valuation with Leverage 509 E
D
Answer: rwacc = r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D 300
200
rwacc = (.12) + (.06)(1  .35) = .0876
300 + 200
300 + 200
Year 0
L
V 0 = 40
(1.0876) 1 + 50
(1.0876) 2 + 60
(1.0876) 3 = $125.69 L
D0 = d × V 0
200 ($125.69) = $50.28
D0 = 300 + 200
Year 1
L
V 1 = 50
(1.0876) 1 + 60
(1.0876) 2 = $96.70 L
D1 = d × V 1
200 ($96.70) = $38.68
D1 = 300 + 200
Year 2
L
V 2 = 60
(1.0876) 1 = $55.17 L
D2 = d × V 2
200 ($55.17) = $22.06
D2 = 300 + 200
Diff: 3
Skill: Analytical 24) Suppose Luther Industries is considering divesting one of its product lines. The product line is
expected to generate free cash flows of $2 million per year, growing at a rate of 3% per year. Luther
has an equity cost of capital of 10%, a debt cost of capital of 7%, a marginal tax rate of 35%, and a
debt  equity ratio of 2. If this product line is of average risk and Luther plans to maintain a constant
debt  equity ratio, what after tax amount must it receive for the product line in order for the
divestiture to be profitable?
2
1
Answer: rwacc = (.10) + (.07)(1  .35) = .063667
3
3
L
$2 million = $59.406 million
V 0 = .063667  .03
Diff: 2
Skill: Analytical 510 Berk/DeMarzo · Corporate Finance 18.3 The Adjusted Present Value Method
1) Which of the following is not a step in the adjusted present value method?
A) Deducting costs arising from market imperfections
B) Calculating the unlevered value of the project
C) Calculating the after  tax WACC
D) Calculating the value of the interest tax shield
Answer: C
Diff: 2
Skill: Conceptual 2) Which of the following statements is false?
A) The firmʹs unlevered cost of capital is equal to its pretax weighted average cost of capital–that is,
using the pretax cost of debt, rd , rather than its after  tax cost, rd (1  τc ).
B) A firmʹs levered cost of capital is a weighted average of its equity and debt costs of capital.
C) When the firm maintains a target leverage ratio, its future interest tax shields have similar risk to
the projectʹs cash flows, so they should be discounted at the projectʹs unlevered cost of capital.
D) The first step in the APV method is to calculate the value of free cash flows using the projectʹs
cost of capital if it were financed without leverage.
Answer: B
Diff: 2
Skill: Conceptual 3) Which of the following statements is false?
A) To determine the projectʹs debt capacity for the interest tax shield calculation, we need to know
the value of the project.
B) To compute the present value of the interest tax shield, we need to determine the appropriate
cost of capital.
C) Because we don’t value the tax shield separately, with the APV method we need to include the
benefit of the tax shield in the discount rate as we do in the WACC method.
D) A target leverage ratio means that the firm adjusts its debt proportionally to the project’s value
or its cash flows.
Answer: C
Diff: 2
Skill: Conceptual Chapter 18 Capital Budgeting and Valuation with Leverage 511 4) Which of the following statements is false?
A) The APV approach explicitly values the market imperfections and therefore allows managers to
measure their contribution to value.
B) We need to know the debt level to compute the APV, but with a constant debt  equity ratio we
need to know the projectʹs value to compute the debt level.
C) The WACC method is more complicated than the APV method because we must compute two
separate valuations: the unlevered project and the interest tax shield.
D) Implementing the APV approach with a constant debt  equity ratio requires solving for the
projectʹs debt and value simultaneously.
Answer: C
Diff: 2
Skill: Conceptual Use the table for the question(s) below.
Consider the information for the following four firms:
Firm
Eenie
Meenie
Minie
Moe Cash Debt Equity 0
0
25
50 150
250
175
350 150
750
325
150 rD
5%
6%
6%
7.50% rE
10%
12%
11%
15% τc
40%
35%
35%
30% 5) The unlevered cost of capital for ʺEenieʺ is closest to:
A) 6.0%
B) 5.5%
C) 7.5%
D) 6.5%
Answer: C
Explanation: E
D
C) runlevered = r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D Firm
Eenie
Meenie
Minie
Moe Diff: 1
Skill: Analytical Cash
0
0
25
50 Debt Equity
150
250
175
350 150
750
325
150 rD
5%
6%
6%
7.50% rE
10%
12%
11%
15% τc
40%
35%
35%
30% runlevered
7.50%
10.50%
9.42%
10.00% 512 Berk/DeMarzo · Corporate Finance 6) The unlevered cost of capital for ʺMoeʺ is closest to:
A) 8.25%
B) 7.75%
C) 8.50%
D) 10.00%
Answer: D
Explanation: D) runlevered = Firm
Eenie
Meenie
Minie
Moe E
D r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D Cash
0
0
25
50 Debt Equity
150
250
175
350 150
750
325
150 rD
5%
6%
6%
7.50% rE
10%
12%
11%
15% τc
40%
35%
35%
30% runlevered
7.50%
10.50%
9.42%
10.00% Diff: 2
Skill: Analytical Use the information for the question(s) below.
Suppose Luther Industries is considering divesting one of its product lines. The product line is expected to
generate free cash flows of $2 million per year, growing at a rate of 3% per year. Luther has an equity cost of
capital of 10%, a debt cost of capital of 7%, a marginal tax rate of 35%, and a debt  equity ratio of 2. This product
line is of average risk and Luther plans to maintain a constant debt  equity ratio.
7) Lutherʹs Unlevered cost of capital is closest to:
A) 8.0%
B) 8.5%
C) 9.0%
D) 6.4%
Answer: A
Explanation:
Diff: 2
Skill: Analytical 1
2
A) runlevered = (.10) + (.07) = .08 or 8%
3
3 Chapter 18 Capital Budgeting and Valuation with Leverage 513 8) The unlevered value of Lutherʹs Product Line is closest to:
A) $25 million
B) $60 million
C) $45 million
D) $40 million
Answer: D
Explanation: 1
2
D) runlevered = (.10) + (.07) = .08 or 8%
3
3
V U = $2 million = $40 million
.08  .03 Diff: 2
Skill: Analytical Use the information for the question(s) below.
Omicron Industriesʹ Market Value Balance Sheet ($ Millions) and Cost of Capital
Assets
Liabilities
Cost of Capital
Cash
0
Debt
200
Debt
Other Assets
500
Equity
300
Equity
τc
Omicron Industries New Project Free Cash Flows
Year
0
1
2
Free Cash Flows
($100)
$40
$50 6%
12%
35% 3
$60 Assume that this new project is of average risk for Omicron and that the firm wants to hold constant its debt to
equity ratio.
9) Omicronʹs Unlevered cost of capital is closest to:
A) 8.75%
B) 7.10%
C) 9.60%
D) 7.50%
Answer: C
Explanation: E
D
C) runlevered = r + r , where D = net debt = Debt  Cash
E + D E E + D D
300
200
runlevered = (.12) + (.06) = .096
300 + 200
300 + 200 Diff: 1
Skill: Analytical 514 Berk/DeMarzo · Corporate Finance 10) The unlevered value of Omicronʹs new project is closest to:
A) $96
B) $124
C) $126
D) $25
Answer: B
Explanation: B) runlevered = E
D r + r , where D = net debt = Debt  Cash
E + D E E + D D 300
200
runlevered = (.12) + (.06) = .096
300 + 200
300 + 200
V U = 40
(1.096)1 + 50
(1.096)2 + 60
(1.096)3 = $123.70 Diff: 2
Skill: Analytical 11) The interest tax shield provided by Omicronʹs new project in year 1 is closest to:
A) $3.00
B) $1.05
C) $50.25
D) $17.60
Answer: B
Explanation: B) rwacc = E
D r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D 300
200
rwacc = (.12) + (.06)(1  .35) = .0876
300 + 200
300 + 200
L
V 0 = 40
(1.0876) 1 + 50
(1.0876) 2 + 60
(1.0876) 3 = $125.69 L
D0 = d × V 0
200 ($125.69) = $50.28
D0 = 300 + 200
So, Interest tax shield in year 1 = 50.28(.06)(.35) = 1.055880 or 1.06
Diff: 3
Skill: Analytical Chapter 18 Capital Budgeting and Valuation with Leverage 515 Use the information for the question(s) below.
Suppose that Rose Industries is considering the acquisition of another firm in its industry for $100 million. The
acquisition is expected to increase Roseʹs free cash flow by $5 million the first year, and this contribution us
expected to grow at a rate of 3% every year there after. Rose currently maintains a debt to equity ratio of 1, its
marginal tax rate is 40%, its cost of debt rD is 6%, and its cost of equity rE is 10%. Rose Industries will maintain a
constant debt  equity ratio for the acquisition.
12) Roseʹs unlevered cost of capital is closest to:
A) 8.0%
B) 7.5%
C) 7.0%
D) 9.0%
Answer: A
Explanation: A) runlevered = E
D r + r , where D = net debt = Debt  Cash
E + D E E + D D 1
1
runlevered = (.10) + (.06) = .08
1 + 1
1 + 1
Diff: 1
Skill: Analytical 13) The unlevered value of Roseʹs acquisition is closest to:
A) $63 million
B) $50 million
C) $167 million
D) $100 million
Answer: D
Explanation: D) runlevered = E
D r + r , where D = net debt = Debt  Cash
E + D E E + D D 1
1
runlevered = (.10) + (.06) = .08
1 + 1
1 + 1
V U = Diff: 2
Skill: Analytical 5 = $100 million
.08  .03 516 Berk/DeMarzo · Corporate Finance 14) Given that Rose issues new debt of $50 million initially to fund the acquisition, the present value of
the interest tax shield for this acquisition is closest to:
A) $24 million
B) $50 million
C) $20 million
D) $15 million
Answer: A
Explanation: A) runlevered = E
D r + r , where D = net debt = Debt  Cash
E + D E E + D D 1
1
runlevered = (.10) + (.06) = .08
1 + 1
1 + 1
Interest tax shield in first year = $50(.06)(.40) = $1.2 million
1.2 = $24 million
PV (tax shield) = .08  .03
Diff: 3
Skill: Analytical 15) Given that Rose issues new debt of $50 million initially to fund the acquisition, the total value of this
acquisition using the APV method is closest to:
A) $100 million
B) $120 million
C) $124 million
D) $115 million
Answer: C
Explanation: E
D
C) runlevered = r + r (1  τc), where D = net debt = Debt  Cash
E + D E E + D D 1
1
runlevered = (.10) + (.06) = .08
1 + 1
1 + 1
V U = 5 = $100 million
.08  .03 Interest tax shield in first year = $50(.06)(.40) = $1.2 million
1.2 = $24 million
PV (tax shield)= .08  .03
V L = V U + PV (interest tax shield) = $100 million + $24 million = $124 million
Diff: 3
Skill: Analytical Use the information for the question(s) below.
Omicron Industriesʹ Market Value Balance Sheet ($ Millions) and Cost of Capital
Assets
Liabilities
Cost of Capital
Cash
0
Debt
200
Debt
Other Assets
500
Equity
300
Equity
τc 6%
12%
35% Chapter 18 Capital Budgeting and Valuation with Leverage 517 Omicron Industries New Project Free Cash Flows
Year
0
1
2
Free Cash Flows
($100)
$40
$50 3
$60 Assume that this new project is of average risk for Omicron and that the firm wants to hold constant its debt to
equity ratio.
16) Calculate the present value of the interest tax shield provided by Omicronʹs new project.
D
E r + r (1  τc), where D = net debt = Debt  Cash
Answer: rwacc = E + D E E + D D 300
200
rwacc = (.12) + (.06)(1  .35) = .0876
300 + 200
300 + 200
Year 0
L
V 0 = 40
(1.0876) 1 + 50
(1.0876) 2 + 60
(1.0876) 3 = $125.69 L
D0 = d × V 0
200 ($125.69) = $50.28
D0 = 300 + 200
Interest tax shield year 1 = 50.28(.06)(.35) = 1.055880 or 1.06
Year 1
L
V 1 = 50
(1.0876) 1 + 60
(1.0876) 2 = $96.70 L
D1 = d × V 1
200 ($96.70) = $38.68
D1 = 300 + 200
Interest tax shield year 2 = 38.68(.06)(.35) = 0.812280 or .81
Year 2
L
V 2 = 60
(1.0876) 1 = $55.17 L
D2 = d × V 2
200 ($55.17) = $22.06
D2 = 300 + 200
Interest tax shield year 3 = 22.06(.06)(.35) = 0.463260 or .46
D
E r + r , where D = net debt = Debt  Cash
runlevered = E + D E E + D D
300
200
runlevered = (.12) + (.06) = .096
300 + 200
300 + 200
PV of tax shield = 1.06
.81
.46 + + = 1.99
1.096 (1.096)2 (1.096)3 518 Berk/DeMarzo · Corporate Finance Diff: 3
Skill: Analytical Use the information for the question(s) below.
Suppose that Rose Industries is considering the acquisition of another firm in its industry for $100 million. The
acquisition is expected to increase Roseʹs free cash flow by $5 million the first year, and this contribution us
expected to grow at a rate of 3% every year there after. Rose currently maintains a debt to equity ratio of 1, its
marginal tax rate is 40%, its cost of debt rD is 6%, and its cost of equity rE is 10%. Rose Industries will maintain a
constant debt  equity ratio for the acquisition.
17) Given that Rose issues new debt of $50 million initially to fund the acquisition, the total value of this
acquisition using the APV method is equal to?
D
E r + r (1  τc), where D = net debt = Debt  Cash
Answer: runlevered = E + D E E + D D 1
1
runlevered = (.10) + (.06) = .08
1 + 1
1 + 1
V U = 5 = $100 million
.08  .03 Interest tax shield in first year = $50(.06)(.40) = $1.2 million
1.2 = $24 million
PV (tax shield)= .08  .03
V L = V U + PV (interest tax shield) = $100 million + $24 million = $124 million
Diff: 3
Skill: Analytical 18.4 The FlowtoEquity Method
1) Which of the following statements is false?
A) In the flow  to equity valuation method, the cash flows to equity holders are then discounted
using the weighted average cost of capital.
B) In the WACC and APV methods, we value a project based on its free cash flow, which is
computed ignoring interest and debt payments.
C) In the flow  to equity (FTE) valuation method, we explicitly calculate the free cash flow
available to equity holders taking into account all payments to and from debt holders.
D) The first step in the FTE method is to determine the project’s free cash flow to equity (FCFE).
Answer: A
Diff: 1
Skill: Conceptual Chapter 18 Capital Budgeting and Valuation with Leverage 519 2) Which of the following statements is false?
A) The projectʹs free cash flow to equity shows the expected amount of additional cash the firm will
have available to pay dividends (or conduct share repurchases) each year.
B) The value of the project’s FCFE should be identical to the NPV computed using the WACC and
APV methods.
C) The value of the project’s FCFE represents the gain to shareholders from the project.
D) Because interest payments are deducted before taxes, we adjust the firmʹs FCF by their
before tax cost.
Answer: D
Diff: 2
Skill: Conceptual 3) Which of the following statements is false?
A) If the debt equity ratio changes over time, the risk of equity–and, therefore, its cost of capital
–will change as well.
B) The FTE method can offer an advantage when calculating the value of equity for the entire firm,
if the firm’s capital structure is complex and the market values of other securities in the firm’s
capital structure are not known.
C) The FTE approach does not have the same disadvantage associated with the APV approach: We
donʹt need to compute the projectʹs debt capacity to determine interest and net borrowing before
we can make the capital budgeting decision.
D) The WACC and APV methods compute the firmʹs enterprise value, so that a separate valuation
of the other components of the firm’s capital structure is needed to determine the value of
equity.
Answer: C
Diff: 2
Skill: Conceptual 4) Which of the following is not a step in valuation using the flow to equity method?
A) Determine the equity cost of capital, rE.
B) Compute the equity value, E, by discounting the free cash flow to equity using the
equity cost of capital.
C) Determine the free cash flow to equity of the investment.
D) Determine the before tax cost of capital, rU.
Answer: D
Diff: 1
Skill: Conceptual 520 Berk/DeMarzo · Corporate Finance Use the information for the question(s) below.
Suppose that Rose Industries is considering the acquisition of another firm in its industry for $100 million. The
acquisition is expected to increase Roseʹs free cash flow by $5 million the first year, and this contribution us
expected to grow at a rate of 3% every year there after. Rose currently maintains a debt to equity ratio of 1, its
marginal tax rate is 40%, its cost of debt rD is 6%, and its cost of equity rE is 10%. Rose Industries will maintain a
constant debt  equity ratio for the acquisition.
5) The Free Cash Flow to Equity (FCFE) for the acquisition in year 0 is closest to:
A) $5 million
B) $100 million
C)  $100 million
D)  $50 million
Answer: D
Explanation: D) FCFE0 =  100 (cost of acquisition) + 50 (issuance of new debt) =  $50 million Diff: 1
Skill: Analytical 6) The Free Cash Flow  to Equity (FCFE) for the acquisition in year 1 is closest to:
A) $4.7 million
B) $6.5 million
C) $8.3 million
D) $6.8 million
Answer: A
Explanation: A) In one year the interest on the debt will be 6% × $50 = $3 million. Because Rose
maintains a constant debt  equity ratio, the debt associated with the acquisition is also
expected to grow at a 3% rate, so D1 = D0(1 + g ) = $50(1.03) = $51.5 million, therefore
the net borrowing (lending) is $51.5  50 = $1.5 million FCFE1 = FCF from project  after tax interest payments + new borrowing
FCFE1 = + 5.0  (1  .40)(3) + 1.5 = $4.7 million Diff: 2
Skill: Analytical 7) Describe the key steps in the flow to equity method for valuing a levered investment.
Answer: The key steps in the flow  to equity method for valuing a levered investment are as follows:
1. Determine the free cash flow to equity of the investment.
2. Determine the equity cost of capital, rE.
3. Compute the equity value, E, by discounting the free cash flow to equity using the
equity cost of capital.
Diff: 2
Skill: Conceptual Chapter 18 Capital Budgeting and Valuation with Leverage 521 18.5 ProjectBased Costs of Capital
1) Which of the following statements is false?
A) In the real world, specific projects should differ only slightly from the average investment made
by the firm.
B) We can estimate rU for a new project by looking at single  division firms that have similar
business risks.
C) The projectʹs equity cost of capital depends on its unlevered cost of capital, rU, and the
debt  equity ratio of the incremental financing that will be put in place to support the project.
D) Projects may vary in the amount of leverage they will support–for example, acquisitions of real
estate or capital equipment are often highly levered, whereas investments in intellectual
property are not.
Answer: A
Diff: 1
Skill: Conceptual 2) Which of the following statements is false?
A) For capital budgeting purposes, the project’s financing is the incremental financing that results if
the firm takes on the project.
B) Projects with safer cash flows can support more debt before they increase the risk of financial
distress for the firm.
C) If the positive free cash flow from a project will increase the firmʹs cash holdings, then this
growth in cash is equivalent to a reduction in the firm’s leverage.
D) The incremental financing of a project corresponds directly to the financing that is directly tied
to the project.
Answer: D
Diff: 1
Skill: Conceptual 3) Consider the following equation:
rwacc = rU  τcdr D
The term d in this equation is
A) the projectʹs unlevered cost of capital.
B) the projectʹs dollar amount of debt.
C) the firmʹs unlevered cost of debt.
D) the projectʹs debt to value ratio.
Answer: D
Diff: 1
Skill: Conceptual 522 Berk/DeMarzo · Corporate Finance 4) Consider the following equation:
rwacc = rU  τcdr D
The term rU in this equation is
A) the firmʹs unlevered cost of debt.
B) the firmʹs cost of debt.
C) the projectʹs unlevered cost of capital.
D) the projectʹs debt to value ratio.
Answer: C
Diff: 1
Skill: Conceptual Use the information for the question(s) below.
The Aardvark Corporation is considering launching a new product and is trying to determine an appropriate
discount rate for evaluating this new product. Aardvark has identified the following information for three single
division firms that offer products similar to the one Aardvark is interested in launching: Comparable Firm
Anteater Enterprises
Armadillo Industries
Antelope Inc. Equity Cost Debt Cost
of Capital of Capital
12.50%
6.50%
13%
6.10%
14%
7.10% Debt to Value
Ratio
50%
40%
60% 5) The unlevered cost of capital for Anteater Enterprises is closest to:
A) 10.1%
B) 9.5%
C) 9.9%
D) 10.3%
Answer: B
Explanation: B) rU = 1  D
D
r + r
D + E E D + E D Comparable Firm
Anteater Enterprises
Armadillo Industries
Antelope Inc.
Diff: 1
Skill: Analytical Equity Cost Debt Cost Debt to Value
rU
of Capital of Capital
Ratio
12.50%
6.50%
50%
9.50%
13%
6.10%
40%
10.30%
14%
7.10%
60%
9.90% Chapter 18 Capital Budgeting and Valuation with Leverage 523 6) The unlevered cost of capital for Armadillo Industries is closest to:
A) 10.3%
B) 10.1%
C) 9.5%
D) 9.9%
Answer: A
Explanation: A) rU = 1  D
D r + r
D + E E D + E D Comparable Firm
Anteater Enterprises
Armadillo Industries
Antelope Inc. Equity Cost Debt Cost Debt to Value
rU
of Capital of Capital
Ratio
12.50%
6.50%
50%
9.50%
13%
6.10%
40%
10.30%
14%
7.10%
60%
9.90% Diff: 1
Skill: Analytical 7) The unlevered cost of capital for Antelope Incorporated is closest to:
A) 10.3%
B) 9.9%
C) 10.1%
D) 9.5%
Answer: B
Explanation: B) rU = 1  D
D r + r
D + E E D + E D Comparable Firm
Anteater Enterprises
Armadillo Industries
Antelope Inc.
Diff: 1
Skill: Analytical Equity Cost Debt Cost Debt to Value
rU
of Capital of Capital
Ratio
12.50%
6.50%
50%
9.50%
13%
6.10%
40%
10.30%
14%
7.10%
60%
9.90% 524 Berk/DeMarzo · Corporate Finance Use the information for the question(s) below.
KT Enterprises is considering undertaking a new project. Based upon analysis of firms with similar projects, KT
has determined that an unlevered cost of equity of 12% is suitable for their project. KTʹs marginal tax rate is 35%,
its borrowing rate is 7%, and KT does not believe that its borrowing rate will change if the new project is accepted.
8) If KT expects to maintain a debt to equity ratio for this project of 1, then KTʹs equity cost of capital, rE,
for this project is closest to:
A) 17.0%
B) 5.0%
C) 15.0%
D) 12%
Answer: A
Explanation: A) rE = rU + D (r  r )
EUD rE = .12 + 1(.12  .07) = .17 or 17%
Diff: 1
Skill: Analytical 9) If KT expects to maintain a debt to equity ratio for this project of .6 then KTʹs equity cost of capital, rE,
for this project is closest to:
A) 5.0%
B) 12%
C) 15.0%
D) 17.0%
Answer: C
Explanation: D
C) rE = rU + (r U  rD)
E
rE = .12 + .6(.12  .07) = .15 or 15% Diff: 1
Skill: Analytical Chapter 18 Capital Budgeting and Valuation with Leverage 525 10) If KT expects to maintain a debt to equity ratio for this project of .6 then KTʹs project based WACC,
rwacc, for this project is closest to:
A) 10.5%
B) 11.1%
C) 9.6%
D) 10.8%
Answer: B
Explanation: B) rwacc = rU  dτ crD .6 (.35)(.07) = .1108 or 11.08%
rwacc = .12  1 + .6 Diff: 2
Skill: Analytical 11) If KT expects to maintain a debt to equity ratio for this project of 1 then KTʹs project based WACC,
rwacc, for this project is closest to:
A) 11.1%
B) 10.8%
C) 9.6%
D) 10.5%
Answer: B
Explanation: B) rwacc = rU  dτ crD
1 (.35)(.07) = .107750 or 10.8%
rwacc = .12  1 + 1 Diff: 2
Skill: Analytical 526 Berk/DeMarzo · Corporate Finance Use the information for the question(s) below.
The Aardvark Corporation is considering launching a new product and is trying to determine an appropriate
discount rate for evaluating this new product. Aardvark has identified the following information for three single
division firms that offer products similar to the one Aardvark is interested in launching: Comparable Firm
Anteater Enterprises
Armadillo Industries
Antelope Inc. Equity Cost Debt Cost
of Capital of Capital
12.50%
6.50%
13%
6.10%
14%
7.10% Debt to Value
Ratio
50%
40%
60% 12) Based upon the three comparable firms, calculate that most appropriate unlevered cost of capital for
Aardvark to use on this new product.
D
D r + r
Answer: rU = 1  D + E E D + E D Comparable Firm
Anteater Enterprises
Armadillo Industries
Antelope Inc. Equity Cost Debt Cost Debt to Value
rU
of Capital of Capital
Ratio
12.50%
6.50%
50%
9.50%
13%
6.10%
40%
10.30%
14%
7.10%
60%
9.90%
average = 9.90% Diff: 2
Skill: Analytical 18.6 APV with Other Leverage Policies
1) Which of the following statements is false?
A) Rather than set debt according to a target debt  equity ratio or interest coverage level, a firm
may adjust its debt according to a fixed schedule that is known in advance.
B) When we relax the assumption of a constant debt  equity ratio, the equity cost of capital and
WACC for a project will change over time as the debt  equity ratio changes.
C) When we relax the assumption of a constant debt  equity ratio, the APV and FTE methods are
difficult to implement.
D) If a firm is using leverage to shield income from corporate taxes, then it will adjust its debt level
so that its interest expenses grow with its earnings.
Answer: C
Diff: 1
Skill: Conceptual Chapter 18 Capital Budgeting and Valuation with Leverage 527 2) Which of the following statements is false?
A) When we relax the assumption of a constant debt  equity ratio, the FTE method is relatively
straightforward to use and is therefore the preferred method with alternative leverage policies.
B) When debt levels are set according to a fixed schedule, we can discount the predetermined
interest tax shields using the debt cost of capital, rD.
C) With a constant interest coverage policy, the value of the interest tax shield is proportional to the
projectʹs unlevered value.
D) When the firm keeps its interest payments to a target fraction of its FCF, we say it has a constant
interest coverage ratio.
Answer: A
Diff: 2
Skill: Conceptual 3) Which of the following statements is false?
A) As a general rule, the WACC method is the easiest to use when the firm will maintain a fixed
debt  to value ratio over the life of the investment.
B) The FTE method is typically used only in complicated settings for which the values of other
securities in the firm’s capital structure or the interest tax shield are themselves difficult to
determine.
C) For alternative leverage policies, the FTE method is usually the most straightforward approach.
D) When used consistently, the WACC, APV, and FTE methods produce the same valuation for the
investment.
Answer: C
Diff: 2
Skill: Conceptual 528 Berk/DeMarzo · Corporate Finance Use the information for the question(s) below.
Aardvark Industries is considering a project that will generate the following free cash flows:
Year
Free Cash Flows 0
($200) 1
$100 2
$80 3
$60 You are also provided with the following market value balance sheet and information regarding Aardvarkʹs cost of
capital:
Assets
Cash
Other Assets 0
1000 Liabilities
Debt
Equity Cost of Capital
Debt
Equity
τc 400
600 4) Aardvarkʹs unlevered cost of equity is closest to:
A) 10.0%
B) 10.4%
C) 9.5%
D) 9.0%
Answer: A
Explanation: A) rU = 1  D
D r + r
D + E E D + E D 400
400
rU = 1  + .07 = 10.0%
400 + 600 .12 400 + 600
Diff: 1
Skill: Analytical 5) The unlevered value of Aardvarkʹs new project is closest to:
A) $205
B) $100
C) $164
D) $202
Answer: D
Explanation: B) rU = 1  D
D rE + r
D + E
D + E D 400
400
rU = 1  .12 + .07 = 10.0%
400 + 600
400 + 600
V U = Diff: 2
Skill: Analytical 100
(1.10) 1 + 80
(1.10) 2 + 60
(1.10) 3 = $202.10 7%
12%
35% Chapter 18 Capital Budgeting and Valuation with Leverage 529 6) Suppose that to fund this new project, Aardvark borrows $120 with the principal to be paid in three
equal installments at the end each year. The present value of Aardvarkʹs interest tax shield is closest
to:
A) $5.15
B) $5.00
C) $5.90
D) $5.25
Answer: D
Explanation: D) PV (interest tax shield) = PV (interest tax shield) = D1 rDτc
D2 rDτc
D0 rDτc + + (1 + rD)1 (1 + rD)2 (1 + rD)3
120(.07)(.35) 80(.07)(.35) 40(.07)(.35) + + = $5.2596
(1.07) 1
(1.07) 2
(1.07) 3 Diff: 3
Skill: Analytical 7) Suppose that to fund this new project, Aardvark borrows $120 with the principal to be paid in three
equal installments at the end each year. The levered value of Aardvarkʹs new project is closest to:
A) $210.15
B) $207.35
C) $207.00
D) $210.50
Answer: B
Explanation: B) rU = 1  D
D r + r
D + E E D + E D 400
400
rU = 1  .12 + 400 + 600 .07 = 10.0%
400 + 600
V U = 100
(1.10) 1 + 80
(1.10) 2 + 60
(1.10) 3 = $202.10 PV (interest tax shield) = D1 rDτc
D2 rDτc
D0 rDτc + + (1 + rD)1 (1 + rD)2 (1 + rD)3 PV (interest tax shield) = 120(.07)(.35) 80(.07)(.35) 40(.07)(.35) + + = $5.2596
(1.07) 1
(1.07) 2
(1.07) 3 V L = V U + PV (interest tax shield) = $202.10 + $5.26 = $207.36
Diff: 3
Skill: Analytical 530 Berk/DeMarzo · Corporate Finance 8) Suppose that to fund this new project, Aardvark borrows $150 with the principal to be paid in three
equal installments at the end each year. Calculate the present value of Aardvarkʹs interest tax shield.
Answer: PV (interest tax shield) = PV (interest tax shield) = D1 rDτc
D2 rDτc
D0 rDτc + + 1 (1 + rD)2 (1 + rD)3
(1 + rD)
150(.07)(.35) 100(.07)(.35) 50(.07)(.35) + + = $6.286
(1.07) 1
(1.07) 2
(1.07) 3 Diff: 2
Skill: Analytical 9) Suppose that to fund this new project, Aardvark borrows $150 with the principal to be paid in three
equal installments at the end each year. Calculate the The levered value of Aardvarkʹs new project.
D
D r + r
Answer: rU = 1  D + E E D + E D
400
400
rU = 1  + .07 = 10.0%
400 + 600 .12 400 + 600
V U = 100
(1.010)1 + 80
(1.010)2 + 60
(1.010)3 = $202.10 PV (interest tax shield) = D1 rDτc
D2 rDτc
D0 rDτc + + (1 + rD)1 (1 + rD)2 (1 + rD)3 PV (interest tax shield) = 150(.07)(.35) 100(.07)(.35) 50(.07)(.35) + + = $6.286
(1.07) 1
(1.07) 2
(1.07) 3 V L = V U + PV (interest tax shield) = $202.10 + $6.29 = $208.39
Diff: 3
Skill: Analytical 18.7 Other Effects of Financing
1) Which of the following questions is false?
A) With perfect capital markets, all securities are fairly priced and issuing securities is a zero  NPV
transaction.
B) The fees associated with the financing of the project are independent of the projectʹs required
cash flows and should be ignored when calculating the NPV of the project.
C) When a firm borrows funds, a mispricing scenario arises if the interest rate charged differs from
the rate that is appropriate given the actual risk of the loan.
D) The WACC, APV, and FTE methods determine the value of an investment incorporating the tax
shields associated with leverage.
Answer: B
Diff: 1
Skill: Conceptual Chapter 18 Capital Budgeting and Valuation with Leverage 531 2) Which of the following questions is false?
A) Sometimes management may believe that the securities they are issuing are priced at less than
(or more than) their true value. If so, the NPV of the transaction, which is the difference
between the actual money raised and the true value of the securities sold, should not be
included inthe value of the project.
B) An alternative method of incorporating financial distress and agency costs is to first value the
project ignoring these costs, and then value the incremental cash flows associated with financial
distress and agency problems separately.
C) When the debt level—and, therefore, the probability of financial distress—is high, the expected
free cash flow will be reduced by the expected costs associated with financial distress and
agency problems.
D) If the financing of the project involves an equity issue, and if management believes that the
equity will sell at a price that is less than its true value, this mispricing is a cost of the project for
the existing shareholders.
Answer: A
Diff: 2
Skill: Conceptual 3) Luther Industries is considering borrowing $500 million to fund a new product line. Given investorsʹ
uncertainty regarding its prospects, Luther will pay a 7% interest rate on this loan. The firmʹs
management knows, that the actual risk of the loan is extremely low and that the appropriate rate on
the loan is 5%. Suppose the loan is for four years, with all principal being repaid in the fourth year. If
Lutherʹs marginal corporate tax rate is 35%, then the net effect of the loan on the value of the new
product line is closest to:
A) $22 million
B) $34 million
C) $35 million
D) $24 million
Answer: D
Explanation: D) Luther Industries is paying (7%  5% = 2%) more for the loan than the risk demands.
However, part of this 2% premium in the interest rate is being offset by the interest
tax shield. Therefore the true cost in any year is the amount of debt × (2%) × (1  τc).
Cost per year = $500M(.02)(.65) = $6.5M, we need to discount this amount each year
by the correct rD of 5%, this is amount is constant and occurs each year for four years
we have an annuity, solving:
PMT = 6.5
I = 5%
FV = 0
N = 4
Compute PV = $23.04 million Diff: 2
Skill: Analytical 532 Berk/DeMarzo · Corporate Finance 18.8 Advanced Topics in Capital Budgeting
1) Consider the following equation for the Project WACC with a fixed debt schedule:
rwacc = rU  dτ c[rD + f (rU  rD)]
The term d in this equations represents
A) a measure of the permanence of the debt level.
B) the annual adjustment percentage to the amount of debt.
C) the debt to value ratio.
D) the dollar amount of debt outstanding.
Answer: C
Diff: 1
Skill: Analytical 2) Consider the following equation for the Project WACC with a fixed debt schedule:
rwacc = rU  dτ c[rD + f (rU  rD)]
The term f in this equations represents
A) the annual adjustment percentage to the amount of debt.
B) a measure of the permanence of the debt level.
C) the dollar amount of debt outstanding.
D) the debt to value ratio.
Answer: B
Diff: 2
Skill: Analytical ...
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This note was uploaded on 02/02/2012 for the course BUS 438 taught by Professor Dutt during the Winter '12 term at Cal Poly.
 Winter '12
 Dutt
 Dividends, Corporate Finance, Leverage, Valuation

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