CHAPTER 18
VALUATION AND CAPITAL BUDGETING
FOR THE LEVERED FIRM
Answers to Concepts Review and Critical Thinking Questions
1. APV is equal to the NPV of the project (i.e. the value of the project for an unlevered firm) plus the
4. The WACC method does not explicitly include the interest cash flows, but it does implicitly include
5. You can estimate the unlevered beta from a levered beta. The unlevered beta is the beta of the assets
of the firm; as such, it is a measure of the business risk. Note that the unlevered beta will always be
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Basic
1. a. The maximum price that the company should be willing to pay for the fleet of cars with all-
equity funding is the price that makes the NPV of the transaction equal to zero. Discounting the
depreciation tax shield at the risk-free rate, the NPV equation for the project is:
b. The adjusted present value (APV) of a project equals the net present value of the project if it
were funded completely by equity plus the net present value of any financing side effects. In
this case, the NPV of financing side effects equals the after-tax present value of the cash flows
resulting from the firm’s debt, so:
The company paid $650,000 for the fleet of cars. Because this fleet will be fully depreciated
over five years using the straight-line method, annual depreciation expense equals:
So, discounting the depreciation tax shield at the risk-free rate, the NPV of an all-equity project
is:
NPV(Financing Side Effects)
The net present value of financing side effects equals the after-tax present value of cash flows
resulting from the firm’s debt, so:
So, the APV of the project is:
2. The adjusted present value (APV) of a project equals the net present value of the project if it were
funded completely by equity plus the net present value of any financing side effects. In this case, the
NPV of financing side effects equals the after-tax present value of the cash flows resulting from the
firm’s debt, so:
NPV(All-Equity)
NPV = –Purchase Price + PV[(1 – tC)(EBTD)] + PV(Depreciation Tax Shield)
Since the initial investment of $1.4 million will be fully depreciated over four years using the
straight-line method, annual depreciation expense is:
NPV(Financing Side Effects)
The net present value of financing side effects equals the aftertax present value of cash flows
resulting from the firm’s debt. So, the NPV of the financing side effects is:
Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, RB.
Since the flotation costs will be amortized over the life of the loan, the annual flotation costs that
will be expensed each year are:
So, the APV of the project is:
3. a. In order to value a firm’s equity using the flow-to-equity approach, discount the cash flows
available to equity holders at the cost of the firm’s levered equity. The cash flows to equity
holders will be the firm’s net income. Remembering that the company has three stores, we find:
Since this cash flow will remain the same forever, the present value of cash flows available to
the firm’s equity holders is a perpetuity. We can discount at the levered cost of equity, so, the
value of the company’s equity is:
b. The value of a firm is equal to the sum of the market values of its debt and equity, or:
VL = B + S
We can substitute the value of equity and solve for the value of debt, doing so, we find:
So, the value of the company is:
4. a. In order to determine the cost of the firm’s debt, we need to find the yield to maturity on its
current bonds. With semiannual coupon payments, the yield to maturity of the company’s bonds
is:
Since the coupon payments are semiannual, the YTM on the bonds is:
b. We can use the Capital Asset Pricing Model to find the return on unlevered equity. According to
the Capital Asset Pricing Model:
Now we can find the cost of levered equity. According to Modigliani-Miller Proposition II with
corporate taxes:
c. In a world with corporate taxes, a firm’s weighted average cost of capital is equal to:
The problem does not provide either the debt–value ratio or equity–value ratio. However, the
firm’s debt–equity ratio is:
Substituting this in the debt–value ratio, we get:
And the equity–value ratio is one minus the debt–value ratio, or:
5. a. The equity beta of a firm financed entirely by equity is equal to its unlevered beta. Since each
firm has an unlevered beta of 1.10, we can find the equity beta for each. Doing so, we find:
North Pole
South Pole
b. We can use the Capital Asset Pricing Model to find the required return on each firm’s equity.
Doing so, we find:
North Pole:
South Pole:
6. a. If flotation costs are not taken into account, the net present value of a loan equals:
b. The flotation costs of the loan will be:
So, the annual flotation expense will be:
If flotation costs are taken into account, the net present value of a loan equals:
NPVLoan = Proceeds net of flotation costs – Aftertax present value of interest and principal
payments + Present value of the flotation cost tax shield
7. First we need to find the aftertax value of the revenues minus expenses. The aftertax value is:
Next, we need to find the depreciation tax shield. The depreciation tax shield each year is:
Depreciation tax shield = Depreciation(tC)
Now we can find the NPV of the project, which is:
NPV = Initial cost + PV of depreciation tax shield + PV of aftertax revenue
8. Whether the company issues stock or issues equity to finance the project is irrelevant. The
company’s optimal capital structure determines the WACC. In a world with corporate taxes, a firm’s
weighted average cost of capital equals:
Now we can use the weighted average cost of capital to discount NEC’s unlevered cash flows. Doing
so, we find the NPV of the project is:
9. a. The company has a capital structure with three parts: long-term debt, short-term debt, and
equity. Since interest payments on both long-term and short-term debt are tax-deductible,
multiply the pretax costs by (1 – tC) to determine the aftertax costs to be used in the weighted
average cost of capital calculation. The WACC using the book value weights is:
b. Using the market value weights, the company’s WACC is:
c. Using the target debt–equity ratio, the target debt–value ratio for the company is:
Substituting this in the debt–value ratio, we get:
And the equity–value ratio is one minus the debt–value ratio, or:
We can use the ratio of short-term debt to long-term debt in a similar manner to find the short-
term debt to total debt and long-term debt to total debt. Using the short-term debt to long-term
debt ratio, we get:
Substituting this in the short-term debt to total debt ratio, we get:
And the long-term debt to total debt ratio is one minus the short-term debt to total debt ratio, or:
Now we can find the short-term debt to value ratio and long-term debt to value ratio by
multiplying the respective ratio by the debt–value ratio. So:
And the long-term debt to value ratio is:
So, using the target capital structure weights, the company’s WACC is:
d. The differences in the WACCs are due to the different weighting schemes. The company’s
WACC will most closely resemble the WACC calculated using target weights since future
Intermediate
10. The adjusted present value of a project equals the net present value of the project under all-equity
financing plus the net present value of any financing side effects. In the joint venture’s case, the NPV
of financing side effects equals the aftertax present value of cash flows resulting from the firms’
debt. So, the APV is:
Since the initial investment will be fully depreciated over five years using the straight-line method,
annual depreciation expense is:
NPV(Financing Side Effects)
The NPV of financing side effects equals the after-tax present value of cash flows resulting from the
firm’s debt. The coupon rate on the debt is relevant to determine the interest payments, but the
resulting cash flows should still be discounted at the pretax cost of debt. So, the NPV of the
financing effects is: