1. Advanced Project Evaluation
Class 10
Advanced Project Evaluation

2. Two Questions
Question 1: What mix of debt and equity is optimal for our firm?
Question 2: Given the capital structure chosen by our firm, how can we use publicly available data from other firms (with capital structures different from ours) to aid in project evaluation decisions?

3. Perfect Capital Markets: The MM Irrelevance Proposition
Assume perfect capital markets:
No taxes or transaction costs
No bankruptcy costs
Modigliani-Miller Irrelevance Proposition: Under perfect capital markets, the firm’s capital structure choice (i.e., mix of debt and equity) has no effect on its total market value or its cost of funds (i.e., the cost of financing its investments).

4. Proof By Arbitrage
Consider two firms with identical operating cash flows, X, but different capital structures.
Firm U is all-equity financed (i.e., unlevered). For an unlevered firm, VU = EU.
Firm L uses both debt and equity financing (i.e., levered). For a levered firm, VL=EL+DL.
We will show that because these two firms have identical operating cash flows, they must have identical total market values, VU = VL, despite having different capital structures.

5. Proof By Arbitrage
Suppose you purchase a fraction a of the equity of the unlevered firm. Your initial cost and future cash flows are as follows:
Investment Future Cash Flow
a VU a X
For simplicity, we assume that all operating cash flows are paid out as dividends to shareholders.

6. Proof By Arbitrage
Now suppose you bought a fraction a of the debt and equity of the levered firm. Your initial cost and future cash flows are as follows: Investment Future Cash Flow a DL a Min[cF,X] a EL a Max[0,X-cF] a VL a X

7. Proof By Arbitrage
Note that the future cash flows on both investments are the same and equal to aX for all future periods.
Since your future cash flows are the same under both investments, the cost of the investments must be equal to prevent arbitrage, aVU = aVL.
This result is M-M Proposition I: In a perfect capital market, the value of the firm is invariant to its capital structure. Hence, VU = VL.

8. Perfect Capital Markets: Leverage and the Cost of Capital
Firm Value VU VL
DL/EL

9. Perfect Capital Markets: Leverage and the Cost of Capital
In a perfect capital market, the firm’s weighted average cost of capital is calculated as follows:
Modigliani-Miller Proposition II: In a perfect capital market, the firm’s weighted average cost of capital is invariant to its capital structure. Hence, r*L = r*U.

10. Perfect Capital Markets: Leverage and the Cost of Capital
r*U
r*L
DL/EL

11. Perfect Capital Markets: Leverage and the Cost of Capital
The WACC formula implies the following relationship between the firm’s cost of equity and its leverage:
In a perfect capital market, r*L = r*U =reU. This represents a return to compensate investors for the inherent business risk of the assets of the firm.

12. Perfect Capital Markets: Leverage and the Cost of Capital
In addition to this business risk, there is a leverage effect. The equityholders in the levered firm demand a higher return to compensate them for the fact that there are debtholders lined up in front of them with a prior claim over the assets of the firm.
As leverage increases two things happen:
the equityholders demand higher returns.
we finance more projects by (relatively cheaper) debt.
In a perfect capital market, these two effects cancel exactly.

13. Perfect Capital Markets: Leverage and the Cost of Capital
Required
Return D L /E r e U = * =r d

14. Perfect Capital Markets: Leverage and the Cost of Capital
The CAPM can be used to compute all of these discount rates:
Use the equity beta to compute the return on equity: E[reL] = rf + beL (E[rm]- rf).
Use the debt beta to compute the return on debt: E[rd] = rf + bd (E[rm]- rf).
Use the asset beta to compute a return commensurate with the business risk of the assets: E[reU] = rf + beU (E[rm]- rf).

15. Perfect Capital Markets: Leverage and the Cost of Capital
Note that the beta of equity in an unlevered firm (beU) is also known as the beta of the assets (ba) since the unlevered firm has no leverage effect.
The only source of risk in the unlevered firm is the inherent business risk of the assets themselves.

16. Perfect Capital Markets: Leverage and the Cost of Capital
The firm’s asset beta is a weighted average of the debt and equity betas:
This implies the following relationship between the firm’s equity beta and its leverage:

17. Perfect Capital Markets Example
An unlevered firm has 10 million shares out-standing, each with a market price of $20 and a beta of The firm is considering issuing $50 million of 10% debt and using the proceeds to pay a dividend to shareholders. What effect will this capital structure change have on the value of the firm, the WACC, the equity beta, the required return on equity, and the wealth of the firm’s shareholders? Assume a riskfree interest rate of rf = 6.0% and a market risk premium of [E(rM)-rf] = 8.0%.

18. Perfect Capital Markets Example
Value of the Unlevered Firm:
VU = 10(20) = 200 million.
Cost of Capital for the Unlevered Firm:
E[reU] = rf + beU (E[rm]- rf).
E[reU] = (0.08) = 0.14.
Since the firm is unlevered, the value of equity and cost of equity are the same as for the firm as a whole.

19. Perfect Capital Markets Example
In perfect capital markets, VL = VU and r*L = r*U.
VL = VU = $200 million
r*L = r*U = 14.0%
Since the cost of debt is 10.0%, the cost of equity is determined as follows: reL = reU + [reU -rd ](D/E) reL = [ ](50/150) =

20. Perfect Capital Markets Example
The equity beta can be determined from the CAPM as follows:
E[reL] = rf + beL (E[rm]- rf).
= beL (0.08).
beL =
The wealth of the firm’s shareholders has not changed.
Shareholder Wealth = Share Value + Dividend
= $150 + $50 = $200 million

21. The Effect of Leverage with Corporate Taxes
Now assume that corporations pay taxes at the rate of t. We continue to assume that bankruptcy costs are zero.
Consider two identical firms: one levered the other unlevered. Both firms produce earnings before interest and taxes of X per year in perpetuity.
What are the yearly cash flows to debt and equity of these two firms? What are the market values of these two firms?

22. The Effect of Leverage with Corportate Taxes
The yearly after-tax cash flows are given below:

23. The Effect of Leverage with Corporate Taxes
The yearly after-tax cash flows to a levered firm are equal to those for the unlevered firm, plus the tax shield on interest.
The value of the levered firm will thus be equal to the following:
VL = VU + PV(ITS)

24. The Effect of Leverage with Corporate Taxes
Assuming debt is perpetual, we have:
The fact that the firm increases its value by using debt implies that the optimal capital structure for the firm is 99.99% debt.
The tax deductibility of interest was one of the driving forces behind the LBO wave of the 1980s.

25. The Relationship Between Firm Value and Leverage
Total Firm Value VL
Present Value of Interest Tax Shields VU
Value of Unlevered Firm
D/E

26. Who Benefits from the Interest Tax Shields?
Consider the unlevered firm from our previous example. The firm currently has 10 million shares outstanding, each with a market price of $20 per share. The firm is considering issuing $50 million in 10% debt. Assume that this debt is perpetual and that the firm’s tax rate is 34%. How does this capital structure change affect the value of the firm and the wealth of the firm’s shareholders?

27. Who Benefits from the Interest Tax Shields?
Since the debt is perpetual, the value of the firm will increase as follows:
VL = VU +tD
VL = 200 +(0.34)(50) = 217 million.
Since the debt is issued at fair market value, the value of equity after the capital structure change is:
Equity Value = $217 - $50 = $167 million.

28. Who Benefits from the Interest Tax Shields?
Since the proceeds from the debt issue are used to pay a dividend to shareholders, their wealth increases by $17 million. This is the value of the interest tax shields on debt.
Shareholder Wealth = Share Value + Dividend
= $167 + $50 = $217 million
If equityholders benefit, who loses?

29. Who Benefits from the Interest Tax Shields?
Unlevered Firm
Levered Firm
Govt
Govt
Equity
Equity
Debt

30. The Effect of Corporate Taxes and Leverage on the Cost of Capital
With corporate taxes, the firm’s weighted average cost of capital is calculated as follows:
Modigliani and Miller have shown that with perpetual debt, the WACC formula can be rewritten as follows:

31. Leverage and the Cost of Capital with Corporate Taxes
r*U
r*L
DL/EL

32. The Effect of Corporate Taxes and Leverage on the Cost of Capital
The WACC formula can be rewritten to give the following expression for the cost of equity:
Using the CAPM, we can derive an expression for the firm’s equity beta:

33. Three Effects
In determining the risk (beta) and return from holding equity in a levered firm, there are three effects to consider:
The inherent business risk of the assets the firm has invested in.
The leverage effect whereby equityholders demand a higher return in compensation for taking a residual claim.
The tax subsidy effect whereby the govt contributes to interest payments on debt.

34. The Effect of Corporate Taxes and Leverage on the Cost of Capital
Rearranging the previous equation gives us an equation for the firm’s asset beta:
The asset beta reflects just the inherent business risk of the assets of the firm. That is, we have purged the equity beta of the leverage and tax subsidy effects.

35. Leverage and the Cost of Capital
Consider once again the firm from our previous example. The firm has a total market value of $217 million, consisting of $50 million in 10% debt and $167 million in equity. The firm’s unlevered (asset) beta is Assuming that the firm faces a tax rate of 34%, what is the WACC, equity beta, and cost of equity for the firm?

36. Leverage and the Cost of Capital
The firm’s new WACC can be determined from its unlevered cost of capital according to the formula:
The firm’s cost of equity is:

37. Leverage and the Cost of Capital
The firm’s equity beta can be determined by the CAPM:
E[reL] = rf + beL (E[rm]- rf).
= beL (0.08).
beL =
To verify the WACC calculation, lets compute it directly using the textbook formula:

38. Example 1
Suppose your firm has identified a potential investment project. The investment project requires you to make an initial outlay of $50 million and is expected to return after-tax cash flows of $8 million per year for the indefinite future. The project has an asset beta of 1.2 and supports $20 million in additional debt capacity. Use the appropriate discount rate to find the project’s NPV. Assume a riskfree rate of 6%, a market risk premium of 8%, and a tax rate of 34%.

39. Example 1 Unlevered Cost of Capital r*U = 0.06 + 1.2(0.08)=0.156.
Present Value of After-Tax Cash Flows
Present Value of Interest Tax Shields

40. Example 1
WACC Calculation
NPV Calculation

41. General Principles
Each investment project has its own cost of capital that depends upon the risk of the investment.
The risk of the investment project depends upon its unlevered (asset) beta.
The unlevered cost of capital can be estimated using the CAPM.
The project’s leverage ratio should depend upon its own debt capacity, not on the particular source of funds used to finance the project.

42. Accounting for Leverage in Capital Budgeting
Suppose your firm is considering an investment in a project different from the firm’s core operations.
NPV must be computed using a discount rate appropriate for the project, not the firm.
How do we find this?
Step 1: Compute the beta of the assets by unlevering another firm’s equity beta.

43. Accounting for Leverage in Capital Budgeting
Step 2: Use the CAPM to determine a required return to compensate investors for bearing this inherent business risk.
Step 3: Adjust this required return to incorporate the leverage and tax subsidy effects associated with this project.
Step 4: Use this required return to find the NPV.

44. Capital Budgeting Example
Your firm is currently in the computer software business, but is considering investing in the development of a new airline. Information on your firm and the airline industry are given below:

45. Capital Budgeting Example
Your airline project is expected to cost $20 million per year for the next 5 years and is expected to generate after-tax cash flows of $10 million per year indefinitely thereafter.
Because of your firm’s current debt position, you will finance the airline project with 50% debt, even though this is less than standard for airline projects.
The corporate tax rate is 34%, the riskfree interest rate is 9%, and the market risk premium is 8%.

46. Capital Budgeting Example
Step 1: Unlever Equity Beta for Airlines
The debt beta, bD comes from the CAPM:

47. Capital Budgeting Example
Step 2: Calculate the Unlevered Cost of Capital
Step 3: Calculate the Levered Cost of Capital

48. Capital Budgeting Example
Step 4: Calculate the NPV of the Project

49. Factors that Influence Debt Policy in Practice
Tax Position of the Corporation
Costs of Bankruptcy and Financial Distress
Variability of the Firm’s Earnings and Cash Flows
Asset Type: Tangible vs. Intangible Assets
Investment (or Growth) Opportunities
The Need for Financial and Operating Flexibility
Informational Asymmetries

50. Tax Shield-Bankruptcy Cost Tradeoff
Firm Value
VU+PV(ITS)
Bankruptcy Costs VL VU
Value of Unlevered Firm
(D/E)*
D/E