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Valuation and levered Betas. Some interesting questions to consider in applications. Today’s plan. Review what we have learned in the last lecture An example of a cash-flow calculation Examine the impact of financing on the cost of equity (levered Betas) Two approaches to calculate NPV I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
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Presentation Transcript ### Valuation and levered Betas

Some interesting questions to consider in applications

FIN 819: lecture 5 Today’s plan
• Review what we have learned in the last lecture
• An example of a cash-flow calculation
• Examine the impact of financing on the cost of equity (levered Betas)
• Two approaches to calculate NPV
• WACC ( weighted average cost of capital approach)
• APV (adjusted present value approach) What have we learned
• Risk, returns and WACC
• Your view of risk in finance
• measure investment performance
• measure risk
• portfolio diversification and two types of risk
• systematic risk and its measurement
• three portfolio rules
• CAPM and the security market line
• Cost of capital and WACC
• The things you have to pay attention to in calculating WACC Example 1
• Based on the CAPM, ABC Company has a cost of capital of 17%. (4 + 1.3(10)). A breakdown of the company’s investment projects is listed below.
• 1/3 Nuclear Parts: β=2.0
• 1/3 Computer Hard Drive: β =1.3
• 1/3 Dog Food Production: β =0.6
• When evaluating a new dog food production investment, which cost of capital should be used and how much? Solution
• Since dog food projects may have similar systematic risk to the dog food division, we use a beta of 0.6 to measure the risk of the projects to be taken.
• Thus the expected return on the project or the cost of capital is 0.04+0.6*(0.1)=0.l or 10% Example 2
• Stock A has a beta of .5 and investors expect it to return 5%. Stock B has a beta of 1.5 and investors expect it to return 13%. What is the market risk premium and the expected rate of return on the market portfolio? Solution
• According to the CAPM Example 3
• You have \$1 million of your own money and borrow another \$1 million at a risk-free rate of 4% to invest in the market portfolio. The expected return for the market portfolio is 12%, what is the expected return on your portfolio? Solution
• We can use two approaches to solve it:
• First, the expected rate of return of a portfolio is the weighed average of the expected rates of return of the securities in the portfolio.
• Second , the beta of a portfolio is the weighed average of the betas of the securities in the portfolio. Then use the CAPM to get the expected rate of return. Solution (continue)
• First approach
• Second approach The cost of capital

Cost of Capital

• The expected return the firm’s investors require if they invest in securities or projects with comparable degrees of risk. Cost of capital with tax benefit
• When tax benefit of debt financing is considered, the company cost of capital is as The cost of capital for the bond
• The cost of capital for the bond
• It is the YTM, the expected return required by the investors.
• That is
• The expected return on a bond can also be calculated by using CAPM Example 2
• A bond with a face value of \$2000 matures in 5 years. The coupon rate is 8%. If the market price for this bond is \$1900.

(a) What is the expected return on this bond or what is the cost of debt for this bond?

(b) Suppose that the YTM is 9%, what is the market value of this bond? Solution

(a)

(b) The cost of capital for a stock
• The cost of capital for a stock is calculated by using
• CAPM
• Dividend growth model Example 3
• Sock A now pays a dividend of \$1.5 per share annually, It is expected that dividend is going to grow at a constant rate of 2%. The current price for stock A is \$25 per share. What is the expected return or the cost of capital by investing in this stock? Another cash flow problem!

Company A has a very old packaging machine which can be used for another two years. It has no book and market values. The maintenance cost for this old machine is \$20,000 every year. Now a new packaging machine is available at the price of \$ 300,000, which is depreciated in three years. If the new packaging machine is used, the maintenance cost is \$10,000 every year. If there is no inflation, the cost capital is 10%, and the tax rate is 40% for company A.

Questions:

a. What is the valuation horizon used in this problem?

b. Should company A invest in the new packaging machine now or

waiting two years later? How does debt financing affect investment?
• When firms issue debt, tax-shield and thus introduced financial risk impact the valuation of the projects and thus investments.
• To understand how financing affects investments or real project valuations, we will introduce several variables. Some terminology
• D: the market value of debt
• E: the market value of equity
• UA: the value of the unlevered asset of the firm ( the value of the asset when D=0)
• A: the value of the levered asset of the firm, i.e., D is positive; sometimes, V is used to refer to the same thing.
• TX: the present value of the tax shield Some terminology (continues)
• : the beta of debt
• : the beta of equity
• : The beta of the unlevered asset
• : the beta of the levered asset
• : the beta of the tax-shield Some terminology (continues)
• : the cost of debt
• : the cost of equity
• : the cost of the unlevered asset
• : the cost of the levered asset
• : the cost of the tax-shield The balance sheet

Assets

Liabilities and Equity

Debt D

Debt Tax shield (TX)

Unlevered asset (UA)

Equity E The relationship among all kinds of values
• From the balance sheet, we can have the following relationships The present value of tax-shield
• If the tax-shield is as risky as debt, and the firm issues risk-free perpetual debt, then the present value of the tax-shield can be regarded as a simple perpetuity with the amount of level cash flow as
• Clearly, The beta of equity
• Using portfolio, we have
• In this text book, we can assume that

is not affected by firms’ capital structure, but decided by firms’ business risk. The betas of equity and asset (continues)
• Thus, for firms with the same business line, should be the same theoretically.
• Two questions?
• Is this making sense?
• Why are we interested in the betas of unlevered assets? An example
• Firm D has the same business as firms A, B and C, whose betas and market values of debt and equity are given in the table in the next slide. Suppose all the firms have the risk-free debt and the risk free rate is 4%, the risk premium on the market portfolio is 8.4% annually and the corporate tax rate is 34%, what is the WACC for firm D? Information for example

Beta

Debt

Equity

Firms

96

A

0.75

4.0

770

230

1.00

B

790

1.08

210

C

800

150

D The two approaches for calculating NPV
• WACC approach:
• Basic idea: calculate free cash flows, as if the project is all-equity financed
• Lower the cost of the capital to incorporate tax-shield; this is taken care of by WACC
• Discount free cash flows by WACC to get NPV APV approach
• In contrast to the WACC approach, the APV approach is strongly recommended in academics.
• Basic idea:
• Calculate free cash flows
• Use the cost of unlevered asset to discount the free cash flows
• In addition, calculate the NPV of the tax shield
• The sum of the two NPVs is the NPV of the project What are the pros and cons of the two approaches
• Which approach would you like ? Why or why not?
• Can you predict which approach will be used more in the future? An example
• Firm D wants to expand its business. Currently the firm has D/V of 40%. The cost of the firm’s equity is 14.6%, the risk free rate is 8% and the debt is risk-free. Suppose that the firm wants to finance the expansion project by issuing \$20 million of risk-free perpetual debt and \$80 millions of equity. The expansion project will generate a perpetual free cash flow of \$5 million at every year, starting next year. The tax rate is 35%. Please use two approaches to calculate the present value of the expansion project? Solution
• First approach:

Suppose that the tax-shield is as risky as debt.