- 110 Views
- Updated on

Download Presentation
## Valuation and levered Betas

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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?

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 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?

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?

Download Presentation

Connecting to Server..