Corporate Finance, Module 16, "Debt Policy"

Homework

(The attached PDF file has better formatting.)

Updated: June 28, 2005

The risk-free interest rate is 10%, the expected return on the market portfolio is 18%, and a firm’s debt-to-equity ratio is 100%, so debt and equity each comprise 50% of capital. Assume the corporate tax rate is zero.

If the cost of debt capital is 12% and the beta of equity is 1.500, what are

The cost of equity capital

The beta of debt

The expected return on assets

The beta of assets

define:

rf: risk free rate

rm: market return

rd: cost of capital for debt

re: cost of capital for equity (not sure if this is a right terminology)

ra: expected return for asset

Bd: beta for debt

Be: beta for equity

Ba: beta for asset

given rf=10%, rm=18%, rd=12%, Be=1.5, D/V=E/V=0.5

(A) re=rf+Be(rm-rf) = 22%

(B) rd = rf+Bd(rm-rf) => Bd = 0.25

(C) ra=D/V * rd + E/V * re =17%

(D) ra=rf+Ba(rm-rf)  => Ba = 0.875

Check:

we know

Ba= D/V * Bd + E/V * Be

=0.5(0.25)+0.5(1.5) = 0.875 (agree with D)

 

    

 

I thought 18% is the expected return on profolio, which is the asset. So i used the formula: re = (D/E)(ra-rd)+ra and get re=24%. Please help me explain. Thanks

In my opinion,the expected return on the market portfolio depends on the aggregate of equity and debt,that is,it is one thing that contains two parts,but when you access the return,you should use the total gain and the total cost.The expected return on assets is just the weighted-average cost.Obviously,they two are different.Welcome for further discussion. 

stay hungry,stay foolish

We think of the Market Portfolio as an Index (ie S&P composite index) that consists of securities that have the same degree of risk as the firm.

The Market Portfolio is not a measure of the return for ONE specific firm.

I agree with all the above posted answers. To clarify for anyone confused, this assignment is based on the CAPM model. The basic formula for CAPM is the following:

Expected return on Y - Risk free rate = Beta of Y x (Expected market return - Risk free rate)

We are given that the risk free rate is .10 and the expected market return is .18 which brings us to the following formula:

Expected return on Y - .10 = Beta of Y x (.18 - .10)

Now all we need to do for each part is fill in the variable "expected return on Y" or the varible "Beta of Y" and solve for the other variable.

A) Given: Beta of equity = 1.5  Solve: Expected return on equity = .22 (22%)

B) Given: Return on debt capital = .12  Solve: Beta of debt capital = .25

C) Here we do a weighted average of the returns on debt and returns on equity. Since we are told that they are equally weighted, we have 1/2(.12) + 1/2(.22) = .17 (17%)

D) Given: Return on assets = .17 (from part C)  Solve: Beta of assets = .875

I hope this helps!