Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $25,000 face value that matures in one year. The current market value of the firm’s assets is $26,100. The standard deviation of the return on the firm’s assets is 34 percent per year, and the annual risk-free rate is 5 percent per year, compounded continuously. The firm is considering two mutually exclusive investments. Project A has an NPV of $2,600, and Project B has an NPV of $3,500. As the result of taking Project A, the standard deviation of the return on the firm’s assets will increase to 54 percent per year. If Project B is taken, the standard deviation will fall to 36 percent per year.

a-1 What is the value of the firm’s equity and debt if Project A is undertaken? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Market value

Equity $ Debt $

a-2 What is the value of the firm’s equity and debt if Project B is undertaken?

Answer 1

Ans a) We can use black scholes formula to find this.

d1 = (ln(Vt/K) + ((r + stadev^2/2)*t))/(root(t)*stadev)

where Vt is current market value of the firm's asset

k is face value of zero counpon bond

r is interest rate

t is time period

d1 = (ln(26100/25000) + (.05 + (.34^2)/2)* 1)/.34 *1

= .44370

d2 = d1 - stadev*root(t)

= .10370

With the help of z-table we will find the value of n(d1) and n(d2)

N(d1) = .67137

N(d2) = .54130

Market value of the firm's equity = Vt * N(d1) - K*e^(-r*t)*N(d2)

= $ 4650.34

Market value of debt = market value of firm's asset - market value of equity

= $26100 - $4650.34 = $21449.66

Ans b) Simiarly we will find the results for project A and B

For A value of Vt = $28700 & stand. dev = 54%

For B value of Vt = $29600 & stand dev = 36%

Market value of equity if project A is undertaken = $8370.53

Market value of debt = $28700 - 8370.53 = $20329.47

Market value of equity if project A is undertaken = $7395.46

Market Value of debt = $29600 - 7395.46

= $ 22204.54