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 41 percent per year, and the annual risk-free rate is 5 percent per year, compounded continuously.

Based on the Black–Scholes model, what is the market value of the firm’s equity and debt?

Answer 1

d1 = [{ln(S0/X)} + {t(r - q + ²/2)}] / [(t)^1/2]

= [{ln(26,100/25,000)} + {1(0.05 + 0.41²/2)}] / [0.41(1)^1/2]

= 0.1771 / 0.41 = 0.4320

d2 = d1 - [(t)^1/2]

     = 0.4320 - [0.41(1)^1/2]

= 0.4320 - 0.41 = 0.0220

Equity = [S0 x e-qt x N(d1)] - [X x e-rt x N(d2)]

= [26,100 x e^-0*1 x N(0.4320)] - [25,000 x e^-0.05*1 x N(0.0220)]

= [26,100 x 0.6671] - [25,000 x e^-0.05*1 x 0.5088]

= 17,345.12 - 12,098.82 = $5,246.29

Debt = Firm Value - Equity = $26,100 - $5,246.29 = $20,853.71