Question

A company has a zero coupon bond issue outstanding with a face value of $40,000 that matures in one year. The current market value of the firm’s assets is $56,000. The standard deviation of the return on the firm’s assets is 56 percent per year, and the annual risk-free rate is 4 percent per year, compounded continuously. Based on the Black– Scholes model, what is the market value of the firm’s equity and debt? Formula for the Black-Scholes model is given below. Standard normal cumulative probability table is attached.

where: Black-Scholes Model C = SN(d) - Ee-Ri Nd.) d. = [In(S/E) + (R+ o2/2)]/Voºt d, = d, - Vot

Answer 1

B с D SO $ sigma 56,000 56% 4% 40,000 X $ T 1 BSM Call Option Pricing Model 2 Current value of the company's assets 3 Standard deviation of the return on assets 4 Annual risk-free rate 5 Exercise Price(Face value of debt) 6 Time to Maturity(yrs) 7 d1 8 d2 9 N(1) 10 N(02) 11 call option value on Firm's Assets 12 13 [In(So/X)+(r+.5*sigma^2) *T]/[sigma*sqrt(T)] [In(S0/X)+(r-.5*sigma^2)*T]/[sigma sqrt(T)] N(D1)=NORM.S.DIST(d1, TRUE) N(d2)=NORM.S.DIST(d2, TRUE) SO*N(d1)-X*exp(-rT)*N(02) 0.9523 =(LN(C2/C5)+(C4+0.5*C3^2) *C6)/(C3*C6^0.5) 0.3923 =(LN(C2/C5)+(C4-0.5*C3^2) *C6)/(C3*C6^0.5) 0.8295 =NORM.S.DIST(C7,TRUE) 0.6526 ENORM.S.DIST(C8,TRUE) $ 21,373.80 =C2C9-C5*EXP(-C4*C6) *C10 (=Value of Equity) 14 Value of equity 15 Value of debt $ $ 21,373.80 34,626.20 -C2-C11

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