Problem $25-18$ Equity as an Option $[$LO$4]$

Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $$43,000$ that matures in one year. The current market value of the firm$$s assets is $$46,600.$ The standard deviation of the return on the firm$$s assets is $35$ percent per year, and the annual risk$-$free rate is $5$ percent per year, compounded continuously.

a$.$

Based on the Black$-$Scholes model, what is the market value of the firm's equity and debt? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the firm's continuously compounded cost of debt? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$