Marshall Corporation has a zero coupon bond that matures in five years with a face value of $$83,000.$ The current value of the company's assets is $$79,000,$ and the standard deviation of its return on assets is $42$ percent per year. The risk$-$free rate is $4$ percent per year, compounded continuously.

a$.$ What is the value of a risk$-$free bond with the same face value and maturity as the current bond? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the value of a put option on the firm's assets with a strike price equal to the face value of the debt? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$-1.$ Using the answers from $($a$)$ and $($b$),$ what is the value of the firm's debt? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

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

d$-1.$ Assume the company can restructure its assets so that the standard deviation of its return on assets increases to $51$ percent per year. What happens to the value of the debt? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

d$-2.$ What is the new continuously compounded yield on the debt? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

e$-1.$ If the company restructures its assets, how much will bondholders gain or lose? $($A loss should be indicated by a minus sign. Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

e$-2.$ If the company restructures its assets, how much will stockholders gain or lose? $($A loss amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$