Problem $25-20$ Equity as an Option and NPV $[$LO$4,5]$

A company has a single zero coupon bond outstanding that matures in five years with a

face value of $$31$ million. The current value of the company's assets is $$24$ million, and

the standard deviation of the return on the firm's assets is $47$ percent per year. The risk$-$

free rate is $5$ percent per year, compounded continuously.

a$.$ What is the current market value of the company's equity? $($Do not round

intermediate calculations and enter your answer in dollars, not millions, rounded to

$2$ decimal places, e$.$g$.,1,234,567\mathrm{.}89.)$

b$.$ What is the current market value of the company's debt? $($Do not round intermediate

calculations and enter your answer in dollars, not millions, rounded to $2$ decimal

places, e$.$g$.,1,234,567\mathrm{.}89.$

c$.$ What is the company'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$.,32\mathrm{.}16.)$

d$.$ The company has a new project available. The project has an NPV of $$2,000,000.$ If

the company undertakes the project, what will be the new market value of equity?

Assume volatility is unchanged. $($Do not round intermediate calculations and enter

your answer in dollars, not millions, rounded to $2$ decimal places, e$.$g$.,$

$1,234,567\mathrm{.}89.$

e$.$ Assuming the company undertakes the new project and does not borrow any

additional funds, what is the new continuously compounded cost of debt? $($Do not

round intermediate calculations and enter your answer as a percent rounded to $2$

decimal places, e$.$g$.,32\mathrm{.}16.)$