Question $18(8\mathrm{.}5$ points$)$

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$($HINT$,$ THIS QUESTION IS NOT THAT DIFFICULT$)$ Your firm has a market value balance sheet of Assets $($$$20)=$ Debt $(14\mathrm{.}3)+$ Equity $($$$5\mathrm{.}7),$ which we can call a Base Case. Other information is the face value of debt is $$40,$ the debt matures in $5$ years, the Asset return standard deviation $=50\%,$ and the risk free rate is $4\%.$ You have three mutually exclusive capital budgeting projects from which to choose.

Project A has an NPV of $$4.$ Project A$\text{'}$s Standard Deviation is $40\%.$ If Project $A$ is accepted, the firm's new Asset Value will be $$24$ and the new Debt Value will be $16\mathrm{.}3.$

Project B has an NPV of $$1.$ Project A$\text{'}$s Standard Deviation is $60\%.$ If Project B is accepted, the firm's new Asset Value will be $$21$ and the new Debt Value will be $12\mathrm{.}9.$

Project $C$ has an NPV of $-$$$1.$ Project A$\text{'}$s Standard Deviation is $80\%.$ If Project $C$ is accepted, the firm's new Asset Value will be $$19$ and the new Debt Value will be $12\mathrm{.}7.$

a$.(3/7$ value$)$ What is the value of the put option associated with the risky debt in Scenario C$?$ Show your work for any credit.