You have collected the information about the Imaginary Company as follows:

The debt of the company: Par value $=$$$1000,$ Annual coupon rate $=8\%,$ Coupon payment is paid once a year, time to maturity $=3$ years

The current total market value of the firm asset $=$$$1500$

The firm's future values follow a two$-$state path with Up state growth multiple $u=1\mathrm{.}2$ and Down state growth multiple $d=0\mathrm{.}7$ each year.

$,$ The annual risk$-$free rate $=2\%$

Answer the questions below.

$(1).$ What is the value of the firm's debt if it is a corporate debt? $(30$pt$)$

$(2).$ Suppose there is a Treasury security with the same par value, annual coupon payments, and time to maturity. What is the value of this Treasury security? $($Hint: Simply use the DCF model to solve for it$.)(6$pt$)$

$(3).$ Will the Treasury security or the straight corporate bond have the higher price? Why? $(6$pt$)$

$(4).$ Calculate the yield spread between the straight corporate bond and the Treasury security. $($Hint: Use the answer you get from $(1)$ as the price of the corporate debt, along with the information from the first bullet point that describes the debt, to find the yield of the corporate bond. Then take the difference between it and the risk$-$free rate.$)(6$pt$)$