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

The debt of the company: Par value $=$$$1000,$ Annual coupon rate $=3\%,$ Coupon payment is paid once a year, time to maturity $=2$ years

The current total market value of the firm asset $=$$$1300$

The firm's future values follow a two$-$state path with Up state growth multiple $u=1\mathrm{.}4$ and Down state growth multiple $d=0\mathrm{.}8$ each year.

The annual risk$-$free rate $=5\%$

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

$(2)$ What is the value of the bond if it is convertible with a convertible ratio of $15$ and $20$ shares outstanding?

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