The Waffle House has $$25$ million of risk$-$free debt outstanding. This debt has an annual coupon rate of

$8\%$ and matures in $2$ years. Coupons are paid once per year. The current term structure is flat at $4\%$ per

year, compounded annually.

a$.$ What is the current market value of the firm's debt? $(2$ points$)$

b$.$ What is the duration of the firm's debt? $(4$ points$)$

c$.$ Suppose yields rise by $200$ basis points $($from $4\%$ to $6\%).$ Calculate the modified duration and use

it to approximate the new market value of the firm's debt. $(4$ points$)$