The cost of debt is the bond's yield to maturity $($VTM$).$

The bond's value $($or price$)$ is the present value of all its expected cash flows. We

can use the annuity formula to find the present value of the interest payments

$($coupons$)$ and then add the present value of the face value.

$P=\frac{\frac{?}{\text{I}\text{N}\text{T}}}{r_d}[1-\frac{1}{(1+r_d{)}^n}]+\frac{M}{(1+r_d{)}^n}$

$=>891\mathrm{.}9=\frac{36}{r_d}[1-\frac{1}{(1+r_d{)}^{10}}]+\frac{1,000}{(1+r_d{)}^{10}}$

Unfortunately, this equation is non$-$linear in $r_d($the YTM$),$ so we cannot just solve

for $r_d.$ Instead, we have to use trial and error, a financial calculator or Excel $($the

RATE$()$ or YIELD$()$ functions$)$ to find $r_d.$

Using a financial calculator:

Note that the current price of the bond $($the PV$)$ must be entered as a negative

number. Calculating $\frac{1}{V}$ gives a value of $r_d=5\%,$ or $0\mathrm{.}05.$

Using Excel $($do not enter the thousand separators$)$:

$=$ RATE$($nper$,$ pmt$,$ pv$,$ fv$)$

$=$ RATE $(10,36,-891\mathrm{.}9,1,000)$

$=0\mathrm{.}05$

Pre$-$tax cost of debt:

$r_d=r_d=0\mathrm{.}05$

Part $2$

What is the company's after$-$tax cost of debt?