# How to calculate the cost of debt

The bonds of ABD Ltd have a face value of $1000$ with one year remaining to maturity. The bonds pay coupons at the rate of $10\%$ p.a.

If the current market price of the bonds is $1018.50$, what is the firms cost of debt?

I know that the annual interest (coupon) paid on the debt is $1000⋅0.10=100$.

So: $$1018.50=1000+100(1+\mathrm{kd})$$ and hence $$\mathrm{kd}=(1100/1018.50)–1=8.0\%$$ But what if the year to maturity is more than 1 year i.e. 6 years? How can i calculate the rate of return(cost of debt)?

Discount the future cash flows to equal the market price of the debt, so if the annual discount factor is $d$ you have $$100(d+d^2+d^3+d^4+d^5)+1100d^6=1018.5$$ Solving numerically you get $d=0.912572$, so $\frac{1}{d}=1.0958$ which corresponds to an interest rate of $9.58\%$.