Question

Powell, Inc. recently sold bonds having a $1,000 par value for $ 1,025. Floatation costs of $ 89.56 per bond reduced the net proceeds from the sale to $ 935.44 per bond. The bond pays $80 in annual year end interest and matures in 10 years. If the marginal tax rate is 34%, what is the after tax cost of bonds?

Answer 1

solution

Let $P$ be the after tax interest from the bond. At a tax rate of $34$ %,

$P = 80 * (1-0.34)=52.8$

The present value of the bond should be equal to the net proceeds from the sale of the bond.

Present value $PV=935.44$

The redemption value $FV$ is the face value of the bond, hence $FV= 1000$

$$PV=P*\frac{1-(1+i)^{-n}}{i}+\frac{FV}{(1+i)^{-n}}$$

Where $i$ is the cost of the bond.

$$935.44=52.8*\frac{1-(1+i)^{-10}}{i}+\frac{1000}{(1+i)^{-10}}$$

Using the Excel formula

$$RATE(nper,pmt,PV,[fv])$$

Where $nper=$ number of payments until maturity, $pmt =$ the annual payments,

$PV=$ the current value of the bond and $FV=$ the redemption value

The cost of the bond $i$ is $6.16$ %

answer: after tax cost of the bond is 6.16%