Question #131564

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?

Expert's answer

**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.

Using the Excel formula

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%*

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