Answer to Question #131564 in Finance for Zainab ameen

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?
1
2020-09-08T10:11:13-0400

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%

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