On January 1, 2013, Drennen, Inc., issued $3 million face amount of 10-year, 14%

Question

On January 1, 2013, Drennen, Inc., issued $3 million face amount of 10-year, 14% stated rate bonds when market interest rates were 12%. The bonds pay semiannual interest each June 30 and December 31 and mature on December 31, 2022. Table 6-4, Table 6-5 (Use appropriate factor from the table provided.)

a. Calculate the proceeds (issue price) of Drennen, Inc.'s, bonds on January 1, 2013, assuming that the bonds were sold to provide a market rate of return to the investor. (Enter your answers rounded to the nearest whole number.) If you could, please show steps. Thank You!

Explanation / Answer

Interest rate = 14% per annum. Amount of semiannual interest = annual interest rate/2*face value = 14%/2*$3 million = $210,000.

Now, issue price = present value of all future cash flows that are discounted at the market interest rate i.e. a rate of 12% per annum. Now, first of all we have a constant cash flow in the form of interest i.e. $210,000 every 6 months. Now the discount rate = 12% per annum or 6% every 6 months. Term = 10 years or 20 semiannual periods. Now, using the PVIFA table for values k = 6% and n = 20, we get the factor as 11.470.

Thus present value of all interest payments = amount of interest*PVIFA = 210,000*11.470 = $2,408,700

Now, at the end of 10 years, the maturity amount will be = the face value = $3 milllion. Present value (PV) of this amount = $3 million * discount factor. Discount factor = 1/(1.06)^20 = 0.3118

Thus PV = $3 million*0.3118 = $935,414.18

Thus proceeds = PV of maturity amount + PV of all interest payments

= $935,414.18+$2,408,700

= $3,344,114.18. This will be rounded off to the nearest whole number i.e $3,344,100

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