Question

On January 1, 2019, Broker Corp. issued $3,700,000 par value 10%, 12-year bonds which pay interest each December 31. If the market rate of interest was 12%, what was the issue price of the bonds? (The present value factor for $1 in 12 periods at 10% is 0.3186 and at 12% is 0.2567. The present value of an annuity of $1 factor for 12 periods at 10% is 6.8137 and at 12% is 6.1944.)

Answer 1

Answer:

Price = $3,241,718

Explanation:

To calculate issue price of the bonds we first calculate NPV of the bonds after 12 years and Interest payments of the bonds for 12 years.

NPV can be calculated by : Bond value * NPV factor after 12 years

so, Bond Value after 12 years = $3700 000 * 0.2567  = $949,790

We take the market interest rate for this.

Now we calculate Yearly interest payment = 3700000 * 10% = $370,000

we discount it back using annuity for 12 years so, 370000 * 6.1944 = $2,291,000. This is the total interest payments for 12 years in NPV terms.

To calculate issue price simply add Interest payments and Bond NPV value so,

Price  =  2291000 + 949790 = $3,241,718

Hope that helps.