Consider two bonds A and B with the following characteristics that have the same
ID: 2735156 • Letter: C
Question
Consider two bonds A and B with the following characteristics that have the same price. Calculate the price of Bond A as a percentage of its notional amount to two decimal places. If you spent $10mm to purchase bond A, how much principal (in mm$ with two decimal places) would you receive on its maturity date? Using the fact that bonds A and B have the same price, what is the coupon rate of bond B (as a percentage with two decimal places)? If you spent $10mm to purchase bond B, what coupon payment (in $) will you receive each year?Explanation / Answer
Answer a.
Price of Bond A = 100/1.05^4
= $82.27
Answer b.
10,000,000*1.05^4 = $12,155,062.5
If we invest 10 Million today in Bond A, then we will get 12.16 mm after 4 years with 5% yield.
Answer c.
Price of Bond B is $82.27. Let x be the annual coupon on the bond.
So, 82.27 = x*PVIFA(6%, 5) + 100*PVFA(6%, 5)
7.54 = x*4.212
X = 1.79 or 1.79%
Answer d.
If we invest 10mm in bond B, then we will receive a coupon of $179,000 (10,000,000*1.79%) every year.