Question

You Corp bonds are selling in the market for $1,020. These 10-year bonds pay 8% interest annually. If they are purchased at the market price, what is the expected rate of return?

Answer 1

Given Information –

Market Price of Corp Bond (PV) = $1,020

Time to Maturity (T) = 10 years

No of periods (n) = 10

Par Value/ Principal (P) = $1,000

Coupon Rate (r) = 8% per annum

Coupon Amount (C) = 1,000 * 0.08 = $80 per annum

Now,

Present Value (PV) = C/(1+r) + C/(1+r)² + ………… + C/(1+r)^n-1 + C/(1+r)ⁿ + [P/(1+r)ⁿ]

PV = {C * [(1+r)ⁿ -1]} / [r * (1+r)ⁿ] + [P/(1+r)ⁿ]

=> 1020 = {80 * [(1+r)¹⁰ -1]} / [r * (1+r)¹⁰] + [1000/(1+r)¹⁰]

Now, bond value is higher than par value which means that the return on bond is lower than 8% (coupon rate)

One way of solving for r is by hit and trial method by taking different values of r and try to find r which gives present value of cash flows equal to today’s market price i.e. $1,020

Rate (r)	Bond Value / Market Price
8.10%	993.32
8.00%	1,000.00
7.90%	1,006.74
7.80%	1,013.54
7.70%	1,020.41
7.60%	1,027.33

Here we see that at r= 7.70%, the bond value is nearest to current market price of $1,020. Further refining gives us the expected rate of return = 7.71%

Alternatively, r can be solved on calculator by putting the following values –

N= 10 PV = -1020    PMT = 80         FV=1000         CPT I/Y to give r= 7.71%