Question

Assume that you are considering the purchase of a 20-year, bond with an annual coupon rate of 10%. The bond has a par value of $1,000, and it makes annual interest payments. If you require an 8% yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? Explain why the price is different from the par value.

Answer 1

Price of a bond includes Present value of Annual Coupon Payments + Present Value of Redemption Vlaue.

Assuming redemption at par on 20^th year end.

P₀ = I*PVAF(8%,20) + F*PVIF(8%,20)

where, P₀ = price today,

I = Annual Coupon(Interest) Payments = $1000*10% = $100 Each Year for 20 Years

F = Redemption amount at the end of year 20 at par = $1000

PVAF = Present Value annuity factors @ 8% for 20 years SUM{1/(1.08)}²⁰ = 9.8181

PVIF Present Value Discounting Factor at 20 Year end (1/1.08)²⁰ = 0.2145

P₀ = 100(9.8181)+1000(0.2145)

= 981.81+214.55

= $1196.36

Maximum Price Willing to pay today for the Bond to earn 8% Yield to Maturity is $1196.36.

Difference Because of YTM.

If you pay $1000 for a bond you will earn higher Yield i.e. 10%

but if you want to earn less Yield than 10% i.e. 8% than you can purchase it at higher cost but maximum i.e. $1196.36.

The Relations between Yield and Price of a Bond is Inverse therefore if Yield increases price of a bond decreses (10% and $1000) and if Yield decreses price of a bond increases (8% and $1196.36).