Question

You bought one of Great White Shark Repellant Co.’s 9 percent coupon bonds one year ago for $780. These bonds make annual payments and mature 12 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 10 percent. If the inflation rate was 3.1 percent over the past year, what was your total real return on investment?

Answer 1

Calculation of Selling Price:

Par Value = $1,000

Annual Coupon Rate = 9.00%
Annual Coupon = 9.00% * $1,000
Annual Coupon = $90

Time to Maturity = 12 years
Annual YTM = 10%

Selling Price = $90 * PVIFA(10%, 12) + $1,000 * PVIF(10%, 12)
Selling Price = $90 * (1 - (1/1.10)^12) / 0.10 + $1,000 / 1.10^12
Selling Price = $931.86

Nominal Return = (Selling Price + Coupon - Purchase Price) / Purchase Price
Nominal Return = ($931.86 + $90.00 - $780.00) / $780.00
Nominal Return = 0.3101

Real Return = (Nominal Return - Inflation Rate) / (1 + Inflation Rate)
Real Return = (0.3101 - 0.0310) / (1 + 0.0310)
Real Return = 0.2707 or 27.07%