Question

A bond issued with a face value of $1,000 pays a 3% coupon rate and matures in seven years. If an investor wants a yield of 4%, what is the investor willing to pay for the bond?

Answer 1

Price of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)

Where Cupon Amount = Face value of bond * Cupon Rate

= $1000 * 3%

= $30

Redemption Amount = $1000

r or Yield to maturity = 4%

n or number of years to maturity = 7 years

Present Value of Annuity Factor (4%, 7) = 6.002055

Present Value of Interest Factor (4%, 7) = 0.759918

Therefore

Bond Price = $30 * 6.002055 + $1000 * 0.759918

Bond Price =$180.06165 + $759.918

Bond Price = $939.97965

Rounding to two decimal places (if required)

Bond Price = $939.98

Notes

• Why did we use Present Value of Annuity Factor for Cupon Amounts

The cupon amounts would be received every year till maturity of the bond. This means for 7 years there will be 7 cupon payments from the bond.

• Why did we use Present Value of Interest Factor for Redemption amount

The Redemption amount would be received only once and that is at the 7th year or the year of maturity of the bond.

• How did we calculate the discounting factors @ 4%

Year 1 = 1/1.04

= 0.961538

Year 2 = 0.961538/ 1.04

= 0.924556

Year 3 = 0.924556/ 1.04

= 0.888996

Year 4 = 0.888996 / 1.04

= 0.854804

Year 5 = 0.854804/ 1.04

= 0.821927

Year 6 = 0.821927/ 1.04

= 0.790315

Year 7 = 0.790315/ 1.04

= 0.759918

Now if we add all these discounting factors we will get the Present Value of Annuity Factor (4%, 7) = 6.002055

For Present Value of Interest Factor we will take discounting factor of Year 7 i.e. 0.759918 since we will receive the redemption amount at year 7.