Question

Bond A has a 7% coupon rate, paid annually. Maturity is in three years. The bond sells at par value &1000. The actual price of the bond if the interest rate immediately decreases from 7% to 6% is ____.

A. 1027.25

B. 1026.68

C. 1026.73

D. 1026.73

Answer 1

The correct answer is C. 1026.73

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 * 7%

= 70

Redemption Amount = 1000

r or Yield to maturity = 6%

n or number of years to maturity = 3 years

Present Value of Annuity Factor (6%, 3) = 2.673011

Present Value of Interest Factor (6%, 3) = 0.839619

Therefore

Bond Price = 70 * 2.673011 + 1000 * 0.839619

=187.1108 + 839.6193

= 1026.7301

Rounding to two decimal places

Bond Price = 1026.73

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 3 years there will be 3 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 3rd year or the year of maturity of the bond.

• How did we calculate the discounting factors @ 6%

Year 1 = 1/1.06

= 0.943396

Year 2 = 0.943396/1.06

= 0.889996

Year 3 = 0.889996 / 1.06

= 0.839619

Now if we add all these discounting factors we will get the Present Value of Annuity Factor (6%, 3) = 2.673011

For Present Value of Interest Factor we will take discounting factor of Year 3 i.e. 0.839619 since we will receive the redemption amount at year 3.