Question

(calculate step by step )

You have bought a bond which carries a coupon rate of 8 percent, has 7 years until maturity and sells at a yield to maturity of 7 percent.

Show your calculations and answer the following questions

1. 4.1) What coupons do bondholders receive each year?

2. 4.2) What is the price that you paid for this bond? (Assume annual coupon payments)

3. 4.3) What will happen to the bond price if the yield to maturity rises to 9 percent? (give

   theoretical and calculation answers)

Answer 1

Answer : 4.1) The amount that bondholder's will receive 80. (1000 * 8 %)

Answer .4.2) Calculation of Price that was paid on the bond :

Price of Bond = (Coupon * PVAF @ YTM for n years) + (Face value * PVF @ YTM for nth year)

Coupon = 1000 * 8% = 80

YTM is yield to maturity i.e 7% or 0.07

n is the years to maturity is 7

Price of Bond = (80 * PVAF @ 7% for 7 years) + (1000 * PVF @ 7% for 7th year)

= (80 * 5.38928940153) + (1000 * 0.62274974185)

= 431.143152122 + 622.74974185

= 1053.89289397 or $1053.89

Note : PVF can be calculated using [1 / (1 + 0.07)7 ] = 0.62274974185

PVAF can be calculated as {[1 - (1 + 0.07)-7 ] / 0.07} = 5.38928940153

Answer .4.3) Calculation of Price that was paid on the bond  if the yield to maturity rises to 9 percent

Price of Bond = (Coupon * PVAF @ YTM for n years) + (Face value * PVF @ YTM for nth year)

Coupon = 1000 * 8% = 80

YTM is yield to maturity i.e 7% or 0.09

n is the years to maturity is 7

Price of Bond = (80 * PVAF @ 9% for 7 years) + (1000 * PVF @ 9% for 7th year)

= (80 * 5.03295283498) + (1000 * 0.54703424482)

= 402.636226798 + 547.03424482

= 949.670471618 or $949.67

Note : PVF can be calculated using [1 / (1 + 0.09)7 ] = 0.62274974185

PVAF can be calculated as {[1 - (1 + 0.09)-7 ] / 0.09} = 5.38928940153