Question

.

Suppose you purchased a 20-year, $500,000 deep discount bond when it was initially offered. 5 years later you

    sell the bond and market interest rates have fallen from 5.45% to 3.9%.

a. Calculate the initial price of the bond.

b. Calculate the current price of the bond.

c. Calculate the annual holding period return on this instrument and compare it to the annual return you were expecting.

d. Explain whether your return would have been relatively greater or less if you had purchased a 10-year instrument.

    Support your conclusion with numerical evidence.

Answer 1

a)

Calculation of initial price of bond:

Face value of bond = $500000

Maturity (n) = 20 years

Market interest rate (r) = 5.45%

Initial price of bond = Face value/(1+r)^n

= 500000/(1.0545)^20 = 500000*1/(1.0545)^20

= 500000*0.34599 = 172995

Initial price of the bond = 172995

b)

Face value of bond = $500000

Years left to maturity (n) = 15 years

Market interest rate (r) = 3.9%

Current price of bond = Face value/(1+r)^n

= 500000/(1.039)^15

= 500000*1/(1.039)^15 = 500000*0.5633 = 281650

Current prie of bond = 281650

c)

Initial price of the bond = 172995

Current prie of bond = 281650

Return on bond in 5 years = 281650 - 172995 = 108655

Return in percentage = (108655/172995) *100 = 62.80%

Annual holding period return = 62.80%/5 = 12.56%

d)

Face value of bond = $500000

Maturity (n) = 10 years

Market interest rate (r) = 5.45%

Initial price of bond = Face value/(1+r)^n

= 500000/(1.0545)^10 = 500000*1/(1.0545)^10

= 500000*0.5882 = 294100

Calculation of initial and current price of bond if the instrument would have been for 10 years:

Face value of bond = $500000

Years left to maturity (n) = 5 years

Market interest rate (r) = 3.9%

Current price of bond = Face value/(1+r)^n

= 500000/(1.039)^5

= 500000*1/(1.039)^5 = 500000*0.82589 = 412945

Return on bond in 5 years = 412945 - 294100 = 118845

Return in percentage = (118845/294100) *100 = 40.41%

Annual holding period return = 40.41%/5 = 8.082%

Return would have been relatively lower if maturity of bond is for 10 years.