. Suppose you purchased a 20-year, $500,000 deep discount bond when it was initi
ID: 2403044 • Letter: #
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.
Explanation / Answer
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.
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