Question

A $1,000 par value bond was issued five years ago at a coupon rate of 8 percent. It currently has 10 years remaining to maturity. Interest rates on similar debt obligations are now 10 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.

a. Compute the current price of the bond using an assumption of semiannual payments. (Do not round intermediate calculations and round your answer to 2 decimal places.)
  

b. If Mr. Robinson initially bought the bond at par value, what is his percentage capital gain or loss? (Ignore any interest income received. Do not round intermediate calculations and input the amount as a positive percent rounded to 2 decimal places.)
  

  
c. Now assume Mrs. Pinson buys the bond at its current market value and holds it to maturity, what will be her percentage capital gain or loss? (Ignore any interest income received. Do not round intermediate calculations and input the amount as a positive percent rounded to 2 decimal places.)
  

d. Why is the percentage gain larger than the percentage loss when the same dollar amounts are involved in parts b and c?
  

	The percentage gain is larger than the percentage loss because the investment is larger.
	The percentage gain is larger than the percentage loss because the investment is smaller.

Answer 1

Answer a
Calculation of current price of bond
Current price of bond = Present value of future semiannual coupon payments + Present value of bond par value
Calculation Present value of future semiannual coupon payments
We can use the present value of annuity formula to calculate this value.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = Present value of future semi annual coupon payments = ?
P = Semi annual coupon payment = $1000 x 8%/2 = $40
r = market interest rate per semi annual period = 10%/2 = 5%
n = number of semi annual periods to maturity = 10 years x 2 = 20
Present value of annuity = 40 x {[1 - (1+0.05)^-20]/0.05}
Present value of annuity = 40 x 12.46221
Present value of annuity = 498.49
Present value of future semi annual interest payments = $498.49
Calculation of present value of bond par value
Present value of bond par value = Par value of bond x discount factor @ 5% for 20th semi annual period
Present value of bond par value = $1000 x (1+0.05)^-20
Present value of bond par value = $1000 x 0.376889
Present value of bond par value = $376.89
Current price of bond = $498.49 + $376.89
Current price of bond = $875.38
Answer b
Percentage capital gain or loss = (Current price of bond - Purchase cost of bond) / Purchase cost of bond
Percentage capital gain or loss = ($875.38 - $1000)/$1000
Percentage capital loss = 12.46%
Answer c
Percentage capital gain or loss = (Maturity value of bond - Purchase cost of bond) / Purchase cost of bond
Percentage capital gain or loss = ($1000 - $875.38)/$875.38
Percentage capital gain = 14.24%
Answer d
The percentage gain is larger than the percentage loss because the investment is smaller.