Question

A $1,000 par value bond was issued five years ago at a 6 percent coupon rate. It currently has 20 years remaining to maturity. Interest rates on similar debt obligations are now 8 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.)
  

Answer 1

a. Bond Price = C * [1- 1/(1+i)^n] / i + M/(1+i)^n

where , C = coupon payment = 1000 * 6%/2 = $30

i = market rate = 8%/2 = 4%

n = periods to maturity = 20*2 = 40

M = Face value = $1000

Bond Price = 30 * [1- 1/(1+.04)^40] / .04 + 1000/(1+.04)^40

= 30*19.79277 + 1000*0.20829

= $802.07

Current Bond price = $802.07

b. Capital Loss = 1000 -802.07 = $197.93

% capital loss = 197.93/1000 * 100 = 19.79%

c. Purchase price = $802.07

Maturity Price = $1000

Capital gain = 1000 - 802.07 = $197.93

% gain = 197.93/802.07 *100 = 24.68%