A $1,000 par value bond was issued five years ago at a coupon rate of 8 percent.

Question

A $1,000 par value bond was issued five years ago at a coupon rate of 8 percent. It currently has 7 years remaining to maturity. Interest rates on similar debt obligations are now 12 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.)
  

Current bond price___

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.)
  

Percentage loss ___%

  
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.)
  

Percentage gain ___%

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 smaller. Appendix B Present value of $1, PVF PV=FV Percent Period 9 7 4 Percent Period 2 1 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.640 0.592 0.549 0.510 0.444 0.613 0.592 0.572 0.552 0.534 0.515 0.499 0.482 0.410 0.350 0.301 0.260 0.198 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 0.262 0.207 0.165 0.133 0.088 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 0.168 0.123 0.091 0.068 0.039 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 0.107 0.073 0.050 0.035 0.017 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.014 0.007 0.003 0.002 0 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 0.004 0.001 0.001 0

Explanation / Answer

Par Value of bond = $1,000

Coupon rate = 8%

Annual Coupon payment = $1,000 × 8%

= $80.

Annual Coupon payment is $80.

Number of year remains in maturity = 7%

Current Value of bond = Present value of coupon payment + Present value of par value

= ($80 × 4.564) + ($1,000 × 0.452)

= $365.12 + $452

= $815.12.

Present value of bond is $815.12.

b.

Purchase price = $1,000

Since, Current calue is less than Par value (Purchase price). so Investor has incur loss.

Percentage capital Loss = ($1,000 - $815.12) / $1,000

= $184.88 / $1,000

= 18.488%

Percentage capital loss is 18.488%.

c.

If purchase price = Current value = $815.12.

Percentage gain = ($1,000 - $815.12) / $815.12

= $184.88 / $815.12

= 22.68%

Capital gain is 22.68%.

d.

Since, Purchase price in case of Mrs. Pinson is lower than purchase price in case of Mr. Robinson, So capital gain is more than capital loss.

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