A $1,000 par value bond was issued five years ago at a coupon rate of 12 percent. It currently has 15 years remaining to maturity. Interest rates on similar debt obligations are now 14 percent. Use Appendix B andAppendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.

A $1,000 par value bond was issued five years ago at a coupon rate of 12 percent. It currently has 15 years remaining to maturity. Interest rates on similar debt obligations are now 14 percent. Use Appendix B andAppendix 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.

 
Explanation:

a.

Price	=	A × ({1 – [1 / (1 + i)n]} / i) + FV / (1 + i)n
	=	[(.12 × $1,000) / 2] × [(1 – {1 / [1 + (.14 / 2)]15 × 2}) / (.14 / 2)] + $1,000 / [1 + (.14 / 2)]15 × 2
	=	$875.91

b.

Percentage gain (loss)	= (Current value – Purchase price) / Purchase price
	= ($875.91 – 1,000) / $1,000
	= –$124.09 / $1,000
	= –.1241, or  –12.41%

  

This is the capital loss. The total gain or loss on the investment would need to include the interest payments received during the period of bond ownership.

c.

Percentage gain (loss)	= (Maturity value – Current value) / Current value
	= ($1,000 – 875.91) / $875.91
	= $124.09 / $875.91
	= .1417, or  14.17%

This is the capital gain. The total gain or loss on the investment would need to include the interest payments received during the period of bond ownership.

d.

The percentage gain is larger than the percentage loss because the investment is smaller ($875.91 vs. $1,000). The gain/loss is the same ($124.09).

  

Calculator Solution:

a.

	N			I/Y			PV			PMT			FV
30			7			CPT PV –875.91			60			1,000

Answer: $875.91

Appendix Solution:

a.

Appendix D
Present value of interest payments:
PVA	=	A × PVIFA (7%, 30)
	=	$60 × 12.409
	=	$744.54

  

Appendix B
Present value of principal payment at maturity:
PV	=	FV × PVIF (7%, 30)
	=	$1,000 × .131
	=	$131.00

Bond price	= PV of interest payments + PV of principal
	= $744.54 + 131.00
	= $875.54