A $1,000 par value bond was issued five years ago at a coupon rate of 12 percent
ID: 2655332 • Letter: A
Question
A $1,000 par value bond was issued five years ago at a coupon rate of 12 percent. It currently has 7 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.
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.)
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.)
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.)
Why is the percentage gain larger than the percentage loss when the same dollar amounts are involved in parts b and c?
A $1,000 par value bond was issued five years ago at a coupon rate of 12 percent. It currently has 7 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.
Explanation / Answer
a) Current price of the bond = PV of future interest payments+ PV of face value@ maturity ie. Coupon payment(1- (1+i)^-n )/ I + FV/(1+i)n where coupon payment = 1000*0.12 =120 ie.semiannually -120/2=60; semi-annual i= 0.14/2= 0.07 n= no.of periods remaining= 7*2= 14 Substituting the values in the formula, we get, 60(1-(1+0.07)^-14/0.07 + 1000/1.07^14 ie.524.73+387.82 =912.55 Current bond price= 912.55 b) Percentage capital loss = (Current price - Purchase price) / Purchase price*100 ie.(912.55-_1000)/1000 *100= 8.745 =8.75%(Loss) c) Current market value = 912.55(Purchase price) Maturity value = 1000 So, capital gain will be =( 1000-912.55)/912.55 *100 = 9.583= 9.58% (Gain) d) The percentage gain is larger than the percentage loss because the investment is smaller ie.912.55 < 1000 , even though the gain/loss in absolute terms remain the same(1000-912.55= 87.45)Related Questions
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