Question

An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 12% annual coupon. Bond L matures in 12 years, while Bond S matures in 1 year.

Assume that only one more interest payment is to be made on Bond S at its maturity and that 12 more payments are to be made on Bond L.

1. What will the value of the Bond L be if the going interest rate is 5%? Round your answer to the nearest cent.
   $  
   
   What will the value of the Bond S be if the going interest rate is 5%? Round your answer to the nearest cent.
   $  
   
   What will the value of the Bond L be if the going interest rate is 9%? Round your answer to the nearest cent.
   $  
   
   What will the value of the Bond S be if the going interest rate is 9%? Round your answer to the nearest cent.
   $  
   
   What will the value of the Bond L be if the going interest rate is 14%? Round your answer to the nearest cent.
   $  
   
   What will the value of the Bond S be if the going interest rate is 14%? Round your answer to the nearest cent.
   $  
   
2. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?
   
   1. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.
   2. Long-term bonds have greater interest rate risk then do short-term bonds.
   3. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.
   4. Long-term bonds have lower interest rate risk then do short-term bonds.
   5. Long-term bonds have lower reinvestment rate risk then do short-term bonds.

Answer 1

In order to calculate coupon rate we would first calculate coupon amount by using the present value of bond formula.
Price of bond	Interest payment*(1-((1+r)^-n)/r) + Face value*(1/(1+r)^n)
where r represents yield to maturity and n represents number of years.
a.
We would first calculate price of bond L under different interest rate
Calculation of price of bond L if interest rate is 5%
Coupon amount	$120	1000*12%
Price of bond	120*((1-(1.05^-12))/0.05)+1000*(1/(1.05^12))
Price of bond	120*8.8635+1000*0.55684
Price of bond	$1,620.43
Calculation of price of bond S if interest rate is 5%
Price of bond	1120*(1/(1.05^1))
Price of bond	1120*0.95238
Price of bond	$1,066.67
Calculation of price of bond L if interest rate is 9%
Price of bond	120*((1-(1.09^-12))/0.09)+1000*(1/(1.09^12))
Price of bond	120*7.1607+1000*0.35553
Price of bond	$1,214.82
Calculation of price of bond S if interest rate is 9%
Price of bond	1120*(1/(1.09^1))
Price of bond	1120*0.91743
Price of bond	$1,027.52
Calculation of price of bond L if interest rate is 14%
Price of bond	120*((1-(1.14^-12))/0.14)+1000*(1/(1.14^12))
Price of bond	120*5.660292+1000*0.207559
Price of bond	$886.79
Calculation of price of bond S if interest rate is 14%
Price of bond	1120*(1/(1.14^1))
Price of bond	1120*0.877193
Price of bond	$982.46
Summary
	5%	9%	14%
Bond L	$1,620.43	$1,214.82	$886.79
Bond S	$1,066.67	$1,027.52	$982.46
b.
This is because longer term bonds are subject to higher interest rate risk as the increase in interest rate would decrease the value of bond.
Thus, long term bonds have greater interest rate risk than do short-term bonds (Option II).