Question

5. Suppose a two year bond has a coupon of 15%, with a face value of $121. The current market interest rate is 10% a. What is the present discounted value of $121 if the interest rate stays at 10% for the foreseeable future? (Hint: what is the amount of money you need to put in the bank now to get $121 in two years at an interest rate of 10%) b. What is the price of this bond if the interest rate stays at 10% for the foreseeable future? c. Now suppose you believe that the interest rate will remain at 10%, but the following year's will increase to 20%. How much are you willing to pay for the bond now? Is this higher or lower than your answer to part (b)? d. Suppose everyone in the market agrees with your prediction of interest rates in the following year. What would happen to the demand for this bond? What would happen to the price of bonds as a result?

Answer 1

a) Let the present discounted value of $121 be P.

Then, P*(1+10%)² = 121 => P = 100.

b) Price of the bond will be equal to the sum of all future cash flows discounted to present. Coupon payment each year = 15% * 121 = $18.15.

So, Price of Bond = 18.15/(1+10%) + (18.15+121)/(1+10%)² = 16.5 + 115 = $131.5

c) Here only the 2nd cash flow will change, so we will calculate that: (18.15+121)/(1+20%)² = $96.63. Now, adding the first cash flow of $16.5, we will get the price of bond as 16.5 + 96.63 = $113.13, which is less that $131.5 that we obtained in b).

d) Since interest rate predicted in second year is 20%, which is greater than the coupon rate of bond (15%), thus demand for bond will decrease as people will prefer deposit their money in bank as they would get 20% return their in the second year. Thus, due to low demand, price of bond will decrease.