Question

Suppose the U.S. government issues a one-year bond with a face value of $1,000 and a zero coupon.

(a) If interest rates on bank deposits are 3 percent, would we expect the yield of the bond to be greater than, less than, or equal to 3 percent? Explain intuitively why this is the case.

(b) What will the market price of the bond be, given the yield?

(c) Suppose the bond is sold for the price you calculated in part (b). One day later, interest rates on bank deposits suddenly decrease from 3% to 2%. What would the bond’s yield adjust to? Calculate the new price of the bond, given this yield. Does the price of the bond increase or decrease? Explain intuitively why this is the case.

Answer 1

Ans: (A) The yield on bond would be equal to 3 percent because the bond yield depend on purchasing price and the prevailing interest rate. Zero coupon bonds have a yield equal to normal rate of return because there is negative relationship between the yield and bond prices; also there is negative relationship between interest rates and bond prices.

So if the bond yield is greater than the interest on bank deposits then the demand for bond will rise; people will be more willing to invest in bond, which will drive up the price of the bond and then bond's yield will decline till it reaches reaches the bank interest rate beacuse we know that there is negative relationship between yield and bond prices; Also if bond's yield is less than the bank interest rate (3%) then people will not invest in bond, demand will decline as then price will also decline which will cause the yield to go up till it reaches the interest rate of bank deposits.

(b) Let P be the market price of the bond and = Yield and F = Face value of bond

where P = market price of the bond    F = Face value of bond = $1000  

   = Yield = 3% = 0.03 ; n = total no of year till bond matures = 1

P = $970.87

Thus discounted Price of bond is $970.87.

(c) If the interest rates on bank deposits decrease from 3% to 2% then the bond's yield will decline from 3% to 2%

Calculating Bond's new price of 2% yield by the formula:

P = $980.39

Thus the price of the bond has increased when the interest rates on bank deposits decline from 3% to 2% because there is negative relationship between interest rates and price, If the interest rate declines which leads to decline in yield of bond, so the investors must be compensated by paying them a higher price, because the yield of the bond has declined which can lead to decrease in return earned by the investors, this must be offset by paying thema higher price for the bond so that it can neutralise the loss of interest rates.