Question

In: Finance

1. Suppose that you are considering the purchase of a coupon bond that has a $200...

1. Suppose that you are considering the purchase of a coupon bond that has a $200 coupon payment every year for 5 years and a $10,000 face value in the 5th year. Suppose the yield to maturity of this bond equals to the market interest rate. a. What is the bond worth today if the market interest rate is 3%? What is the bond’s current yield? (Hint: knowing the interest rate, the value of the bond is how much you should pay for the bond—the price of the bond) b. Suppose one year has elapsed, you have received the first coupon payment of $200 and the market rate is still 3%. How much would another investor be willing to pay for the bond now? Given the price that the other investor is willing to pay (the price at which you can sell the bond), what was your total rate of return on the bond? c. Suppose that one year has elapsed, you have received the first coupon payment of $200 but the market rate suddenly jumps to 5%. In that case how much would another investor be willing to pay for the bond now? What was your total rate of return on the bond? d. Compare your answers from b and c, and explain the relation between the yield to maturity (here the market rate) and the price of bond.

Solutions

Expert Solution

a.) Annual Coupon Payment (P) = $200

Face Value (FV) = $1000

Market Interest (r) or YTM = 3%

Maturity (n) = 5 years

Therefore,

Bond Price = $1778.55

Current Yield = Annual Coupon/Bond Price = 200/1778.55 = 11.25%

b.) Now, everything else is same except Maturity, which is 4 years now.

Therefore, using the same equation:

Bond Price = $1631.90

Total Return on Bond = [ Coupon Received + Current Bond Price - Beginning Bond price ]/ Beginning Bond Price

Total Return on bond = [ 200 + 1631.90 - 1778.55 ] / 1778.55 = .03 or 3%

c.) Now, Maturity = 4 years and Market Interest (r) = 5%

Using the same equation,

Bond Price = $1531.89

Total Return = [ 200 + 1531.89 - 1778.55 ]/ 1778.55 = -.02623 or -2.623 %

d.) In Part b.), when YTM is 3%, Bond Price is $1631.90 but as YTM increases to 5% in Part c.), Bond price dropped to $1531.89. So, we can say that there is an inverse relationship between the YTM and the Bond Price, i.e. if YTM increases, Bond price will decrease.


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