Question

1. (15 points) David is considering buying two bonds in order to service a payment due in 5 years. Bond A is a 5 year bond with 4% annual coupon selling at par (100%). Bond B is a 3 year zero coupon bond (i.e. bond with no coupons and selling at discount) yielding 3.5% (annual compounding). a. Should the reinvestment rate of the cash flows received is 4.5% throughout 5 years, which bond is a better 5 year investment? Show your working. (8 points) (Assuming that you can invest in odd amount of par value, down to a dollar. Hint: Assume initial investment of $100 in both scenarios and calculate the corresponding future values.) b. David is a conservative investor and has the view that interest rates will go up in the coming 3 years. What do you think he will do? Please explain. (4 points) c. At what yield should the 3 year zero coupon bond be trading for the two investments to have the same performance in 5 years should reinvestment rate of the cash flows is 4.5 throughout the 5 years? (3 points)

Answer 1

Let the par value of both Bonds A and B be $100

Price of Bond A is $100 since it is selling at par

Price of Bond B = 100/1.035^3 = $90.194271

a) If $100 is invested in A to purchase 1 bond

$ 4 received after 1 year is reinvested at 4.5% for 4 years to get 4*1.045^4 = $4.77 after 5 years

$ 4 received after 2 years is reinvested at 4.5% for 3 years to get 4*1.045^3 = $4.5647 after 5 years

$ 4 received after 3 years is reinvested at 4.5% for 2 years to get 4*1.045^2 = $4.3681 after 5 years

$ 4 received after 4 years is reinvested at 4.5% for 1 year to get 4*1.045 = $4.18 after 5 years

$ 104 received after 5 years was not reinvested

Total amount received after 5 years = 4.77+4.5647+4.3681+4.18+104 = $121.88

If $100 is invested in B to purchase 100/90.194271 = 1.1087179 bonds

After 3 years , maturity amount = $100* 1.1087179 = $110.87179 is received which is reinvested at 4.5% for 2 years to get 110.87179*1.045^2 =$121.0747

So, Same amount invested results in a bigger amount after 5 years for bond A

So, Bond A is a better investment

b) If David thinks that the interest rates are going to increase in the coming 3 years, it is better to have as much money in hands as possible. In this case, it may be better for David to purchase the 3 year coupon bond and then reinvest the entire amount at the increased rates for the last 2 years. For example, if the reinvestment rate increases beyond 5% , then Bond B becomes a better investment than Bond A.

c)   As calculated earlier, Bond A with a reinvestment rate of 4.5% gives an amount of $121.88

For investment of $100 in Bond B to give an amount of $121.88 ,

After 3 years , Bond B value should amount to = 121.88/1.045^2 = 111.61177

So, the no. of bonds B to be purchased with $100 = 111.61177/100 = 1.1161177

So, the price of one bond B today =100/1.1161177 = $89.596289

So, the yield (y) of Bond B = (100/89.596289)^(1/3) - 1 = 0.0372975 = 3.72975%