Question

Maria has about $200,000 to invest for 5 years. Given her current investments, her adviser has recommended that she invest the money in corporate bonds. Her adviser has suggested two alternatives. Alternative 1 is $200,000 face value of bonds with quarterly coupon payments and a coupon rate of 8% APR compounded quarterly. These bonds were issued five years ago and have exactly five years remaining. They are selling at a price that implies a yield to maturity of 7.90% APR compounded quarterly. Alternative 2 is a five-year zero-coupon bond with a face value of $297,000 and a current price of $200,000. Assume annual compounding on the zero-coupon bond.

1. What is the current price of the $200,000 face value bonds?
2. What is the yield to maturity on the zero-coupon bond?
3. Assuming the two alternatives have the same default risk, which of these two alternatives would you recommend to Maria and why? You can assume that Maria will hold the investments until maturity and will be able to reinvest any intervening cash flows at that investment’s yield to maturity. Be sure to address the comparative return of each investment and whether the pattern of cash flows matters under the assumptions given.

Answer 1

What is the current price of the $200,000 face value bonds? (4 marks)
=((8%*100/4)/(7.90%/4)*(1-1/(1+7.90%/4)^(4*5))+100/(1+7.90%/4)^(4*5))*200000/100=200819.5476

What is the yield to maturity on the zero-coupon bond? (2 marks)
=(297000/200000)^(1/5)-1=8.23%

Assuming the two alternatives have the same default risk, which of these two alternatives would you recommend to Maria and why? You can assume that Maria will hold the investments until maturity and will be able to reinvest any intervening cash flows at that investment’s yield to maturity. Be sure to address the comparative return of each investment and whether the pattern of cash flows matters under the assumptions given. (4 marks)

As Maria will be able to reinvest the cash flows at ytm, yield realized on Alternative1 will be 7.90% but on Alternative 2 will be 8.23%. There is no reinvestment risk in Alternative 2 as there will be no coupon payments but reinvestment risk will be there in Alternative1. Choose Alternaitve 2. In Alternative 1, the returns will comprise of negative capital gains yield and positive current yield but in case of Alternative2, the returns will comprise only of capital gains yield.