Question

Note: These two problems are answered based on the question below. I believe the interest payments are (A)$100 and i believe the cash flows based on interest is (A)132.88

Consider a bond paying a coupon rate of 10% per year, compounded annually. Assume that the market interest rate (YTM or return on investments of like risk) is 15% per year. In other words you want a 15% return on the bond. The bond has three years until maturity. The par value is $1,000. Assume that you buy the bond today for $885.84.

What are the interest payments that you will receive in yr 1, yr 2, and yr 3?   

a. $100

b. $88.85

c. $85.84

d. $150

e. None of above

What are the cash flows (interest only) that you want to receive in yr 1, yr 2, and yr 3 (based on the 15% return)?

a. $132.88

b. $150

c. $88.58

d. $100

e. None of above

Answer 1

Solution:

a. $100.

Interest payments are the coupon payments on the bond and they are fixed and based on frequency of payment and the face value of the bond. In this case the coupon interest is 10% annually and amounts to 10% x $1,000 = $100

d. $100

Cash flows (interest only) than an investor would want or expect to receive on his investment of $885.84 on the bond based on the 15% return would be $100 since the present value of these cash flows of interest added to the present value of the terminal payment of face value when discounted at 15% result in repayment of our investment. Here's how: discounting by @15%, the cash flows of 3 interest payments and 1 terminal value to arrive at the sum of their present value:

[$100 (1+0.15)¹] + [$100 (1+0.15)²] + [$100 (1+0.15)³] + [$1000 (1+0.15)³]

= [$100 1.15¹] + [$100 1.15²] + [$100 1.15³] + [$1000 1.15³]

= [$100 1.15¹] + [$100 1.15²] + [$100 1.15³] + [$1000 1.15³]

= 86.9565 + 75.6144 + 65.7516 + 657.5162

= 885.8387

Hence, the valuation of the bond based on present values of its cash flows discounted @15% is 885.84 which is nothing but the amount invested which means the cash flows generate 15% return over and above our investment.

Hence, the cash flows (interest component only) we would want to receive in yr 1, 2 and 3 based on the 15% return is $100.

(Note: On discounting with 15%, had the PV been below 885.84, we would have said the cash flows generate less than 15% and would have expected them to be higher than $100 for interest and $1000 terminal payment. Had the PV been greater than 885.84, the return would be greater than 15% and in that case we would be satisfied with the cash flows since they get us our minimum expected return. As long as the present value is 885.84 or more i.e. the amount we invested, we would not want to change anything. If the present value was less, we would be dissatisfied with the investment and wanted to receive higher cash flows to compensate for the less than 15% return)