Question

1. A $10,000 corporate bond matures in one year, meaning that it returns $10,000 principal to the owner in one year. The bond also makes four quarterly interest payments on the way to maturity: it pays $150 after three months, $150 again after six months $150 again after nine months, and a final interest payment of $150 at the same time that the principal is returned.

(a) Based on the $10,000 original price of the bond, and the sum of the interest payments received per year, what is the original rate of interest on the bond?

(b) If after four months the yield on the bond is 5%, then calculate its price to the nea rest dollar.

(c) If after four months the current market price of the bond is exactly $10,100, then show exactly how to calculate the internal rate of return on the bond. Based on your answer to part (b), what can you immediately say about the internal rate of return (without doing any calculations)?

(d) Continuing part (c), and using a calculator, find the internal rate of return on the bond to the nearest hundredth of a percent.

Answer 1

a) Total Sum of Interest Payments = 150*4 = 600

Original Rate of Interest per year = 600/10000*100 = 6%

b) Price of the bond is represented by the present value of future cash inflows. One month yield rate = 5/12 = 0.4167%

Future Remaining Cash Inflows	Remaining Time period (months)	Dis Factor (.4167%)	Present Value
150	2	0.92	138
150	5	0.82	122
150	8	0.72	108
10000	8	0.72	7,214
			7,582

Hence, the price of the bond with 5% yield should be 7582 after 4 months.

c) To calculate IRR using the formula, one would set NPV equal to zero and solve for the discount rate (r), which is the IRR. Because of the nature of the formula, however, IRR cannot be calculated analytically and must instead be calculated either through trial-and-error or using software programmed to calculate IRR.

Formula for IRR

​0=NPV=t=1∑T​(1+IRR)tCt​​−C0

​where:

Ct​=Net cash inflow during the period

tC0​=Total initial investment costs

IRR=The internal rate of return

t=The number of time periods​