Question

5. A 30-year 1000 par value bond with coupons at 9% payable semiannually and a redemption value of 1100 is purchased for a price that results in a yield of 12% compounded semiannually. Suppose that the bond is called (i.e. redeemed) prior to the actual maturity date and results in an actual nominal yield rate convertible semiannually of 14%. Note: Assume that the bond is called immediately after a coupon payment is made. Calculate the number of years the bond was held. Round your answer to the nearest whole number. Answer:

Answer 1

First we find the purchase price that yields 12% return i.e 6% semiannual return

We know, value of bond is the present value of the future cash flows

Value of bonds = 45 (P/A, 6%, 60 semiannual intervals) + 1100 (P/F, 6%, 60 th interval)

Value of bonds = 760

Now, we are given that, bonds are redeemed before maturity and it results in yield to increase to 7%.

We calculate DF for each year using 7% rate.

DF for each year = 1/(1+7%)^N

Then we keep on reducing the period, such that PV of the cashflows comes to original purchase price. We find that , at 20 intervals, PV comes to 760, which is our original purchase price

Year	Cashflows	DF	PV
1	45	0.934579	42.05607
2	45	0.873439	39.30474
3	45	0.816298	36.7334
4	45	0.762895	34.33028
5	45	0.712986	32.08438
6	45	0.666342	29.9854
7	45	0.62275	28.02374
8	45	0.582009	26.19041
9	45	0.543934	24.47702
10	45	0.508349	22.87572
11	45	0.475093	21.37918
12	45	0.444012	19.98054
13	45	0.414964	18.6734
14	45	0.387817	17.45178
15	45	0.362446	16.31007
16	45	0.338735	15.24306
17	45	0.316574	14.24585
18	45	0.295864	13.31388
19	45	0.276508	12.44287
20	1145	0.258419	295.8898
			760.9915

Bond was held for 20 intervals, i.e effective 10 years.