Question

A company issues a 10-year, 4% coupon bond with semiannual coupon payments. On release, it has a price of $90 per $100 of face value. What is the yield to maturity of this bond when it is released?  

A. 5.31%
B. 2.65%
C. 3.18%
D. 5.30%

C is incorrect. which one is correct and why?

Answer 1

Yield to maturity here can be find out by trail and error method.

Since here it is semi annual payment, coupon payment is 2% for 6 month ($2) and number of period = 10 years * 2 = 20 period.

Yield to maturity after considering time value of money is internal rate of return (IRR). IRR is the rate at which NPV = 0

So first we will take 5.31% per annum which means 2.655% per 6 month.

Discount Factor is calculated by 1/(1+0.02655)1 = 0.9741 for ist period

1/(1+0.02655)2 = 0.9489 for 2nd period

Likewise for 3rd period = 1/(1+0.02655)3 and so on (same can be easily calculated by using excel)

PERIOD	CASHFLOW	DISCOUNT FACTOR @ 2.655% PER PERIOD	PRESENT VALUE
0	-$90	1.0000	-$90.00
1	$2	0.9741	$1.95
2	$2	0.9489	$1.90
3	$2	0.9244	$1.85
4	$2	0.9005	$1.80
5	$2	0.8772	$1.75
6	$2	0.8545	$1.71
7	$2	0.8324	$1.66
8	$2	0.8109	$1.62
9	$2	0.7899	$1.58
10	$2	0.7695	$1.54
11	$2	0.7496	$1.50
12	$2	0.7302	$1.46
13	$2	0.7113	$1.42
14	$2	0.6929	$1.39
15	$2	0.6750	$1.35
16	$2	0.6575	$1.32
17	$2	0.6405	$1.28
18	$2	0.6240	$1.25
19	$2	0.6078	$1.22
20	$102	0.5921	$60.39
		NPV =	-$0.06

Since NPV = -$0.06, which is not equal to zero

Since NPV is close to 0, we will next take option D = 5.30 % per annum = 2.65% per period

PERIOD	CASHFLOW	DISCOUNT FACTOR @ 2.65% PER PERIOD	PRESENT VALUE
0	-$90	1.0000	-$90.00
1	$2	0.9742	$1.95
2	$2	0.9490	$1.90
3	$2	0.9245	$1.85
4	$2	0.9007	$1.80
5	$2	0.8774	$1.75
6	$2	0.8548	$1.71
7	$2	0.8327	$1.67
8	$2	0.8112	$1.62
9	$2	0.7903	$1.58
10	$2	0.7699	$1.54
11	$2	0.7500	$1.50
12	$2	0.7306	$1.46
13	$2	0.7118	$1.42
14	$2	0.6934	$1.39
15	$2	0.6755	$1.35
16	$2	0.6580	$1.32
17	$2	0.6411	$1.28
18	$2	0.6245	$1.25
19	$2	0.6084	$1.22
20	$102	0.5927	$60.46
		NPV =	$0.01

NPV is equal to zero (the minor difference is due to decimol place taken for discount factor)

So option D is correct, 5.30% per annum is IRR and also yield to maturity considering time value of money.