Question

​(Yield to​ maturity) A​ bond's market price is ​$900. It has a ​$1,000 par​ value, will mature in 8 ​years, and has a coupon interest rate of 8 percent annual​ interest, but makes its interest payments semiannually.

What is the​ bond's yield to​ maturity? % ​ (Round to two decimal​ places.)

What happens to the​ bond's yield to maturity if the bond matures in 16 ​years? % ​ (Round to two decimal​ places.)

What if it matures in 4 ​years? % ​ (Round to two decimal​ places.)

Answer 1

Yield to maturity of a bond can be computed using excel as IRR of cash outflow and inflow during the periods and maturity.

Year 0 cash out flow is the price of bond i.e. $ 900

Cash flow in year 1 through 8 is the coupon amount.

Coupon amount = Face value x Coupon rate/Coupon payment frequency in a year

                          = $ 1,000 x 0.08/2 = $ 1,000 x 0.04 = $ 40

Number of coupons in 8 years = 8 x 2 = 16

Computations of IRR using excel:

	A	B
1	Periods	Cash Flow
2	0	($900.00)
3	1	$40
4	2	$40
5	3	$40
6	4	$40
7	5	$40
8	6	$40
9	7	$40
10	8	$40
11	9	$40
12	10	$40
13	11	$40
14	12	$40
15	13	$40
16	14	$40
17	15	$40
18	16	$1,040
19	IRR	4.92%

If excel sheet looks like above table,

Insert formula “=IRR(B2:B18)” in cell B19 to get IRR as 4.917 %

4.917 % is the semiannual rate.

Yield to maturity of bond = 2 x 4.917 % = 9.83 %

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If bond matures in 16 year, number of coupon payments = 16 x 2 = 32

Computation of IRR using excel:

	A	B
1	Year	Cash Flow
2	0	($900.00)
3	1	$40
4	2	$40
5	3	$40
6	4	$40
7	5	$40
8	6	$40
9	7	$40
10	8	$40
11	9	$40
12	10	$40
13	11	$40
14	12	$40
15	13	$40
16	14	$40
17	15	$40
18	16	$40
19	17	$40
20	18	$40
21	19	$40
22	20	$40
23	21	$40
24	22	$40
25	23	$40
26	24	$40
27	25	$40
28	26	$40
29	27	$40
30	28	$40
31	29	$40
32	30	$40
33	31	$40
34	32	$1,040
35	IRR	4.603%

If excel sheet looks like above table,

Insert formula “=IRR(B2:B34)” in cell B35 to get IRR as 4.603 %

Yield to maturity of bond = 2 x 4.603 % = 9.21%

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If bond matures in 4 year, number of coupon payments = 4 x 2 = 8

Computation of IRR using excel:

	A	B
1	Year	Cash Flow
2	0	($900.00)
3	1	$40
4	2	$40
5	3	$40
6	4	$40
7	5	$40
8	6	$40
9	7	$40
10	8	$1,040
11	IRR	5.58%

If excel sheet looks like above table,

Insert formula “=IRR(B2:B10)” in cell B11 to get IRR as 5.584 %

Yield to maturity of bond = 2 x 5.584 % = 11.17%