Question

Leonidas Corporation has bonds trading on the secondary market for $985.84. The bonds will mature in 7 years and have a face value of $1,000. The bonds pay semi-annual coupons with a 6.21% APR. What is the yield to maturity for an investor who buys the bonds today? (Express as an APR)

Answer 1

YTM is the Rate at which PV of Cash Inflows are equal to Bond Price.

Period	CF	PVF @3%	Disc CF	PVF @3.5%	Disc CF
0	$ -985.84	1.0000	$ -985.84	1.0000	$ -985.84
1	$      31.05	0.9709	$    30.15	0.9662	$    30.00
2	$      31.05	0.9426	$    29.27	0.9335	$    28.99
3	$      31.05	0.9151	$    28.42	0.9019	$    28.01
4	$      31.05	0.8885	$    27.59	0.8714	$    27.06
5	$      31.05	0.8626	$    26.78	0.8420	$    26.14
6	$      31.05	0.8375	$    26.00	0.8135	$    25.26
7	$      31.05	0.8131	$    25.25	0.7860	$    24.41
8	$      31.05	0.7894	$    24.51	0.7594	$    23.58
9	$      31.05	0.7664	$    23.80	0.7337	$    22.78
10	$      31.05	0.7441	$    23.10	0.7089	$    22.01
11	$      31.05	0.7224	$    22.43	0.6849	$    21.27
12	$      31.05	0.7014	$    21.78	0.6618	$    20.55
13	$      31.05	0.6810	$    21.14	0.6394	$    19.85
14	$      31.05	0.6611	$    20.53	0.6178	$    19.18
14	$ 1,000.00	0.6611	$ 661.12	0.6178	$ 617.78
NPV			$    26.02		$   -28.98

YTM per 6 Months = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 0.5% inc in disc rate ] * 0.5%

= 3% + [ 26.02 / 55 ] * 0.5%

= 3% + (0.47 * 0.5%)

= 3% + 0.24%

= 3.24%

YTM per anum = YTM per 6 Months * 12/ 6

= 3.24% * 12 / 6

= 6.47%