Question

A company buys a 100 par value bond with 5% annual coupons. The company pays a price that will give it a yield rate of 4% effective if the bond matures at par at the end of 7 years. The company receives all coupons when due. However, at the end of 7 years, the company receives a maturity value of only 90, due to the bankruptcy of the issuer of the bond. The company's effective annual yield rate over the 7- year period is i. Determine i.

Pls. Show formula used

Answer 1

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

Bond Price = PV of CFs

Year	CF	PVF @4%	Disc CF
1	$      5.00	0.9615	$      4.81
2	$      5.00	0.9246	$      4.62
3	$      5.00	0.8890	$      4.44
4	$      5.00	0.8548	$      4.27
5	$      5.00	0.8219	$      4.11
6	$      5.00	0.7903	$      3.95
7	$      5.00	0.7599	$      3.80
7	$ 100.00	0.7599	$   75.99
Price of Bond	$ 106.00

YTM:

Year	CF	PVF @2%	Disc CF	PVF @3%	Disc CF
0	-106	1	-106	1.0000	$ -106.00
1	$      5.00	0.9804	$      4.90	0.9709	$       4.85
2	$      5.00	0.9612	$      4.81	0.9426	$       4.71
3	$      5.00	0.9423	$      4.71	0.9151	$       4.58
4	$      5.00	0.9238	$      4.62	0.8885	$       4.44
5	$      5.00	0.9057	$      4.53	0.8626	$       4.31
6	$      5.00	0.8880	$      4.44	0.8375	$       4.19
7	$      5.00	0.8706	$      4.35	0.8131	$       4.07
7	$   90.00	0.8706	$   78.35	0.8131	$    73.18
NPV	$      4.71		$     -1.67

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 1 % inc in Rate ] * 1%

= 2% + [ 4.71 / 6.38 ] * 1%

= 2% + [ 0.74 * 1% ]

= 2 % + 0.74%

= 2.74%