Question

A los bonos de Severn Company les faltan cuatro años para vencer. El interés se paga cada año, los bonos tienen un valor a la par de $1 000 y la tasa de interés del cupón es de 9 por ciento. a. Calcule el rendimiento al vencimiento para los bonos si el precio de mercado actual es 1) $829 o 2) $1104. b. ¿Pagaría $829 por uno de esos bonos si pensara que la tasa de interés adecuada es de 12 por ciento; es decir, si rd =12%? Explique su respuesta.

Answer 1

Price of Bond = PV of CFs from it.

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

If Price is $ 829

Year	CF	PVF @14%	Disc CF	PVF @15%	Dsic CF
0	$ -829.00	1.0000	$ -829.00	1.0000	$ -829.00
1	$      90.00	0.8772	$    78.95	0.8696	$    78.26
2	$      90.00	0.7695	$    69.25	0.7561	$    68.05
3	$      90.00	0.6750	$    60.75	0.6575	$    59.18
4	$      90.00	0.5921	$    53.29	0.5718	$    51.46
4	$ 1,000.00	0.5921	$ 592.08	0.5718	$ 571.75
NPV	$    25.31		$     -0.30

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

= 14% + [ 25.31 / 25.61 ] * 1%

= 14% + [ 0.99 * 1% ]

= 14.99%

If Price is $ 1104:

Year	CF	PVF @5%	Disc CF	PVF @6%	Dsic CF
0	$ -1,104.00	1.0000	$ -1,104.00	1.0000	########
1	$        90.00	0.9524	$        85.71	0.9434	$    84.91
2	$        90.00	0.9070	$        81.63	0.8900	$    80.10
3	$        90.00	0.8638	$        77.75	0.8396	$    75.57
4	$        90.00	0.8227	$        74.04	0.7921	$    71.29
4	$ 1,000.00	0.8227	$     822.70	0.7921	$ 792.09
NPV	$        37.84		$     -0.05

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

= 5% + [ 37.84 / 37.88 ] * 1%

= 5% + [ 0.99 * 1% ]

= 5.99%

Part C:

Price of Bond if Required Rate is 12%

Year	CF	PVF @12%	Disc CF
1	$        90.00	0.8929	$        80.36
2	$        90.00	0.7972	$        71.75
3	$        90.00	0.7118	$        64.06
4	$        90.00	0.6355	$        57.20
4	$ 1,000.00	0.6355	$     635.52
Price of Bond	$     908.88

If the bond is aiavilable for $ 829, we can buy it as it is underpriced.