Question

1. Consider two bonds, each with an interest rate (i) of 5%, coupon payments (C) of $20, and face values (F) of $1000. The first bond matures in 20 years and the second bond matures in 10 years.

(a) Find the prices of the two bonds. Next price a console with the same interest rate and coupon payment. Report F × i.

(b) Repeat part (a) when the coupon payment is $100.

(c) Repeat part (a) once again with a coupon payment of $50.

(d) What does this tell you about the price of a console relative to long-run bonds?

Answer 1

Pls see the values of the two bonds under different Coupon payment scenarios in the table below.

The values of the Consol under the three scenarios are:

a) $20 / 0.05 = $400

b) $100 / 0.05 = $2000

c) $50 / 0.05 = $1000

	a)				b)				c)
Time	CF first bond	PV first bond = CF/1.05^time	CF second bond	PV second bond = CF/1.05^time	CF first bond	PV first bond = CF/1.05^time	CF second bond	PV second bond = CF/1.05^time	CF first bond	PV first bond = CF/1.05^time	CF second bond	PV second bond = CF/1.05^time
1	20.00	19.05	20.00	19.05	100.00	95.24	100.00	95.24	50.00	47.62	50.00	47.62
2	20.00	18.14	20.00	18.14	100.00	90.70	100.00	90.70	50.00	45.35	50.00	45.35
3	20.00	17.28	20.00	17.28	100.00	86.38	100.00	86.38	50.00	43.19	50.00	43.19
4	20.00	16.45	20.00	16.45	100.00	82.27	100.00	82.27	50.00	41.14	50.00	41.14
5	20.00	15.67	20.00	15.67	100.00	78.35	100.00	78.35	50.00	39.18	50.00	39.18
6	20.00	14.92	20.00	14.92	100.00	74.62	100.00	74.62	50.00	37.31	50.00	37.31
7	20.00	14.21	20.00	14.21	100.00	71.07	100.00	71.07	50.00	35.53	50.00	35.53
8	20.00	13.54	20.00	13.54	100.00	67.68	100.00	67.68	50.00	33.84	50.00	33.84
9	20.00	12.89	20.00	12.89	100.00	64.46	100.00	64.46	50.00	32.23	50.00	32.23
10	20.00	12.28	1,020.00	626.19	100.00	61.39	1,100.00	675.30	50.00	30.70	1,050.00	644.61
11	20.00	11.69			100.00	58.47			50.00	29.23
12	20.00	11.14			100.00	55.68			50.00	27.84
13	20.00	10.61			100.00	53.03			50.00	26.52
14	20.00	10.10			100.00	50.51			50.00	25.25
15	20.00	9.62			100.00	48.10			50.00	24.05
16	20.00	9.16			100.00	45.81			50.00	22.91
17	20.00	8.73			100.00	43.63			50.00	21.81
18	20.00	8.31			100.00	41.55			50.00	20.78
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