Question

Price a 10% coupon $1000 face value, 20-year bond if the appropriate discount rate is 8% for the first 10-years and 6% for the second 10-years. Show your return in dollars and percent if you hold this bond for 4-years. (Note: show all work and do not use a finance calculator.)

Answer 1

Here price of the bond = present value of all coupon payments and the maturity value of the bond. Annual coupon payments = 10% of $1000 = $100.

Period	Cash flow	1+r	PVIF = 1/(1+r)^n	PV = Cash flow * PVIF
1	100	1.08	0.9259	92.59
2	100	1.08	0.8573	85.73
3	100	1.08	0.7938	79.38
4	100	1.08	0.7350	73.50
5	100	1.08	0.6806	68.06
6	100	1.08	0.6302	63.02
7	100	1.08	0.5835	58.35
8	100	1.08	0.5403	54.03
9	100	1.08	0.5002	50.02
10	100	1.08	0.4632	46.32
11	100	1.06	0.5268	52.68
12	100	1.06	0.4970	49.70
13	100	1.06	0.4688	46.88
14	100	1.06	0.4423	44.23
15	100	1.06	0.4173	41.73
16	100	1.06	0.3936	39.36
17	100	1.06	0.3714	37.14
18	100	1.06	0.3503	35.03
19	100	1.06	0.3305	33.05
20	1100	1.06	0.3118	342.99
			Total	1,393.80

Thus price = $1,393.80 (rounded to 2 decimal place)

The working and the formulas can be viewed in image attached below.

Return in dollars = 1000 - 1,393.80 + sum of all coupons = 1,000 - 1,393.80 + (100*20) = $1,606.20

Return in % = 1,606.20/1,393.80 = 115.24%. (Note the annualized return rate = (1+115.24%)^(1/20) - 1 = 3.91%)