Question

An alternating annuity pays $1 in one year, −$2 in two years, $4 in three years, −$8 in four years, which each subsequent payment doubling and changing sign for 20 years. If the risk-free discount rate is 5%, what is the value of this alternating annuity?

Answer 1

Calculating the Present Value of Alternating Annuity by excel method:-

Year	Cash Flows of Alternating Annuity($)	PV Factor @5%	Present Value of Alternating Annuity ($)
1	1.00	0.9524	0.95
2	(2.00)	0.9070	(1.81)
3	4.00	0.8638	3.46
4	(8.00)	0.8227	(6.58)
5	16.00	0.7835	12.54
6	(32.00)	0.7462	(23.88)
7	64.00	0.7107	45.48
8	(128.00)	0.6768	(86.64)
9	256.00	0.6446	165.02
10	(512.00)	0.6139	(314.32)
11	1,024.00	0.5847	598.71
12	(2,048.00)	0.5568	(1,140.40)
13	4,096.00	0.5303	2,172.20
14	(8,192.00)	0.5051	(4,137.52)
15	16,384.00	0.4810	7,880.98
16	(32,768.00)	0.4581	(15,011.40)
17	65,536.00	0.4363	28,593.14
18	(131,072.00)	0.4155	(54,463.12)
19	262,144.00	0.3957	103,739.28
20	(524,288.00)	0.3769	(197,598.63)
			(129,572.55)

Note- Cash flows are calculated with each subsequent payment doubling and changing sign for 20 years

So, the value of this alternating annuity is -$129,572.55

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