Question

Assume you can either take a 20-year annuity that will first pay you $17,000 and
increase by 2.4% each year, or a perpetuity that will pay you $15,500 the first year
and increase by 2% each year. Assuming the interest rate of 11% and that the
interest rate will compound annually, which one has a higher present value?
Explain.

Answer 1

Present Value of Annuity

Year	Cash Flow	Discounting Factor	Discounting Cash Flow
1	$ 17,000.00	0.90	$                    15,300.00
2	$ 17,408.00	0.81	$                    14,100.48
3	$ 17,825.79	0.73	$                    13,012.83
4	$ 18,253.61	0.66	$                    12,047.38
5	$ 18,691.70	0.59	$                    11,028.10
6	$ 19,140.30	0.53	$                    10,144.36
7	$ 19,599.67	0.48	$                       9,407.84
8	$ 20,070.06	0.43	$                       8,630.13
9	$ 20,551.74	0.39	$                       8,015.18
10	$ 21,044.98	0.35	$                       7,365.74
11	$ 21,550.06	0.32	$                       6,896.02
12	$ 22,067.26	0.29	$                       6,399.51
13	$ 22,596.87	0.26	$                       5,875.19
14	$ 23,139.19	0.23	$                       5,322.01
15	$ 23,694.53	0.21	$                       4,975.85
16	$ 24,263.20	0.19	$                       4,610.01
17	$ 24,845.52	0.17	$                       4,223.74
18	$ 25,441.81	0.15	$                       3,816.27
19	$ 26,052.41	0.14	$                       3,647.34
20	$ 26,677.67	0.12	$                       3,201.32
Present Value	$                 1,58,019.29

Present Value of Perpetuity

PV = Cash Flow / (Interest Rate - Growth)

PV = $15,500 / (0.11 - 0.02)

PV = $15,500 / 0.09

PV = $ 172,222.22

Present Value of Perpetuity is greater than Present Value of Annuity