Question

Jeff bought an increasing perpetuity due with annual payments starting at 100 and increasing by 10 each year until the payment reaches $250; the payments remain at $250 thereafter. The annual effective rate is 6%. Determine the present value of this perpetuity.

Answer 1

From year 15 annual payment is $250. Value of it at that period = $250/6% = $4,166.67

Period	Payment	× discount factor	Present value
0	$          100	1	$    100.00
1	$          110	0.943396	$    103.77
2	$          120	0.889996	$    106.80
3	$          130	0.839619	$    109.15
4	$          140	0.792094	$    110.89
5	$          150	0.747258	$    112.09
6	$          160	0.704961	$    112.79
7	$          170	0.665057	$    113.06
8	$          180	0.627412	$    112.93
9	$          190	0.591898	$    112.46
10	$          200	0.558395	$    111.68
11	$          210	0.526788	$    110.63
12	$          220	0.496969	$    109.33
13	$          230	0.468839	$    107.83
14	$          240	0.442301	$    106.15
15	$ 4,166.67	0.417265	$ 1,738.60
			$ 3,378.18

Present value of perpetuity is $3,378.18

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