Question

An investment is offered with the following conditions.
An initial investment of $ 100,000 and annual payments of $ 12,000 from the third year at a rate of 10% APR for 8 years. After 8 years, annual payments of $ 7,500 are made at a rate of 11.5% APR for 5 years and the accumulated of the past 8 years is maintained for those 5 years at 11.5% APR. 
Calculate the following:
1) The present value of the investment
2) The future value of the investment 
3) The profit obtained
4) The investor is willing to sell the investment with a 40% discount from the projected profit. How much is the price you should ask for?

Answer 1

Answer :

(1). First calculate the 5 payments at the end of 10 years

Discount rate	10.0000%	-	-
Cash flows	Year	Discounted CF = Cash flows /(1+rate)^year	Cummulative cash flow
(100,000.000)	0	(100,000.00)	(100,000.00)
-	1	-	(100,000.00)
-	2	-	(100,000.000)
12,000.000	3	9,015.78	(90,948.222)
12,000.000	4	8,196.16	(82,788.061)
12,000.000	5	7,451.06	(75,337.01)
12,000.000	6	6,773.69	(68,563.318)
12,000.000	7	6,157.90	(62,405.42)
12,000.000	8	5,598.09	(56,807.33)
12,000.000	9	5,089.17	(51,718.16)
12,000.000	10	4,626.52	(47,091.64)
27,374.084	10	10,553.89	(36,537.75)

Present value = - 36,537.75

(2). Future value after 15 years = - 36,537.75*1.10*1.115^5 = 163,321.35

(3) Gain = - 36,537.75

(4). Price = 100,000 + 40%* - 36,537.75 = 85,384.90

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