Question

You have the opportunity to buy a business for $35,000. The business is a portable car washing business. It comes with a truck and trailer that has everything needed to wash cars anywhere. The owner hired students to wash the cars. The business owner is graduating from college and wants to sell. The business has paid the owner’s tuition, books, fees, and rent for the last three years. The net income was $13,000 per year. You have the $35,000 in your college fund. You are planning on going for a PhD and believe you can graduate in 8 years. You are conservative and estimate the business will generate following net income for the next eight years

Year	Income
1	$10,000
2	$11,000
3	$12,000
4	$13,000
5	$13,000
6	$13,500
7	$14,000
8	$14,500

What return would you have to get on the $35,000 to equal the income from buying the business? (Hint: use the IRR function.) Internal rate of return (IRR) is the interest rate at which the net present value of all the cash flows (both positive and negative) from a project or investment equal zero. Internal rate of return is used to evaluate the attractiveness of a project or investment. Double-check this by finding the NPV of the cash flows using the interest rate calculated by the IRR. Your income estimate may be high. If you only get 75% of the projected income, what is the IRR for the investment? Should you buy the business at 75% income?

Answer 1

Year	Cash Flow
0	$                (35,000)
1	$                   10,000
2	$                   11,000
3	$                   12,000
4	$                   13,000
5	$                   13,000
6	$                   13,500
7	$                   14,000
8	$                   14,500
IRR	29.4852%

IRR = 29.4852 % or 29.49 %

Year	Cash Flow(C)	PV Factor calculation	PV Factor @ 29.4852% (F)	PV (=C x F)
0	$                (35,000)	1/(1+0.294852)^0	1	$      (35,000.00)
1	$                   10,000	1/(1+0.294852)^1	0.772289034	$           7,722.89
2	$                   11,000	1/(1+0.294852)^2	0.596430352	$           6,560.73
3	$                   12,000	1/(1+0.294852)^3	0.46061662	$           5,527.40
4	$                   13,000	1/(1+0.294852)^4	0.355729164	$           4,624.48
5	$                   13,000	1/(1+0.294852)^5	0.274725733	$           3,571.43
6	$                   13,500	1/(1+0.294852)^6	0.212167671	$           2,864.26
7	$                   14,000	1/(1+0.294852)^7	0.163854765	$           2,293.97
8	$                   14,500	1/(1+0.294852)^8	0.126543238	$           1,834.88
			NPV	$                   0.04

PV = Cash flow (C) x Present value factor (F)

Calculate PV factor using the formula below for each and every year.

PV factor = 1/(1+r)^n

r = rate of interest and n = No. of year

Multiply PV factor with cash flow of respective year to get PV of cash flows.

Add PV of every years to get NPV.

NPV at discount rate of 29.4852 % is $ 0.04

Year	Cash Flow(C)
0	$                (35,000)
1	$                     7,500
2	$                     8,250
3	$                     9,000
4	$                     9,750
5	$                     9,750
6	$                   10,125
7	$                   10,500
8	$                   10,875
IRR	19.6936%

If the income e is 75 %, IRR for investment is 19.6936 % or 19.69 %.

As the IRR is positive, the business can be purchased.