You have the opportunity to buy a business for $35,000. The business is a portab
ID: 2553044 • Letter: Y
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?
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
Explanation / Answer
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.
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%
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