Answer:
- The complete present value calcuation is below.
- The net present value of this project is: $77,930.58 (assuming a value for the sale of the business equal to the purchase price).
Explanation:
For this problem, the first and basic question is:
- <em>Prepare a net present value calculation for this project. What is the net present value of this project?</em>
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<h2>Solution</h2>
The net present value is equal to: the present value of the future cash flows less present value of the investements.
<u>1. Present value of the future cash flows:</u>
The discount factor is equal to 1 / [1 + (1 + r)ⁿ]
Where:
- r = 5% = 0.05
- n = the number of year
Year Cash flow Discount factor Present value
1 $30,000 1/(1 + 0.05) $30,000/1.05 = $28,571.43
2 $30,000 1/(1 + 0.05)² $30,000/(1.05)² = $27,210.88
3 $30,000 1/(1 + 0.05)³ $30,000/(1.05)³ = $25,915.13
4 $30,000 1/(1 + 0.05)⁴ $30,000/(1.05)⁴ = $24,681.07
5 $30,000 1/(1 + 0.05)⁵ $30,000/(1.05)⁵ = $23,505.78
5 $240,000* 1/(1 + 0.05)⁵ $240,000/(1.05)⁵ = $188,046.28
*For the year 5 you must also consider the value of the business, which is unknow. You should have some information about it. Although unrealistic, at this stage we can just assume a value: let's say it is the same purchase price: $240,000. That is what the last line shows:
The discount the value of the value of the business is:
- $240,000 / (1.05)⁵ = $188,046.28
The total present value of the future cash flows is the sum of the present values of all the cash flows:
$28,571.43 + $27,210.88 + $25,915.13 + $24,681.07 + $23,505.78 + $188,046.28 = $317,930.58
<u>2. Calculate the net present value:</u>
= Total present value of future cash flows - investment
- Net present value = $317,930.58 - $240,000 = $77,930.58
