Question

Your neighborhood self-service laundry is for sale and you consider investing in this business. For the business alone and no other assets (such as building and land), the purchase price is $240,000. The net cash flows for the project are $30,000 per year for the next 5 years. You plan to borrow the money for this investment at 5%.

Answer 1

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:

• Prepare a net present value calculation for this project. What is the net present value of this project?

Solution

The net present value is equal to: the present value of the future cash flows less present value of the investements.

1. Present value of the future cash flows:

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

2. Calculate the net present value:

• Net present value =

                     = Total present value of future cash flows - investment

• Net present value = $317,930.58 - $240,000 = $77,930.58