Yoshika Landscaping is contemplating purchasing a new ditch-digging machine that promises savings of $5,600 per year for 10 years. The machine costs $21,970, and no salvage value is expected. The company's cost of capital is 12%. You have been asked to advise Yoshika relative to this capital investment decision. As part of your analysis, compute:
1.
To advise Yoshika Landscaping on the capital investment decision, we need to calculate the net present value (NPV) of the new ditch-digging machine.
First, we need to calculate the annual cash savings by subtracting the cost of the machine from the promised savings. In this case, the annual cash savings would be $5,600.
Next, we need to calculate the present value factor for a 10-year period at a cost of capital of 12%. The present value factor can be found using the formula:
PVF = 1 / (1 + r)^n
Where:
PVF = Present Value Factor
r = Cost of Capital (as a decimal)
n = Number of periods (years)
Given that the cost of capital is 12% (or 0.12) and the number of periods is 10, we can calculate the present value factor:
PVF = 1 / (1 + 0.12)^10
PVF ≈ 0.322
Now we can calculate the net present value (NPV) using the formula:
NPV = Annual Cash Savings x PVF - Initial Investment
In this case:
NPV = $5,600 x 0.322 - $21,970
NPV ≈ $1,803 - $21,970
NPV ≈ -$20,167
The calculated NPV is negative (-$20,167). A negative NPV suggests that the investment may not be economically viable. In this case, the new ditch-digging machine may not be a financially sound investment decision for Yoshika Landscaping.