Question 17.12: Your company is looking at purchasing a front-end loader at ...
Your company is looking at purchasing a front-end loader at a cost of $120,000. The loader would have a useful life of five years with a salvage value of $12,000 at the end of the fifth year. The loader can be billed out at $95.00 per hour. It costs $30.00 per hour to operate the front-end loader and $25.00 per hour for the operator.
Using 1,200 billable hours per year, determine the rate of return for the purchase of the loader. If your company’s MARR was 20%, should your company purchase the loader?
The hourly profit on the loader equals the billing rate less the operation cost and the cost of the operator, and is calculated as follows:
\text { Hourly Profit }=\$ 95.00 / hr -\$ 30.00 / hr -\$ 25.00 / hr
\text { Hourly Profit }=\$ 40.00 / hr
The annual profit on the loader equals the hourly profit times the number of billable hours per year and is calculated as follows:
\text { Annual Profit }=(\$ 40.00 / hr )(1,200 hr / yr )=\$ 48,000 / yr
The cash flow for the purchase of the loader in Example 17-12 is shown in Figure 17-10 .
The present value of the annual profits is determined by using Eq. (15-9) as follows:
p=A\left[\frac{(1+i)^{n}-1}{i(1+i)^{\pi}}\right] (15-9)
P_{ AP }=\$ 48,000\left[\frac{(1+i)^{5}-1}{i(1+i)^{5}}\right]
The present value of the annual profits is positive because it is a cash receipt.
The present value of the salvage value is determined by using Eq. (15-3) as follows:
P=\frac{F}{(1+i)^{n}} (15-3)
P_{ SV }=\frac{\$ 12,000}{(1+i)^{5}}
The present value of the salvage value is positive because it is a cash receipt.
The present value of the purchase price of the loader is equal to the purchase price because the NPV is measured at the time of the initial investment. The present value of the purchase price is negative because it is a cash disbursement.
To find the rate of return, one must write an equation that includes the present values representing all of the cash flows and set the NPV to zero. The NPV for purchasing the loader equals the sum of the present values of the individual cash flows and is calculated as follows:
0=\$ 48,000\left[\frac{(1+i)^{5}-1}{i(1+i)^{5}}\right]+\frac{\$ 12,000}{(1+i)^{5}}+(-\$ 120,000)
Solving for i by trial and error, we find that i equals 30.06%.
The rate of return for the investment is 30.06%. Because the rate of return is greater than the MARR of 20%, the present value will be positive and your company should invest in the front-end loader.
