Question 17.15: Your company is looking at purchasing a new hydraulic excava...
Your company is looking at purchasing a new hydraulic excavator. The excavator has a purchase price of $120,000, a useful life of five years, and a salvage value of $12,000 at the end of the fifth year. The excavator can be billed out at $95.00 per hour. It costs $30.00 per hour to operate the excavator and $25.00 per hour for the operator. Using a MARR of 20% and the capital recovery with return method, determine the minimum number of billable hours in a year that will make purchasing the excavator financially attractive. How many hours will need to be billed if the billing rate were reduced to $90.00 per hour?
For the purchase of the excavator to be financially attractive, the annual profit must be equal to the capital recovery with return, which is equal to the annual equivalents of the purchase price and salvage value at the MARR.
The purchase price for the excavator is converted to a uniform series of annual cash flows by Eq. (15-11) as follows:
A=P\left[\frac{i(1+i)^{n}}{(1+i)^{n}-1}\right] (15-11)
A_{ PP }=-\$ 120,000\left[\frac{0.20(1+0.20)^{5}}{(1+0.20)^{5}-1}\right]=-\$ 40,126
The salvage value for the excavator is converted to a uniform series of annual cash flows by Eq. (15-7) as follows:
A=F\left[\frac{i}{(1+i)^{n}-1}\right] (15-7)
A_{ SV }=\$ 12,000\left[\frac{0.20}{(1+0.20)^{5}-1}\right]=\$ 1,613
The capital recovery with return for purchasing the excavator equals the sum of the uniform series representing each of the individual cash flows and is calculated as follows:
CR =-\$ 40,126+\$ 1,613=-\$ 38,513
For the purchase of the excavator to be financially attractive, it must generate $38,513 in profit (revenue less noncapital costs) each year. The hourly profit on the excavator 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. Solving for the number of billable hours, we get the following:
\text { Billable Hours }=\frac{\text { Annual Profit }}{\text { Hourly Profit }}
Calculating the minimum number of billable hours per year required to offset the capital recovery with return, we get the following:
\text { Billable Hours }=\frac{\$ 38,513 / yr }{\$ 40.00 / hr }=963 hr / yr
At a billing rate of $95.00 per hour, one would need to bill 963 hours per year. If the billing rate were reduced to $90.00 per hour, the hourly profit on the excavator would be:
\text { Hourly Profit }=\$ 90.00 / hr -\$ 30.00 / hr -\$ 25.00 / hr
\text { Hourly Profit }=\$ 35.00 / hr
Calculating the minimum number of billable hours per year required to offset the capital recovery with return, we get the following:
\text { Billable Hours }=\frac{\$ 38,513 / yr }{\$ 35.00 / hr }=1,100 hr / yr
At a billing rate of $90.00 per hour, one would need to bill 1,100 hours per year or an additional 137 (1,100 – 963) hours per year.