Question

An owner of a large ranch is considering the purchase of a tractor with a front-end loader to clean his corrals instead of hiring workers that do it with a pitch fork. He has given you the following information and has asked you to evaluate this investment. The equipment costs $40,000. The rancher expects that he will save $11,500 a year that is usually paid to workers that clean out the corral by hand. However, he will incur an additional cost of $1,000 for fuel, repairs and maintenance. The rancher plans on keeping the equipment for 3 years before replacing it with a new one. He thinks he can sell the old equipment for $25,000 in three years. The rancher anticipates that his marginal tax rate will be 20 percent over the next three years. The IRS will allow the rancher to depreciate the tractor over seven years using the straight-line method. The rancher requires at least a 15% pretax rate of return on capital (pretax). What is the maximum fuel, repairs and maintenance cost that can be paid each year to operate the loader and still find this investment profitable?A table showing the relationship between the NPV and operating expenses shows a downward sloping curve?If operating expenses were $1,180, what would the NPV be based on the table showing the relationship between the NPV and operating expenses?

Answer 1

We can put the information in a worksheet as below:

Note the following:

• Depreciation is straight line for 7 years hence after 3 years the book value would be (40000-5714.29-5714.29-5714.29) = $ 22857.14 ; hence when the equipment is sold for $ 25000, there will be a notional profit of (25000-22857.14) = 2142.86
• The NPV is $ 409.79
• We can play around with the operating expenses and as long as the NPV remains above 0, it will be profitable to make this investment. A table showing different levels of operating expenses and respective NPV (calculated using the above work sheet ) is enclosed below:

As we can see that as the operating expenses increase the NPV keeps on decreasing and at $1213 it becomes almost zero (it actually equals zero at 1213.27) hence the maximum operating expenses should upto $ 1213.

At $ 1180, the NPV should postive at 63.93 and we can see from the table also since at 1150 the NPV is 121.57 and at 1200 it is 25.50, hence at 1180 it will be between this NPV range.