Question

"A highway contractor is considering buying a new trench excavator that costs $353,000 and can dig a 3-foot-wide trench at the rate of 15 feet per hour. The annual number of feet to dig each year is 4,900. The machine's production rate will remain constant for the first 2 years of the operation and then decrease by 2 feet per hour for each additional year. The maintenance and operating costs will be $57 per hour. The contractor will depreciate the equipment with a five-year MACRS. At the end of 5 years, the excavator can be sold for $78,000. The contractor will earn an additional annual revenue of $117,000 with this new machine. Assuming the contractor's tax rate is 32% per year, determine the net present worth of the cash flow from this machine. The company's MARR is 15%."

Answer 1

The after tax salavge value is calculated as shown below:

Sale value =78000

Book Value = 353000*0.0576 =20,332.80

Taxable value = 78000-20332.80 = 57,667.20

Taxes = 32%*57667.20 = 18,453.504

After tax salavage value =78000-18453.504 = 59,546.50

The NPV is calculated as follows:

Year	0	1	2	3	4	5
Initial Cost	-353000
Revenue		117000.00	117000.00	117000.00	117000.00	117000.00
Feet dug each year		4900	4900	4900	4900	4900
Rate of digging		15	15	13	11	9
Number of hours of operation		326.6667	326.66667	376.9231	445.4545	544.4444
Cost /hour		57	57	57	57	57
Total Operating cost		-18620.00	-18620.00	-21484.62	-25390.91	-31033.33
Depreciation		-70600.00	-112960.00	-67776.00	-40665.60	-40665.60
Profit before tax		27780.00	-14580.00	27739.38	50943.49	45301.07
Taxes at 32%		-8889.6	4665.6	-8876.603	-16301.92	-14496.34
Profit after tax		18890.40	-9914.40	18862.78	34641.57	30804.73
Add back depreciation		70600.00	112960.00	67776.00	40665.60	40665.60
Operating cash flow		89490.40	103045.60	86638.78	75307.17	71470.33
After tax salavge value						59546.5
Net cash flow	-353000	89490.40	103045.60	86638.78	75307.17	131016.83
NPV at 15%	$ -32,102.94