Question

A tractor for over-the-road hauling is to be purchased by AgriGrow for $80,000. It is expected to be of use to the company for 6 years, after which it will be salvaged for $3,800. Transportation cost savings are expected to be $140,000 per year; however, the cost of drivers is expected to be $53,000 per year, and operating expenses are expected to be $47,000 per year, including fuel, maintenance, insurance, and the like. The company’s marginal tax rate is 25 percent, and MARR is 10 percent on after-tax cash flows. Suppose that, to AgriGrow’s surprise, they actually dispose of the tractor at the end of the fourth tax year for $5,800. Develop tables using a spreadsheet to determine the ATCF for each year and the after-tax PW, AW, IRR, and ERR after only 4 years.

-Use straight-line depreciation (no half-year convention).

-After-tax IRR:
-After-tax ERR:

Answer 1

Step 1:

Calculation of after tax cash flow, no depreciation is considered since it is irrelevant for this investment decision

Year	savings	cost	Net savings	Tax cost @ 25%	After tax cash flow(ACTF)
0		-80000	-80000		-80000
1	140000	100000	40000	10000	30000
2	140000	100000	40000	10000	30000
3	140000	100000	40000	10000	30000
4	145800	100000	45800	11450	34350

Let us now calculate present worth

PV factor@10%	ACTF
1	-80000
0.9090	30000
0.8264	30000
0.7513	30000
0.6830	34350

To get present worth we will have to multiply pv facotor * ACTF

Present worth of after tax cash flow

-80000

27270

24792

22539

23461

Total of PWACTF= 18062 , which is positive. Therefore this project shall be accepted

Annual worth shall be = PWACTF/4 year PV factor

=18062/3.1697

=5698

Let us now calculate IRR, we will have to follow trail and error method

At 10% PV = NPV is 18062

At 20% PV= NPV is -244

Therefore IRR falls in between 10% to 20%.

By applying trail and error method we get IRR= 19.84% at this rate NPV =0

i.e., Initial investment - cash flows = 0

If ERR>MARR then accept the project

If ERR<MARR then reject the project

To calculate ERR in excel by using the following formula

[80000(P/F,0.1,1)][(F/P,I,4)]=30000(F/A,0.1,3)+34350(F/A,0.1,1)

we get approx=2%