Question

Your firm, Agrico Products, is considering a tractor that would have a cost of $37,000, would increase pretax operating cash flows before taking account of depreciation by $13,000 per year, and would be depreciated on a straight-line basis to zero over 5 years at the rate of $7,400 per year, beginning the first year. (Thus, annual cash flows would be $13,000 before taxes plus the tax savings that result from $7,400 of depreciation.) The managers are having a heated debate about whether the tractor would actually last 5 years. The controller insists that she knows of tractors that have lasted only 4 years. The treasurer agrees with the controller, but he argues that most tractors actually do give 5 years of service. The service manager then states that some last for as long as 8 years.

Assume that if the tractor only lasts 4 years, then the firm would receive a tax credit in Year 4 because the tractor's salvage value at that time is less than its book value. Under this scenario, the firm would not take depreciation expense in Year 5.

Given this discussion, the CFO asks you to prepare a scenario analysis to determine the importance of the tractor's life on the NPV. Use a 40% marginal federal-plus-state tax rate, a zero salvage value, and a 9% WACC. Assuming each of the indicated lives has the same probability of occurring (probability = 1/3), what is the tractor's expected NPV?

Do not round intermediate calculations. Negative values, if any, should be indicated by a minus sign. Round your answers to the nearest cent.

1. Tractor's NPV if actual life is 5 years.
   $  
2. 
   
3. Tractor's NPV if actual life is 4 years.
   $  
4. 
   
5. Tractor's NPV if actual life is 8 years.
   $  
6. 
   
7. Tractor's expected NPV.
   $  

Answer 1

	NPV is calculated below, for all alternative assumptions as to life:
a)	LIFE 5 YEARS:	0	1	2	3	4	5	6	7	8
	Pretax operating cash flows		$         13,000	$   13,000	$    13,000	$     13,000	$   13,000
	Depreciation		$           7,400	$     7,400	$       7,400	$       7,400	$     7,400
	Incremental EBIT		$           5,600	$     5,600	$       5,600	$       5,600	$     5,600
	Tax at 40%		$           2,240	$     2,240	$       2,240	$       2,240	$     2,240
	Incremental NOPAT		$           3,360	$     3,360	$       3,360	$       3,360	$     3,360
	Add: Depreciation		$           7,400	$     7,400	$       7,400	$       7,400	$     7,400
	Incremental OCF		$         10,760	$   10,760	$    10,760	$     10,760	$   10,760
	Capital expenditure	$        37,000
	FCF	$      -37,000	$         10,760	$   10,760	$    10,760	$     10,760	$   10,760
	PVIF at 9%	1	0.91743	0.84168	0.77218	0.70843	0.64993
	PV at 9%	$      -37,000	$           9,872	$     9,056	$       8,309	$       7,623	$     6,993
	NPV	$          4,853
b)	LIFE 4 YEARS:	0	1	2	3	4
	Pretax operating cash flows		$         13,000	$   13,000	$    13,000	$     13,000
	Depreciation		$           7,400	$     7,400	$       7,400	$       7,400
	Incremental EBIT		$           5,600	$     5,600	$       5,600	$       5,600
	Tax at 40%		$           2,240	$     2,240	$       2,240	$       2,240
	Incremental NOPAT		$           3,360	$     3,360	$       3,360	$       3,360
	Add: Depreciation		$           7,400	$     7,400	$       7,400	$       7,400
	Incremental OCF		$         10,760	$   10,760	$    10,760	$     10,760
	Capital expenditure	$        37,000
	Tax credit = 7400*40 =					$       2,960
	FCF	$      -37,000	$         10,760	$   10,760	$    10,760	$     13,720
	PVIF at 9%	1	0.91743	0.84168	0.77218	0.70843
	PV at 9%	$      -37,000	$           9,872	$     9,056	$       8,309	$       9,720
	NPV	$              -44
c)	LIFE 8 YEARS:	0	1	2	3	4	5	6	7	8
	Pretax operating cash flows		$         13,000	$   13,000	$    13,000	$     13,000	$   13,000	$      13,000	$         13,000	$      13,000
	Depreciation		$           7,400	$     7,400	$       7,400	$       7,400	$     7,400	$               -	$                  -	$               -
	Incremental EBIT		$           5,600	$     5,600	$       5,600	$       5,600	$     5,600	$      13,000	$         13,000	$      13,000
	Tax at 40%		$           2,240	$     2,240	$       2,240	$       2,240	$     2,240	$        5,200	$           5,200	$        5,200
	Incremental NOPAT		$           3,360	$     3,360	$       3,360	$       3,360	$     3,360	$        7,800	$           7,800	$        7,800
	Add: Depreciation		$           7,400	$     7,400	$       7,400	$       7,400	$     7,400	$               -	$                  -	$               -
	Incremental OCF		$         10,760	$   10,760	$    10,760	$     10,760	$   10,760	$        7,800	$           7,800	$        7,800
	Capital expenditure	$        37,000
	FCF	$      -37,000	$         10,760	$   10,760	$    10,760	$     10,760	$   10,760	$        7,800	$           7,800	$        7,800
	PVIF at 9%	1	0.91743	0.84168	0.77218	0.70843	0.64993	0.59627	0.54703	0.50187
	PV at 9%	$      -37,000	$           9,872	$     9,056	$       8,309	$       7,623	$     6,993	$        4,651	$           4,267	$        3,915
	NPV	$        17,685
d)	Expected NPV = 4853*1/3-44/1/3+17685*1/3 =			$     7,498