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 $12,000 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 $12,000 before taxes plus the tax savings that result from $7,400 of depreciation.) The managers disagree about whether the tractor would 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 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 10% WACC. Assuming each of the indicated lives has the same probability of occurring (probability = 1/3), what is the tractor's expected NPV?

Round your answers to two decimal places. Do not round intermediate calculations. Negative amount should be indicated by a minus sign.

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

Solutions:

A.)

If life = 5 years, depreciation = $7400
after tax cash flow = ($12000 - $7400)*(1-40%) + $7400 = $10,160
life = 5 years
Year Cash Flow, 5years
Year 0 -37000
Year 1 10,160
Year 2 10,160
Year 3 10,160
Year 4 10,160
Year 5 10,160
NPV = (Annual cash flow × PVIFA 10%, 5 years)-initial investment

= ($10,160 × 3.791) – 37,000

NPV = $1,516.56

b.)

If life = 4 years, depreciation = $9250
after tax cash flow = ($12--000 - $9250)*(1-40%) + $9250 = $10,900
N = 4 years
NPV = (Annual cash flow × PVIFA 10%, 4 years)-initial investment

= ($10,900 × 3.170) – 37,000

NPV = -$3,447

.
c.)
If life = 8 years, depreciation = $4625
after tax cash flow = ($12000 - $4625)*(1-40%) + $4625 = $ 9,050
N = 8 years
NPV = (Annual cash flow × PVIFA 10%, 8 years)-initial investment

= ($9,050 × 5.335) – 37,000

NPV = $ 11,281.75

.
d.)

EXPECTED NPV = 1/3*NPV OF 4 YEARS + 1/3*NPV OF 8 YEARS + 1/3*NPV OF 5 YEARS
Expected NPV = (-3,447 + 1,516.56+ 11,281.75)/3 =$3,117.10