Question

Your firm, Agrico Products, is considering a tractor that would have a cost of $35,000, 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 $7,000 per year beginning the first year. (Thus, annual cash flows would be $13,000 before taxes plus the tax savings that result from $7,000 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 12% 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.

Tractor's NPV if actual life is 5 years. $

Tractor's NPV if actual life is 4 years. $

Tractor's NPV if actual life is 8 years. $

Tractor's expected NPV.$

Answer 1

Solution:

Given informaton:

Cost of Asset =$ 35,000

Method of Depriciation = Stright Line Method

Salvage Value = 0

Annual cash flows before tax = $13,000 after tax = 13,000 * 60/100 = $7,800

Tax rate 40% WACC= 12%

Life of Asset- 4 years, 5years, 8years

a) Life of tractor is 5 years

Depreciation = 35,000/5 =$7,000

Tax saving on Depreciation = 7,000 * 40/100 = $2,800

Net cash flows = Annual cash flow after tax + tax saving on depreciation

= 7800 + 2800 = $10,600

Present Value of Net cash flows = Cash flows * PVAF (12%,5years)

= $10,600 * 3.60

= $38,210

NPV (5years) = PV of cash flows - Intial Investment

= 38,210 - 35,000 = $3,210

b) Life of tractor is 4 Years

Depreciation = $35000/4 = 8,750

Tax Savings on Depreciation = 8,750*40/100 = $3,500

Net cash flows= 7,800 + 3,500 = $11,300

PV of net cash flows = 11,300 * PVAF (12%,4years)

= 11,300 * 3.04 = $34,352

NPV (4years) = $34352- $35,000 = - 648

c) Life of tractor is 8 Years

Depreciation = $35000/8 = $4,375

Tax Savings on Depreciation = 4,375*40/100 = $1,750

Net cash flows= 7,800 + 1,750 = $9,550

PV of net cash flows = $9,550 * PVAF (12%,8years)

= 11,300 * 4.97 = $56,134

NPV (8years) = $56134- $35,000 = $ 21,134

Calculation of Expected Net Present value

Expected NPV = NPV of each event * probability of event

= (3210 * 1/3) + (-648 *1/3) + (21134 * 1/3)

=$ 7,899 (aprox.)