Question

An owner of a large ranch is considering the purchase of a tractor with a front-end loader to clean his corrals instead of hiring workers that do it with a pitch fork. He has given you the following information and has asked you to evaluate this investment. The equipment costs $40,000. The rancher expects that he will save $11,500 a year that is usually paid to workers that clean out the corral by hand. However, he will incur an additional cost of $1,000 for fuel, repairs and maintenance. The rancher plans on keeping the equipment for 3 years before replacing it with a new one. He thinks he can sell the old equipment for $25,000 in three years. The rancher anticipates that his marginal tax rate will be 20 percent over the next three years. The IRS will allow the rancher to depreciate the tractor over seven yearsusing the straight-line method. The rancher requires at least a 15% pretax rate of return on capital (pretax).
1. What is the annual after-tax Net Returns?
A. 11,500
B. 9,200
C. 10,500
D. 8,400
E. None of the Above
2. What is the tax savings from depreciation?
A. 5,714
B. 40,000
C. 1,143
D. 2,667
E. None of the above
3. What is the after- tax terminal value in three years?
A. 24,571
B. 25,000
C. 40,000
D. 17,145
E. none of the above
4. What is the accumulated depreciation over the three years?
A. 5,715
B. 40,000
C. 8,000
D. 17,145
E. none of the above
5. What is the after- tax discount rate?
A. 15%
B. 12%
C. 3%
D 10%
E. None of the above
6. What is the present value of the after- tax net returns?
A. 40,000
B. 410
C. 17,489
D. 2,755
E. 20,175
F. None of the above
7. What is the present value tax savings from depreciation?
A. 40,000
B. 410
C. 17,489
D. 2,755
E. 20,175
F. None of the above
8. What is the present value of the after- tax terminal value?
A. 40,000
B. 410
C. 17,489
D. 2,755
E. 20,175
F. None of the above
9. What is the Net Present Value?
A. 40,000
B. 410
C. 17,489
D. 2,755
E. 20,175
F. none of the above
10. What is the maximum fuel, repairs and maintenancecost that can be paid each year to operate the loader and still find this investment profitable?
A. 1,213
B. 10,287
C. 11,500
D. 867
E. None of the above

Answer 1

Answer:

1) none of the above  $3828.57 ( E )

2) $1143 ( c )

3)  $24571 ( A )

4)  $17142.86 ( E )

5) 12% ( B )

6) $410 ( B )

7) $2744.95 ( f )

8) $17,489 ( c )

9) $24282.36 ( F )

10) 867

Explanation:

1)  The annual after-tax net returns

net income = cash flow - depreciation

                 = $10500 - $\frac{cost of equipment}{estimated life}$  =   10500 - (40000/7) = $4785.71

calculate the annual net after tax returns = net income * (1 - Tax rate ) = 4785 * (0.80) = $3828.57

2) Tax savings from depreciation

Tax savings from depreciation = Depreciation amount * Tax rate

                                                   = $(\frac{equipment cost}{estimated life} ) * Tax rate$

                                                  = (40000/7) * 0.2 = $1142.86 ≈ $1143

3) After tax terminal value in three years

Sale value = $25000,

Book value = 40000 - ( 5714.29 * 3 ) = $22857.13

Gain on sale = sale value - book value = $2142.87

tax rate = gain on sale * tax rate = 2142.87 * 0.2 = $428.57

Terminal value = sales value - tax rate = 25000 - 428.57 ≈ $24571

4) Accumulated depreciation over the three years

= depreciation amount * 3 years

=5714.29 * 3 = $17142.86

5) After tax discount rate

= discount rate * (1 - tax rate )

= 15% * 0.80 = 12%

6) Present value of the after-tax net returns

SOLUTION attached below

7) Present value tax savings from depreciation

= Tax savings from depreciation / ( 1+r)^n  note ; n = 3

= $1142.86 / ( 1 + 0.12 )^3 = $2744.95

8) present value of the after-tax terminal value

Pv of terminal value = Terminal value / ( 1 + r ) ^n

                                = $24571.43 / ( 1 + 0.12 ) ^3 = $17,489

9) Net present value

= net cash flows / ( 1 + r ) ^n

= 34114.29 / ( 1 + 0.12) ^3

= $34114.29 /  1.4049 = $24282.36

AT