A rancher is considering the purchase of a bulldozer. He can choose to buy eithe

Question

A rancher is considering the purchase of a bulldozer. He can choose to buy either a new or used bulldozer. The new and used bulldozers provided the same service so revenues can be ignored. The new bulldozer costs $46,400, has a before-tax net return of -$7,800, a life of 11 years, and a terminal value of $21,400. The used bulldozer costs $55,200, has a before-tax net return of -$8,000, a life of 3 years, and a terminal value of $29,500. Suppose that the pre-tax rate of return is 6%, the marginal tax rate of 29%, and the IRS allows him to depreciate the new and used bulldozer over 13 years using the straight-line method. The inflation rate is assumed to be 0.

(i)        What is the NPV of the new bulldozer?
                        a.        -$74,389.69                b.         -$52,497.37
                        c.          -$93,930.90                d.         -$71,775.91

Enter Response Here:

(ii)       What is the NPV of the used bulldozer?
                        a.         -$37,635.95                b.         -$44,544.87
                        c.          -$78,267.54               d.       -$38,138.30

Enter Response Here:

(iii)      What is the annuity equivalent of the new bulldozer?
                        a.         -$10,873.01                b.         -$8,308.45
                        c.          -$6,076.85                 d.       -$8,611.01

Enter Response Here:

(iv)      What is the annuity equivalent of the used bulldozer?
                        a.         -$28,342.88                b.         -$16,130.95
                        c.          -$13,629.04               d.       -$13,810.95

Enter Response Here:

(v)       Which bulldozer should this rancher choose?
                        a.        A                      b.         B

Explanation / Answer

1. -74389.69

2. -38,138.3

3. -8611.01

=(4.26%*-74389.69)/(1-1.046^-11)

4. -13810.95

=(4.26%*-38138.3)/(1-1.046^-3)

5. He should select the used bulldozer

WORKING: NPV of new bulldozer

Tax on Capital gain

NPV of old bulldozer

Tax on Capital loss

2.

Year Initial cost Return before tax Depreciation Return after depreciation Tax Cash flows Salvage post tax Net cash flows 0 -46400 -46400 1 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 2 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 3 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 4 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 5 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 6 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 7 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 8 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 9 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 10 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 -4502.9231 11 -7800 -3569.230769 -11369.2 3297.076923 -4502.923077 17264.15 12761.2308 4.2600% NPV ($74,389.69)

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