Question

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Suppose that Elena Company is considering the purchase of a newer, more efficient yogurt-making machine. If purchased, it would require the new machine on January 2, year 1. Elena expects to sell 600,000 gallons of milk in each of the next five years at a $2 per gallon selling price.

Elena has two options:

(1) continue to operate the old machine purchased four years ago or

(2) sell it and purchase the new machine.

Elena is subject to a 40% income tax rate on all income. Assume the company uses the straight-line method for books and tax purposes. Assume that tax depreciation is calculated without regard to salvage value. Use an after-tax discount rate of 10%.

The following information has been prepared to help decide which option is more desirable.

	Old Machine	New Machine
Original cost of machine at acquisition	$ 1,600,000	$ 2,000,000
Useful life from date of acquisition	7 years	5 years
Expected annual cash operating expenses:
Variable cost per gallon	$1.20	$1.00
Total fixed cash costs	$ 400,000	$ 160,000
Estimated cash value of machines follows:	Old Machine	New Machine
January 2, Year 1	$ 400,000	$ 2,000,000
December 31, Year 3	$200,000	0
December 31, Year 5	0	$500,000

Answer 1

$ calculation of salvage value at year 3 Salvage value at end of 5th year PVF at (10%, 3year) Present value of salvage value (500000*0.75131) Less: Tax @ 40% Net salvage value 200,000.00 0.75131 =PV(10%,3,0,-1) 150,263 $ $ $ -60,105.18 90,157.78 Old machine NPV Particulars Sales Less:Variable cost Contribution Less: fixed costs Less: Depreciation (1600000/7) Cash flow before tax Less: tax @ 40% Cash flow after tax Add: Depreciation Net cash inflow Present value annuity(10%, 7 years) Present value of cash flows Add: Net salvage value Total cash inflows Cash inflow at year O is NPV (a) Present value annuity(10%, 7 years) (b) Equivated NPV (a/b) Amount ($) $ 1,200,000 $ -720,000 $ 480,000 $ -400,000 $ -228,571 $ -148,571 $ 59,429 $ -89,143 $ 228,571 $ 139,428 2.48685 =PV(10%,3,-1,0,0) $ 346,737.15 $ 90,157.78 $ 436,894.93 $ -514,286 $ -77,390.78 2.48685 $ -31,119.98 If machine is sold at year 4, cash inflow is Book value after 4 years (1600000*3/7) Less: sale value loss Tax @ 40% saving Total inflow is (400000+114286) $ $ $ $ $ -685,714 400,000 -285,714 114,286 514,286

$ 500,000.00 0.62092 =PV(10%,5,0,-1) 310,461 NPV of New machine Particulars Sales Less:Variable cost Contribution Less: fixed costs Less: Depreciation (2000000)/5 Cash flow before tax Less: tax @ 40% Cash flow after tax Add: Depreciation Net cash inflow Present value annuity(10%,5 years) Present value of cash flows Add: Net salvage value Total cash inflows Less : Initial cash outflow (2,000,000-400,000) NPV Present value annuity(10%,5 years) Equivated NPV calculation of salvage value Salvage value at end of 5th year PVF at (10,5year) Present value of salvage value (500000*0.62092) Less: Tax @ 40% Net salvage value $ Amount ($) $ 1,200,000 $ -600,000 $ 600,000 $ - 160,000 $ -400,000 $ 40,000 $ 16,000 $ 24,000 $ 400,000 $ 424,000 3.79079=PV(10%,5,-1,0,0) S 1,607,293.59 186276.3969 $ 1,793,569.99 $ -1,600,000.00 $ 193,569.99 3.79079 $ 51,063.27 $ $ -124,184.26 186,276.40 So, it is better to go with New machine, as it has higher NPV I hope this solves your doubt. Feel free to comment if you still have any query or need something else. I'll help asap.