Question

3D Productions is considering a new packaging design for the virtual reality goggles the company produces. Management estimates that the new design will result in the following probabilities for possible effects on the firm's current estimate of annual sales of $8 million: Probability .05 .20 .40 .20 .15 Change in Sales ( 30,000) 40,000 100,000 150,000 250,000 The machinery required to incorporate the new design in the packaging is priced at $600,000. Since the new machine is technically superior to the current machine, it is expected to decrease packaging materials costs from 15% of revenues to only 12%. The life of the machine is estimated to be only three years and it would be depreciated using the MACRS depreciation method for 3-year assets (33%, 45%, 15%, 7%). The new machine is expected to have a salvage value of only $100,000 after three years. The old machine was purchased one year ago for $400,000 and is also being depreciated using the MACRS method for 3-year assets. Although it has a resale value of $250,000 currently, the estimated salvage value at the end of its remaining three years of expected useful life is only $60,000. The expected change in sales is anticipated to require an initial $100,000 in additional working capital. Any working capital requirements will be recovered at the end of three years. The company is in the 40% tax bracket. What are the relevant cash flows for investment evaluation purposes?

Expected change in sales = $114,000 per year

Year 0 Year 1 Year 2 Year 3

Net Cash Flows (442,800) 211,392 288,192 369,792

Answer 1

Prob.	Chg. In sales	Prob.*Chg.in sales
0.05	-30000	-1500
0.2	40000	8000
0.4	100000	40000
0.2	150000	30000
0.15	250000	37500
Expected change =		114000

	Old m/c	New m/c
Cost	400000	600000
Less MACRS 33%	-132000	-558000	(33%, 45%, 15%
Carrying value	268000	42000
Sale value	-250000	-100000
Loss on sale	18000	58000	Gain
Tax saved on loss(40%*18000)	7200	23200	Tax on gain
So, total proceeds from selling now(250000+7200)	257200	76800	(100000-23200)

	Year 0	1	2	3
Cost of new machine	-600000
After-tax sale proceeds of old machine	257200
Additional working capital introduced	-100000
WC recovered				100000
After-tax salvage of new machine				76800
Net CAPEX& WC	-442800	0	0	176800
Operating cash flows:
Incremental Sales		114000	114000	114000
Add: Incl.savings in decrease in packaging costs(3%*914000)		27420	27420	27420
Less: MACRS Depreciation		-198000	-270000	-90000
Incl.earning before tax		-56580	-128580	51420
Net savings in tax 40%		22632	51432	-20568
After-tax		-33948	-77148	30852
Add back depn.		198000	270000	90000
Incl.operating cash flow		164052	192852	120852
Net annual cash flows	-442800	164052	192852	297652