You purchase a widget-making machine that can produce $5,000 worth of widgets each year for up...

You purchase a widget-making machine that can produce $5,000 worth of widgets each year for up to four years. However, there is a 12% chance that the machine will break entirely at the end of each year after the cash for that year has been produced. (This is roughly the process describing how incandescent light bulbs burn out, too.) What is the expected NPV of this widget machine? Assume a 8.9% discount factor, applicable beginning with the first $5,000

Expert Solution

Probability of widget running succesfully each year end				=	1-0.12=0.88 or 88%

Calculation of probability of widget running each year

	Year 1 start	100% (because the failure ocurs at year end after generating first year cashflow.Hence first year probabilty will be 100%
	Year 2 start	100%*88%=88%
	Year 3 start	100%88%88%=77.44%
	Year 4 start	100%88%88%*88%=68.15%


Calculation of expected cashflow and NPV

Year	1	2	3	4	Total
Cashflow	$5,000	$5,000	$5,000	$5,000
Probabilty	100%	88%	77.40%	68.15%
expected CF	$5,000	$4,400	$3,870	$3,408
PVF @8.9%	0.9183	0.8432	0.7743	0.7110
Discounted CF	$4,591.37	$3,710.20	$2,996.59	$2,422.84	$13,720.99


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