Question

XYZ is now evaluating the purchase of a new machine for $210,000 installed with no NWC change. They plan to sell the machine at the end of 3 years for $30,000. MACRS 3 year depreciation. With the more efficient machine, labor savings per year are expected to be $70,000, $94,000 and $76,000 respectively. 40% tax. The cost of capital for this project is 8.%

What is the discounted payback for this project?

	a.	2.99 years
	b.	2.52 years
	c.	2.94 years
	d.	3.2 years years

Answer 1

Discounted Payback period in the time required to break even the initial cost of project considering time value of money

In the case of xyz limited as 40% Tax is applicable after subtracting depreciation, MACRS 3 class depreciation must be provided@33.33% for 1^st year,44.45% for year 2 and 14.81% for third year.After deducting tax@40%,depreciation must be added back as depreciation is a non cash expenses.

Discounted payback period=year, penultimate to year at which cumulative discounted cash flow becomes positive(n)+absolute value of cumulative cash flow for year n/Discounted cash flow for next year

year	DF@8%	machine	savings	MACRS dep	EBT	tax@40%	EAT	EAT+DEP	DF*cash flow	Cumilative CF
0	1	-210,000							-210000	-210,000
1	0.925926		70,000	69993	7	2.8	4	69,997	64,812	-145,188
2	0.857339		94000	93345	655	262	393	93,738	80,365	-64,823
3	0.793832		76000	31101	44,899	17959.6	26,939	58,040	46,074	-18,748
3	0.793832	30000			30,000	5775.6000	24,224	24,224	19230.10974	482

Tax on salvage value={salvage value-(machine value-total depreciation)}*40/100

                                           ={$30,000-($210,000-$194,439)}*40/100

                                      =($30,000-$15,561)*40/100

                                    =$14,439*40/100=$5775.6

Discounted payback period=year, penultimate to year at which cumulative discounted cash flow becomes positive(n)+absolute value of cumulative cash flow for year n/Total cash flow for year n+1

Discounted payback period=2+(64,823/(46074+19230))

                                            =2+64,823/65304=2.99years