Question

The Marcus Company is evaluating the proposed acquisition of a new  machine. The machine's base price is $350,000, and it would cost another $125,000 to modify it for special use.  The machine falls into the MACRS 3-year class, and it would be sold after 4 years for $40,000.  The machine would require an increase in net working capital of $20,000. The machine would have no effect on revenues, but it is expected to save the firm $170,000 per year for 4 years in before-tax operating costs. .  The company's marginal tax rate is 30 percent and its cost of capital is 10 percent.

Calculate NPV. Should the machinery be purchased? Why or why not?

Answer 1

Computation of annual depreciation:

Year	*Cost Basis of asset	MACRS Rate	Annual depreciation	Book Value
1	$475,000	33.33%	$158,317.50	$316,682.50
2		44.45%	$211,137.50	$105,545.00
3		14.81%	$70,347.50	$35,197.50
4		7.41%	$35,197.50	$0

*Cost Basis of asset = Base price + modification cost = $ 350,000 + $ 125,000 = $ 475,000

Computation of operating cash flow:

	Year 1	Year 2	Year 3	Year 4
Savings in operating costs	$170,000	$170,000	$170,000	$170,000
Less: Depreciation expense	$158,317.50	$211,137.50	$70,347.50	$35,197.50
Savings before tax	$11,682.50	($41,137.50)	$99,652.50	$134,802.50
Less: Taxes at 30 %	$3,504.75	($12,341.25)	$29,895.75	$40,440.75
Savings after tax	$8,177.75	($28,796.25)	$69,756.75	$94,361.75
Add: Depreciation expense	$158,317.50	$211,137.50	$70,347.50	$35,197.50
Net operating cash flow	$166,495.25	$182,341.25	$140,104.25	$129,559.25

Non operating terminal cash flow = after tax salvage value + working capital release

After tax salvage value = (Market value – Book value) x (1- tax rate)

                                      = ($ 40,000 - $ 0) x (1 – 0.3)

                                      = $ 40,000 x 0.7 = $ 28,000

Non operating terminal cash flow = $ 28,000 + $ 20,000 = $ 48,000

Computation of NPV:

Initial cash outflow = $ 475,000 + $ 20,000 = $ 495,000

Cash inflows in year 1, 2, 3 are $ 166,495.25, $ 182,341.25, $ 140,104.25 respectively

Cash inflow in year 4 = $ 129,559.25 + $ 48,000 + $ 20,000 = $ 177,559.25

NPV = PV of future cash inflows – Initial cost

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 10 % (F)	PV (C x F)
0	($495,000)	1/(1+0.1)^0	1	($495,000.00)
1	$166,495.25	1/(1+0.1)^1	0.909090909090909	$151,359.32
2	$182,341.25	1/(1+0.1)^2	0.826446280991735	$150,695.25
3	$140,104.25	1/(1+0.1)^3	0.751314800901578	$105,262.40
4	$177,559.25	1/(1+0.1)^4	0.683013455365071	$121,275.36
			NPV	$33,592.32

NPV is $ 33,592.32

As the NPV is positive, machinery should be purchased.