Question

Rowing Company is analyzing the replacement of one of its machines. The machine was purchased ten years ago at a cost of $35,000 and has been depreciated to a book value of zero. If Rowing replaces the machine, it will be able to bid on larger projects that require the capabilities of the new machine. The new machine will cost the firm $50,000, which will be depreciated over 4 years according to the following depreciation rates: 30% in each of years 1 and 2, and 20% in each of years 3 and 4. The new machine qualifies for an immediate 3%investment tax credit. Pioneer anticipates that at the end of the machine's eight year economic life it will be sold for $10,000. Pioneer estimates that its existing machine can be sold today for $6,000. If Rowing does not replace the machine, it anticipates being able to use the existing machine for eight more years at which time its salvage value would be zero. Without the purchase of the new machine, Rowing expects to generate revenue of $200,000 per year.

The company's use of its existing machine is expected to generate operating expenses of $120,000 per year. If the new machine is purchaseµ, Rowing expects the annual revenues and operating costs to increase to $250,000 and $150,000 respectively. Rowing's marginal tax rate is 25%. To fund this project, Rowing will raise 30% of the capital from debt and 70% of the capital from equity; its after-tax cost of debt is 8% and the cost of equity is 18%.

1. Calculate the NPV

2. Calculate the IRR

Answer 1

		WEIGHTED AVERAGE COST OF CAPITAL
		Wd	Weight of debt		30%
		We	Weight of Equity		70%
		Cd	Cost of Debt		8	percent
		Ce	Cost of equity		18	percent
		WACC=Wd*Cd+We*Ce	Weighted Average Cost of Capital		15	percent
		INCREMENTAL DEPRECIATION
		N	A	B=A*50000	C	D=C*35000	E=B-D	F	G=E*F
		Year	Depreciation Rate for new equipment	Depreciation on New Equipment	Depreciation Rate for OLD equipment	Depreciation on old Equipment	Incremental Depreciation	Tax Rate	Tax shield benefit
		1	30.00%	$15,000	0.00%	$0	$15,000	25%	$3,750
		2	30.00%	$15,000	0.00%	$0	$15,000	25%	$3,750
		3	20.00%	$10,000	0.00%	$0	$10,000	25%	$2,500
		4	20.00%	$10,000	0.00%	$0	$10,000	25%	$2,500
		AFTER TAX   COST SAVINGS
		Annual Revenue from new machine		$250,000
		Annual Revenue from old machine		$200,000
		Increase in Revenue		$50,000	(250000-200000)
		Annual Operating cost of new machine		$150,000
		Annual Operating cost of Old machine		$120,000
		Increase in Costs		$30,000	(150000-120000)
		Before tax annual savings		$20,000	(50000-30000)
		After Tax annualSavings		$15,000	(20000*(1-0.25)
		ADD DEPRECIATION TAX SHIELD AND AFTER TAX COST SAVINGS
		N	A	B	C=(1-0.25)*10000	D=A+B+C	PV=D/(1.15^N)
		Year	Tax shield benefit	After tax cost savings	After tax Salvage Value	Total annualCash Flow	Present value of total annual cash flow
		1	$3,750	$15,000		$18,750	$16,304
		2	$3,750	$15,000		$18,750	$14,178
		3	$2,500	$15,000		$17,500	$11,507
		4	$2,500	$15,000		$17,500	$10,006
		5		$15,000		$15,000	$7,458
		6		$15,000		$15,000	$6,485
		7		$15,000		$15,000	$5,639
		8		$15,000	$7,500	$22,500	$7,355
						SUM	$78,931
	Present value of annual cash flow	$78,931