Question

NVidia Ltd is considering replacing an old machine with a new one. The old one cost $100,000; the new one will cost $70,000. The new machine will be depreciated prime cost to zero over its 5-year life. It will probably be worth about $15,000 after 5 years. The old machine is being depreciated at a rate of $5,000 per year. It will be completely written off in 5 years. If Nvidia does not replace it now, it will have to replace it in 5 years. Nvidia can sell it now for $55,000. In 5 years, it will probably be worth nothing. The new machine will save $10,000 per year in operating costs. The tax rate is 30%, tax is paid in the year of income.

NVidia Ltd has several classes of outstanding bonds, and the average yield is 8%. Its beta is 1.3, historical risk premium is 7.94%, and the treasury yield is 5%. If NVidia’s capital structure is 40% debt and 60% equity, should NVidia Ltd purchase the new machine? Explain your answer.

Answer 1

We need to calculate NPV or net present value of replacing the old machine with new one. if this NPV of replacement is positive then NVidia Ltd should replace the old machine and purchase the new machine.

NPV = sum of present value of cash inflows - net cash outflow at year 0

sum of present value of cash inflows = year 1 cash inflow/(1+WACC) + year 2 cash inflow/(1+WACC)² ... + year 5 cash inflow/(1+WACC)⁵

WACC is the weighted average cost of capital.

WACC = weight of debt*after-tax cost of debt + weight of equity*cost of equity

cost of debt is the yield to maturity of the bonds which is 8%.

after-tax cost of debt = cost of debt*(1-tax rate) = 8%*(1-0.30) = 8%*0.70 = 5.6%

cost of equity = risk-free rate or treasury yield + stock's beta*risk premium = 5% + 1.3*7.94% = 5% + 10.322‬% = 15.322‬%

WACC = 0.40*5.6% + 0.60*15.322% = 2.24‬% + 9.1932‬% = 11.43%

Tax on Salvage value old machine = (salvage value - book value)*tax rate

book value of old machine = cost of old machine - accumulated depreciation

accumulated depreciation = no. of years machine depreciated*depreciation per year

cost of old machine is $100,000 and depreciation per year $5,000. so life of old machine is $100,000/$5,000 = 20 years. remaining depreciation to be applied is for 5 years. so, no. of years machine depreciated is 20 - 5 = 15 years.

accumulated depreciation = 15*$5,000 = $75,000

book value of old machine = $100,000 - $75,000 = $25,000

Tax on Salvage value old machine = ($55,000 - $25,000)*30% = $30,000*30% = $9,000

book value of new machine is zero at the end of project's life. so tax will be applied on entire $15,000 salvage value.

NPV of replacement is $17,577.70 or $17,578. so NVidia Ltd should purchase the new machine as NPV is positive and new machine will generate incremental profits.

	Years	0	1	2	3	4	5
	cost of new machine	-$70,000
	Savings in operating costs	$0	$10,000	$10,000	$10,000	$10,000	$10,000
Less:	New Depreciation	$0	$14,000	$14,000	$14,000	$14,000	$14,000
Plus:	Old Depreciation	$0	$5,000	$5,000	$5,000	$5,000	$5,000
	Earnings before tax	$0	$1,000	$1,000	$1,000	$1,000	$1,000
Less:	Taxes @30%	$0	$300	$300	$300	$300	$300
	Earnings after tax	$0	$700	$700	$700	$700	$700
Plus:	New Depreciation	$0	$14,000	$14,000	$14,000	$14,000	$14,000
Less:	Old Depreciation	$0	$5,000	$5,000	$5,000	$5,000	$5,000
Plus:	Salvage value old machine	$55,000	$0	$0	$0	$0	$0
Less:	Tax on Salvage value old machine	$9,000	$0	$0	$0	$0	$0
Plus:	Salvage value new machine	$0	$0	$0	$0	$0	$15,000
Less:	Tax on Salvage value new machine	$0	$0	$0	$0	$0	$4,500
	Net cash flows	-$24,000	$9,700	$9,700	$9,700	$9,700	$20,200
	NPV	$17,577.70

Calculations