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

Answer:

Yes,

NVidia Ltd should purchase the new machine.

NPV of replacing with new machine = $17,577.70

As NPV is positive, NVidia Ltd should purchase the new machine

Working:

Let us calculate cost of capital (WACC) first:

Using CAPM:

Cost of equity = Rf + Beta * Rp = 5% + 1.3 * 7.94% = 15.32%

After tax cost of debt = 8% * (1 - 30%) = 5.60%

WACC = Cost of equity * Weight of equity + after-tax cost of debt * Weight of debt

= 15.32% * 60% + 5.60% * 40%

= 11.43%

WACC = 11.43%

Old Machine:

The old machine is being depreciated at a rate of $5,000 per year. It will be completely written off in 5 years.

Current book value = 5000 * 5 = $25,000

Current sale value = $55,000

Tax on Gain = (55000 - 25000) * 30% = 30000 * 30% = $9000

Sale value net of tax = 55000 - 9000 = $46,000

The incremental cash flows and NPV are calculated as below:

Above excel with 'show formula' is as below: