Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $650,000; the new one will cost $780,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $140,000 after five years. The old computer is being depreciated at a rate of $130,000 per year. It will be completely written off in three years. If we don't replace it now, we will have to replace it in two years. We can sell it now for $230,000; in two years it will probably be worth $90,000. The new machine will save us $125,000 per year in operating costs. The tax rate is 38 percent, and the discount rate is 14 percent.

Suppose we consider only whether we should replace the old computer now with­ out worrying about what's going to happen in two years. Calculate the NPV of the project.

{ Hint: In 2 years time you sell the old machine,s o you need to calculate the cashflows for it:

Aftertax salvage value = $90,000 + ($130,000 – 90,000)(.38) = $105,200}

Answer 1

The NPV of the project has to be broken down into three parts:

1. Initial Investment - As the initial cost of the new machine is $ 780,000, hence CF(0) = - $ 780,000

2. Operating Cash Flows - The operating cash flows of the company can be calculated as follows:

After-Tax Operating Cash Flows = After-Tax Operating Cash Flows = ((Sales – Cash operating expenses – Depreciation) * (1 - tax rate)) + Depreciation

Increase in Depreciation = ($ 780,000 / 5) - $ 130,000 = $ 26,000

Decrease in Operating costs = $ 125,000

Hence, net effect = Benefit due to depreciation-tax offset + Savings due to reduced operational costs

= $ (26,000 * 0.38) + $ 125,000 * (1 - 0.38) = $ 87,380

3. After-tax non operating cash flows = Aftertax salvage value = $90,000 + ($130,000 – 90,000)(.38) = $105,200

Hence NPV can be computed as the sum of all the above three components as shown in the image below: