Question

A company can buy a machine that is expected to have a three-year life and a $30,000 salvage value. The machine will cost $1,800,000 and is expected to produce a $200,000 after-tax net income to be received at the end of each year. If a table of present values of $1 at 12% shows values of 0. 8929 for one year, 0. 7972 for two years, and 0. 7118 for three years, what is the net present value of the cash flows from the investment, discounted at 12%?

Answer 1

The net present value (NPV) of the machine, when considering the after-tax net income for three years and the salvage value discounted at 12%, is -$1,298,266 after subtracting the initial investment of $1,800,000.

Step-by-step explanation:

To calculate the net present value (NPV) of the cash flows from the investment, you need to discount the expected net incomes and the salvage value to their present values using the provided discount factors for different years. You then subtract the initial cost of the machine from the sum of these present values to find the NPV.

Net income for each year is $200,000, and the discount factors for 12% are 0.8929 for year one, 0.7972 for year two, and 0.7118 for year three. The salvage value of $30,000 at the end of year three also needs to be discounted. Here are the calculations:

• Year 1 NPV: $200,000 × 0.8929 = $178,580
• Year 2 NPV: $200,000 × 0.7972 = $159,440
• Year 3 NPV (net income): $200,000 × 0.7118 = $142,360
• Year 3 NPV (salvage value): $30,000 × 0.7118 = $21,354

Add the NPVs for all three years plus the salvage value, and then subtract the initial investment to get the total NPV:

Total NPV = ($178,580 + $159,440 + $142,360 + $21,354) - $1,800,000 = $501,734 - $1,800,000 = -$1,298,266