Western Industrial Products is considering a project with a five-year life and an initial cost of $220,000. The discount rate for the project is 11 percent. The firm expects to sell 2,900 units a year. The cash flow per unit is $40. The firm will have the option to abandon this project at the end of year three (after year three's sales) at which time the project's assets could be sold for an estimated $60,000. The firm should abandon the project at the end of year three if the expected level of annual sales, starting with year 4, falls to units or less. Ignore taxes.

875 units or less

Explanation:

5 year project $220,000

discount rate 11%

cash flow per year = 2,900 units x $40 = $116,000

after year 3, the project's assets should have a salvage value of $60,000

year                    cash flow

0                         -220,000

1                             116,000

2                            116,000

3                            116,000

4                            116,000

5                            116,000

the project's NPV = $208,724

year                    cash flow

0                         -220,000

1                             116,000

2                            116,000

3                            176,000

the NPV of the first 3 years, including salvage value = $107,342

the difference between both NPVs = $208,724 - $107,342 = $101,382

to determine the number of units sold to make abandoning the project more profitable:

101,382 = x/1.11⁴ + x/1.11⁵ = 0.65873x + 0.59345x = 1.25218x

x = 101,382 / 1.25218 = 80,964 / $40 per unit = 2,024.1 ⇒  2,025 units

so the units sold during years 4 and 5 should be = 2,900 - 2,025 = 875

if total sales lower to 875 units during years 4 and 5, the cash flows should be:

year                    cash flow

0                         -220,000

1                             116,000

2                            116,000

3                            116,000

4                            35,000

5                            35,000

the NPV = $107,297, which is actually lower than the NPV obtained by abandoning the project in year 3.

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