The Problem The new equipment costs $300,000 and is expected to have a useful life of

The Problem The new equipment costs $300,000 and is expected to have a useful life of

five years. The new equipment will be depreciated for tax purposes using MACRS and a five-year classified life. At the end of its useful life, manage- ment expects to sell the new equipment for $100,000. Meanwhile, the new equipment is expected to reduce production costs by $60,000 each year. In addition, since it is more efficient, Hirshleifer can reduce its raw material and work-in-process inventories. Hirshleifer expects to reduce its inven- tory by $10,000 as soon as the new equipment is placed in service.

EXHIBIT 12.4 Estimated Incremental Cash Flows from the Williams 5 & 10 Expansion

End of Year

Investment cash flows Purchase and sale of building

+$350,000 Tax on sale of building

− 4,047 Purchase and sale of equipment

+50,000 Tax on sale of equipment

− 13,272 Change in working capital

Investment cash flows

+$432,681 Change in operating cash flows Change in revenues, ∆ R

Less: change in expenses, ∆ E − 100,000

–24,218 –24,218 Change in taxable income

Less: change in depreciation, ∆ D –32,698

–52,735 –1,735 Change in income after tax,

Less: taxes, τ ( ∆ R −∆ E −∆ D)

+$123,047 +$4,047 (1 −τ )( ∆ R −∆ E −∆ D)

+24,218 +24,218 Change in operating cash flows, ∆ OCF

Add: depreciation, ∆ D +32,698

+$147,265 +$28,265 Net cash flows

Capital Budgeting: Cash Flows

The income of Hirshleifer is taxed at a rate of 35%. There are no tax credits available for this equipment. What cash flows would result for each of the five years from this replacement?

The Analysis This is a replacement project. We need to decide whether to continue

with the present equipment or replace it. To do this, we look at the change in cash flows if we replace the equipment—relative to the cash flows of keeping the existing equipment. Instead of analyzing the prob- lem line-by-line as we did for the Williams 5&10, we first look at the cash flows related to acquiring and disposing assets and then look at the operating cash flows.

Investment Cash Flows The new equipment requires an immediate cash outlay of $300,000. It

will be depreciated using the specified rates, where 20.00% + 32.00% + 19.20% + 11.52% + 11.52% = 94.24% of its cost is depreciated by the end of the fifth year. That leaves a tax basis of 5.76% of $300,000, or $17,280. The expected sale price of the new equipment at the end of the fifth year is greater than the equipment’s book value, so there is a gain on the sale of the equipment of $100,000 − $17,280 = $82,720.

Because the sales price is less than the original cost, this gain is taxed as a recapture of depreciation at ordinary tax rates. The sale of the new equipment in the fifth year creates a gain of $82,720. The cash outflow for taxes on this gain is 0.35 × $82,720 = $28,952.

The $200,000 cost of the old equipment is a sunk cost and is not directly relevant to our analysis. However, we need to consider the tax basis of the old equipment in computing a gain or loss on its sale. We also need to consider the cost of the old equipment to assess whether any gain on its sale would be a capital gain or a recapture of depreciation.

By selling the old equipment for $120,000, the firm will incur a gain of the selling price less the tax basis, or $120,000 − $100,000 = $20,000. This is a recapture of depreciation—taxed at 35%—since the sales price is less than the original cost, the $200,000.

Disposing of the old equipment has two tax-related cash flows: the tax on the sale of the old equipment when the new equipment is pur- chased, an outflow of 0.35 × $20,000 = $7,000; and the tax we would have had to pay on the sale of the old equipment in the fifth year, an inflow of 0.35 × $10,000 = $3,500.

If the firm replaces the old equipment today, it foregoes the sale of the equipment in five years for $10,000. We need to consider both the foregone cash flow from this sale, as well as any forgone taxes or tax benefit on this sale.

LONG-TERM INVESTMENT DECISIONS

And let’s not forget about the change in net working capital. The reduc- tion in inventory is a cash inflow since inventory can be reduced. If we assume it is reduced immediately, there is a $10,000 cash inflow initially. Assuming that inventory returns to its previous level at the end of the new equipment’s life, there will be a $10,000 cash outflow at the end of the fifth year.

Let’s summarize the investment cash flows: Initially:

Purchase of new equipment −$300,000 Sale of old equipment

+120,000 Tax on sale of old equipment

−7,000 Decrease in inventory

+10,000 Total investment cash flow

−$177,000 Fifth year: Sale of new equipment

+$100,000 Tax on sale of new equipment

−28,952 Foregone sale of old equipment

−10,000 Foregone tax on sale of old equipment

+3,500 Increase in inventory

–10,000 Total investment cash flow

+$54,548 Operating Cash Flows

If the old equipment is kept, depreciation would continue to be $200,000/

10 years = $20,000 per year for each of the next five years. If it is replaced, there would no longer be this depreciation expense. The new equipment will be depreciated over five years. Comparing the depreciation expense with the old and the new equipment, we determine the change in the taxes from the change in the depreciation tax shield:

Depreciation Change in Depreciation on

Rate of

Depreciation

Expense of Depreciation Year New Equipment New Equipment Old Equipment

Expense of

$100,000 The reduction in costs is a cash inflow—less cash is paid out with the

new than with the old equipment. But there is also additional taxable

Capital Budgeting: Cash Flows

income—the new machine will reduce expenses by $60,000 each year, so that increases taxable income by $60,000 each year, increasing taxes each year.

Using equation (12-1),

Change in Change in Change

Operating in

After Taxes Cash Flow Revenues Expenses Depreciation ( ∆ R −∆ E −∆ D) ( ∆ R −∆ E −∆ D)(1 −τ ) Year

29,536 44,096 Or, using equation (12-2),

Change in Change

Change in

Change in Operating in

Change

Revenues

in and Expenses Depreciation Cash Flow Revenues Expenses

Tax Shield ( ∆ R −∆ E)(1 −τ ) Year

After Taxes

∆ E ( ∆ R– ∆ E)(1– τ )

5,096 44,096 The project’s cash flows are shown in Exhibit 12.5. Investing

$177,000 initially is expected to generate cash inflows shown in the time line in the next five years. Our task, which we will take up in the next chapter, is to evaluate these cash flows to see whether taking on this project will increase owners’ wealth.