Relevant Cash Flows in Discounted Cash Flow Analysis

Learning Objective 5 Identify relevant cash inflows and outflows for capital budgeting decisions

the differences in expected future cash flows resulting from the investment

So far, we have examined methods for evaluating long-term projects in settings where the expected future cash flows of interest were assumed to be known. One of the biggest challenges in capital budgeting, particularly DCF analysis, however, is determining which cash flows are relevant in making an investment selection. Relevant cash flows are the differences in expected future cash flows as a result of making the investment. In the Vector example, the relevant cash flows are the differences in expected future cash flows that will result from continuing to use one of the firm’s old buses versus purchasing a new hybrid bus. When reading this section, focus on identifying expected future cash flows and the differences in expected future cash flows.

To illustrate relevant cash flow analysis, consider a more complex version of the Vector example with these additional assumptions:

Vector is a profitable company. The income tax rate is 40% of operating income each year.
The before-tax additional operating cash inflows from the hybrid bus are $220,000 in years 1–4 and $170,000 in year 5.
For tax purposes, Vector uses the straight-line depreciation method and assumes there is no terminal disposal value of the bus.
Gains or losses on the sale of depreciable assets are taxed at the same rate as ordinary income.
The tax effects of cash inflows and outflows occur at the same time that the cash inflows and outflows occur.
Vector uses an 8% required rate of return for discounting after-tax cash flows.

The data for the buses follow:

<p>A table shows data for the buses</p

The table depicts purchase price, current book value, current disposal value, terminal disposal value 5 years from now, annual depreciation, and working capital required for the old bus and the new hybrid bus. The details of the table are as follows:

1. Purchase price

Old bus: Blank
New hybrid bus: 660,000 dollars

2. Current book value

Old bus: 60,000 dollars
New hybrid bus: Blank

3. Current disposal value

Old bus: 28,500 dollars
New hybrid bus: Not applicable

4. Terminal disposal value 5 years from now

Old bus: 0 dollars
New hybrid bus: 0 dollars

5. Annual depreciation

Old bus, 60,000 dollars divided by 5 years: 12,000 dollars
New hybrid bus, 660,000 dollars divided by 5 years: 132,000 dollars

6. Working capital required

Old bus: 6,000 dollars
New hybrid bus: 36,000 dollars

Relevant After-Tax Flows

We use the concepts of differential cost and differential revenue introduced in Chapter 12. We compare (1) the after-tax cash outflows as a result of replacing the old bus with (2) the additional after-tax cash inflows generated from using the new bus rather than the old bus.

As Benjamin Franklin said, “Two things in life are certain: death and taxes.” Income taxes are a fact of life for most corporations and individuals. It is important to understand how income taxes affect cash flows in each year. Exhibit 22-5 shows how investing in the new bus will affect Vector’s cash flow from operations and its income taxes in year 1. Recall that Vector will generate $220,000 in before-tax additional operating cash inflows by investing in the new bus, but it will record additional depreciation of $120,000 $begin inline style left parenthesis $ text 132,000? end text minus ? text $12,000 end text right parenthesis end style$ for tax purposes.

Panel A and B shows effect on cash flow from operations, net of income taxes, in Year 1 for Vector’s Investment in the New Hybrid Bus.

Panel A: Two Methods Based on the Income Statement

C: Operating cash inflows from investment in bus: $220,000
D: Additional depreciation deduction: 120,000
OI: Increase in operating income: 100,000
T: Income taxes (Income tax rate t times OI ) = 40% times $100,000: 40,000
NI: Increase in net income: 60,000
Increase in cash flow from operations, net of income taxes;
Method 1: C - T = $220,000 - $40,000 = $180,000; or
Method 2: NI + D = $60,000 + $120,000 = $180,000

PANEL B: Item-by-Item Method Effect of cash operating flows

C: Operating cash inflows from investment in bus: $220,000
t times C: Deduct income tax cash outflow at 40%: 88,000
C times (1 - t): After-tax cash flow from operations: $132,000 (excluding the depreciation effect)
Effect of depreciation D Additional depreciation deduction: $120,000
t times D: Income tax cash savings from additional depreciation deduction at 40% times $120,000: 48,000
C times (1 - t ) + t times D: Cash flow from operations, net of income taxes: $180,000.

Panel A shows, using two methods based on the income statement, that the year 1 cash flow from operations, net of income taxes, equals $180,000. The first method focuses on cash items only, the $220,000 operating cash inflows minus income taxes of $40,000. The second method starts with the $60,000 increase in net income (calculated after subtracting the $120,000 additional depreciation deductions for income tax purposes) and adds back the $120,000 because depreciation is an operating cost that reduces net income but is a noncash item itself.

Panel B of Exhibit 22-5 describes a third method frequently used to compute the cash flow from operations, net of income taxes. The easiest way to interpret the third method is to think of the government as a 40% (equal to the tax rate) partner in Vector. Each time Vector obtains operating cash inflows, C, its income is higher by C, so it will pay 40% of the operating cash inflows (0.40C) in taxes. This results in additional after-tax cash operating flows of $inline style begin inline style C minus 0.40 C end style$ , which in this example is $$ 220,000 - (0.40 \times $ 220,000) = $ 132,000$ , or $$ 220,000 \times (1 - 0.40) = $ 132,000$ .

To achieve the higher operating cash inflows, C, Vector incurs higher depreciation charges, D, from investing in the new bus. Depreciation costs do not directly affect cash flows because depreciation is a noncash cost, but a higher depreciation cost lowers Vector’s taxable income by D, saving income tax cash outflows of 0.40D, which in this example is $0.40 \times $ 120,000 = $ 48,000$ .

Letting $t = tax$ rate, cash flow from operations, net of income taxes, in this example equals the operating cash inflows, C, minus the tax payments on these inflows, $t \times C$ , plus the tax savings on depreciation deductions, $t \times D$ : $$ 220,000 - (0.40 \times $ 220,000) +$ $(0.40 \times $ 120,000) = $ 220,000 - $ 88,000 + $ 48,000 = $ 180,000$ .

By the same logic, each time Vector has a gain on the sale of assets, G, it will show tax outflows, $t \times G$ ; and each time Vector has a loss on the sale of assets, L, it will show tax benefits or savings of $t \times L$ .