Discounted Cash Flow

Learning Objective 2 Use and evaluate the two main discounted cash flow (DCF) methods: the net present value (NPV) method and the internal rate-of-return (IRR) method

• to explicitly consider all project cash flows and the time value of money

Discounted cash flow (DCF) methods measure all expected future cash inflows and outflows of a project discounted back to the present point in time. The key feature of DCF methods is the Time value of money, which means that a dollar (or any other monetary unit) received today is worth more than a dollar received at any future time. The reason is that $1 received today can be invested at, say, 10% per year so that it grows to $1.10 at the end of 1 year. The time value of money is the opportunity cost (the return of $0.10 forgone per year) from not having the money today. In this example, $1 received 1 year from now is worth $\mathrm{\$}1÷\text{1.10}=\mathrm{\$}\text{0.9091}$ today. Similarly, $100 received 1 year from now will be weighted by 0.9091 to yield a discounted cash flow of $90.91, which is today’s value of that $100 next year. In this way, discounted cash flow methods explicitly measure cash flows in terms of the time value of money. Note that DCF focuses exclusively on cash inflows and outflows rather than on operating income as calculated under accrual accounting. The compound interest tables and formulas used in DCF analysis are in Appendix A. If you are unfamiliar with compound interest, do not proceed until you have studied Appendix A, as the tables in Appendix A will be used frequently in this chapter.

The two DCF methods we describe are the net present value (NPV) method and the internal rate-of-return (IRR) method. Both DCF methods use the required rate of return (RRR), the minimum acceptable annual rate of return on an investment. The RRR is set internally by the organization, usually by upper management, and typically represents the return that an organization could expect to receive elsewhere for an investment of comparable risk. The RRR is also called the discount rate, hurdle rate, cost of capital, or opportunity cost of capital. Let’s suppose the chief financial officer (CFO) at Vector has set the required rate of return for the firm’s investments at 8% per year.

Net Present Value Method

The net present value (NPV) method calculates the expected monetary gain or loss from a project by discounting all expected future cash inflows and outflows back to the present point in time using the required rate of return. To use the NPV method, apply the following three steps:

1. Step 1: DRAW A SKETCH OF RELEVANT CASH INFLOWS AND OUTFLOWS. The right side of Exhibit 22-2 shows arrows that depict the cash flows of the new hybrid bus. The sketch helps the decision maker visualize and organize the data in a systematic way. Note that parentheses denote relevant cash outflows throughout all of the exhibits in this chapter. Exhibit 22-2 includes the outflow for the acquisition of the new bus at the start of year 1 (also referred to as end of year 0) and the inflows over the subsequent 5 years. The NPV method specifies cash flows regardless of their source, such as operations, the purchase or sale of equipment, or an investment in or recovery of working capital. However, accrual-accounting concepts such as sales made on credit or noncash expenses are not included because the focus of the NPV method is on cash inflows and outflows.

1. Step 2: DISCOUNT THE CASH FLOWS USING THE CORRECT COMPOUND INTEREST TABLE FROM APPENDIX A AND SUM THE DISCOUNTED CASH FLOWS. In the Vector example, the cash inflows all have the same dollar value and thus constitute an annuity, which is a series of equal cash flows at equal time intervals. So, we can compute the present value of an annuity using Table 4. Alternatively, we can discount each year’s cash flow separately using Table 2. (Both tables are in Appendix A.) If we use Table 2, we find the discount factors for periods 1–5 under the 8% column. Approach 1 in Exhibit 22-2 uses the five discount factors. To obtain the present value amount, multiply each discount factor by the corresponding amount represented by the arrow on the right in Exhibit 22-2 $(-\$\text{648,900}\times \text{1.00\hspace{0.05em}\hspace{0.05em}\hspace{0.05em}}\mathrm{0};\hspace{0.17em}\$\text{180,000}\times \text{0.926}$; and so on to $\mathrm{\$}\text{180,000}\times \text{0.681}$). Because the investment in the new bus produces an annuity, we may also use Table 4. Under Approach 2, we find that the annuity factor for five periods under the 8% column is 3.993, which is the sum of the five discount factors used in Approach 1. We multiply the uniform annual cash inflow by this factor to obtain the present value of the inflows $(\$\text{718,740}= \$\text{180,000}\times \text{3.993})$. Subtracting the initial investment then yields the NPV of the project as $69,840 $(\$\text{69,840}= \$\text{718,740\hspace{0.17em}}- \$\text{648,900})$.

1. Step 3: MAKE THE PROJECT DECISION ON THE BASIS OF THE CALCULATED NPV. An NPV that is zero or positive suggests that from a financial standpoint, the company should accept the project because its expected rate of return equals or exceeds the required rate of return. If the NPV is negative, the company should reject the project because its expected rate of return is below the required rate of return.

Exhibit 22-2 calculates an NPV of $69,840 at the required rate of return of 8% per year. The project is acceptable based on financial information. The cash flows from the project are adequate to (1) recover the net initial investment in the project and (2) earn a return greater than 8% per year on the investment tied up in the project over its useful life.

Managers must also weigh nonfinancial factors such as the effect that purchasing the bus will have on Vector’s brand. The financial benefits that accrue from Vector’s brand are difficult to estimate. Nevertheless, managers must consider brand effects before reaching a final decision. Suppose, for example, that the NPV of the hybrid bus is negative. Vector’s managers might still decide to buy the bus if it maintains Vector’s technological image and reputation for environmental responsibility. These are factors that could increase Vector’s financial outcomes in the future, such as by attracting more riders or generating additional contracts from government transit agencies. For example, Unilever, the consumer goods corporation, recognized customers’ growing taste for sustainable products and acquired the sustainable cleaning products company Seventh Generation in 2016.

Pause here. Do not proceed until you understand what you see in Exhibit 22-2. Compare Approach 1 with Approach 2 in Exhibit 22-2 to see how Table 4 in Appendix A merely aggregates the present value factors of Table 2. That is, the fundamental table is Table 2. Table 4 just simplifies calculations when there is an annuity.