# 8.3: Net Present Value

- Page ID
- 881

Skills to Develop

- Evaluate investments using the net present value (NPV) approach.

*Question*: Now that we have the tools to calculate the present value of future cash flows, we can use this information to make decisions about long-term investment opportunities. How does this information help companies to evaluate long-term investments?

**Answer:**-
The

**net present value (NPV)**method of evaluating investments adds the present value of all cash inflows and subtracts the present value of all cash outflows. The term^{4}*discounted cash flows*is also used to describe the NPV method. In the previous section, we described how to find the present value of a cash flow. The term net in*net present value*means to combine the present value of all cash flows related to an investment (both positive and negative).Recall the problem facing Jackson’s Quality Copies at the beginning of the chapter. The company’s president and owner, Julie Jackson, would like to purchase a new copy machine. Julie feels the investment is worthwhile because the cash inflows over the copier’s life total $82,000, and the cash outflows total $57,000, resulting in net cash inflows of $25,000 (= $82,000 – $57,000). However, this approach ignores the timing of the cash flows. We know from the previous section that the further into the future the cash flows occur, the lower the value in today’s dollars.

*Question*: How do managers adjust for the timing differences related to future cash flows?

**Answer:**-
Most managers use the NPV approach. This approach requires three steps to evaluate an investment:

### Step 1. Identify the amount and timing of the cash flows required over the life of the investment.

### Step 2. Establish an appropriate interest rate to be used for evaluating the investment, typically called the required rate of return

^{5}.(This rate is also called the

*discount rate*or*hurdle rate*.)### Step 3. Calculate and evaluate the NPV of the investment.

Let’s use Jackson’s Quality Copies as an example to see how this process works.

### Step 1. Identify the amount and timing of the cash flows required over the life of the investment.

*Question*: What are the cash flows associated with the copy machine that Jackson’s Quality Copies would like to buy?

**Answer:**-
Jackson’s Quality Copies will pay $50,000 for the new copier, which is expected to last 7 years. Annual maintenance costs will total $1,000 a year, labor cost savings will total $11,000 a year, and the company will sell the copier for $5,000 at the end of 7 years. Figure 8.1 summarizes the cash flows related to this investment. Amounts in parentheses are cash outflows. All other amounts are cash inflows.

**Figure 8.1**- Cash Flows for Copy Machine Investment by Jackson’s Quality Copies

*Question*: How do managers establish the interest rate to be used for evaluating an investment?

**Answer:**-
Although managers often estimate the interest rate, this estimate is typically based on the organization’s

*cost of capital*. The**cost of capital**is the weighted average costs associated with debt and equity used to fund long-term investments. The cost of debt is simply the interest rate associated with the debt (e.g., interest for bank loans or bonds issued). The cost of equity is more difficult to determine and represents the return required by owners of the organization. The weighted average of these two sources of capital represents the cost of capital (finance textbooks address the complexities of this calculation in more detail).^{6}The general rule is the higher the risk of the investment, the higher the required rate of return (assume

*required rate of return*is synonymous with*interest rate*for the purpose of calculating the NPV). A firm evaluating a long-term investment with risk similar to the firm’s average risk will typically use the cost of capital. However, if a long-term investment carries higher than average risk for the firm, the firm will use a required rate of return higher than the cost of capital.The accountant at Jackson’s Quality Copies, Mike Haley, has established the cost of capital for the firm at 10 percent. Since the proposed purchase of a copy machine is of average risk to the company, Mike will use 10 percent as the required rate of return.

### Step 3. Calculate and evaluate the NPV of the investment.

*Question*: How do managers calculate the NPV of an investment?

**Answer:**-
Figure 8.2 shows the NPV calculation for Jackson’s Quality Copies. Examine this table carefully. The cash flows come from Figure 8.1. The present value factors come from Figure 8.9 in the appendix (r = 10 percent; n = year). The bottom row, labeled present value is calculated by multiplying the total cash in (out) × present value factor, and it represents total cash flows for each time period in today’s dollars. The bottom right of Figure 8.2 shows the NPV for the investment, which is the sum of the bottom row labeled present value.

**Figure 8.2**- NPV Calculation for Copy Machine Investment by Jackson’s Quality Copies*The NPV is $1,250. Because NPV is > 0, accept the investment. (The investment provides a return greater than 10 percent.)*

## The NPV Rule

*Question*: Once the NPV is calculated, how do managers use this information to evaluate a long-term investment?

**Answer:**-
Managers apply the following rule to decide whether to proceed with the investment:

NPV Rule: If the NPV is greater than or equal to zero, accept the investment; otherwise, reject the investment.

As summarized in Figure 8.3, if the NPV is greater than zero, the rate of return from the investment is higher than the required rate of return. If the NPV is zero, the rate of return from the investment equals the required rate of return. If the NPV is less than zero, the rate of return from the investment is less than the required rate of return. Since the NPV is greater than zero for Jackson’s Quality Copies, the investment is generating a return greater than the company’s required rate of return of 10 percent.

**Figure 8.3**- The NPV RuleNote that the present value calculations in Figure 8.3 assume that the cash flows for years 1 through 7 occur at the end of each year. In reality, these cash flows occur throughout each year. The impact of this assumption on the NPV calculation is typically negligible.

Business in Action 8.2

### Cost of Capital by Industry

Cost of capital can be estimated for a single company or for entire industries. **New York University’s Stern School of Business** maintains cost of capital figures by industry. Almost 7,000 firms were included in accumulating this information. The following sampling of industries compares the cost of capital across industries. Notice that high-risk industries (e.g., computer, e-commerce, Internet, and semiconductor) have relatively high costs of capital.

Air transportation | 11.48 percent |

Auto and truck | 11.04 percent |

Auto parts | 9.56 percent |

Beverage (soft drinks) | 8.16 percent |

Computer | 14.49 percent |

E-commerce | 15.65 percent |

Grocery | 9.79 percent |

Internet | 15.98 percent |

Retail store | 9.30 percent |

Semiconductor | 19.03 percent |

Source: New York University’s Stern Business School, “Home Page,” http://pages.stern.nyu.edu.

## Annuity Tables

*Question*: Notice in Figure 8.1 that the rows labeled maintenance cost and labor savings have identical cash flows from one year to the next. Identical cash flows that occur in regular intervals, such as these at Jackson’s Quality Copies, are called an **annuity ^{7}**. How can we use annuities in an alternate format to calculate the NPV?

**Answer:**-
In Figure 8.4, we demonstrate an alternative approach to calculating the NPV.

**Figure 8.4**- Alternative NPV Calculation for Jackson’s Quality Copies**Because this is not an annuity, use Figure 8.9 in the appendix.****Because this is an annuity, use Figure 8.10 in the appendix. The number of years (n) equals seven since identical cash flows occur each year for seven years.**Note: the NPV of $1,250 is the same as the NPV in Figure 8.2.*The

*purchase price*and*salvage value*rows in Figure 8.4 represent one-time cash flows, and thus we use Figure 8.9 in the appendix to find the present value factor for these items (these are not annuities). The*annual maintenance costs*and*annual labor savings*rows represent cash flows that occur each year for seven years (these are annuities). We use Figure 8.10 in the appendix to find the present value factor for these items (note that the number of years, n, equals seven since the cash flows occur each year for seven years). Simply multiply the cash flow shown in column (A) by the present value factor shown in column (B) to find the present value for each line item. Then sum the present value column to find the NPV. This alternative approach results in the same NPV shown in Figure 8.2.

Business in Action 8.3

### Winning the Lottery

*© Thinkstock*

Like many other states, California pays out lottery winnings in installments over several years. For example, a $1,000,000 lottery winner in California will receive $50,000 each year for 20 years.

Does this mean that the State of California must have $1,000,000 on the day the winner claims the prize? No. In fact, California has approximately $550,000 in cash to pay $1,000,000 over 20 years. This $550,000 in cash represents the present value of a $50,000 annuity lasting 20 years, and the state invests it so that it can provide $1,000,000 to the winner over 20 years.

Source: California State Lottery, “California State Lottery Home Page,” http://www.calottery.com.

KEY TAKEAWAY

Present value calculations tell us the value of cash flows in today’s dollars. The NPV method adds the present value of all cash inflows and subtracts the present value of all cash outflows related to a long-term investment. If the NPV is greater than or equal to zero, accept the investment; otherwise, reject the investment.

REVIEW PROBLEM 8.2

The management of Chip Manufacturing, Inc., would like to purchase a specialized production machine for $700,000. The machine is expected to have a life of 4 years, and a salvage value of $100,000. Annual maintenance costs will total $30,000. Annual labor and material savings are predicted to be $250,000. The company’s required rate of return is 15 percent.

- Ignoring the time value of money, calculate the net cash inflow or outflow resulting from this investment opportunity.
- Find the NPV of this investment using the format presented in Figure 8.2.
- Find the NPV of this investment using the format presented in Figure 8.4.
- Should Chip Manufacturing, Inc., purchase the specialized production machine? Explain.

**Answer:**-
- The net cash inflow, ignoring the time value of money, is $280,000, calculated as follows:

- The NPV is $(14,720), calculated as follows:

- The alternative format used for calculating the NPV is shown as follows. Note that the NPV here is identical to the NPV calculated previously in part 2.

*Because this is not an annuity, use Figure 8.9 in the appendix.

**Because this is an annuity, use Figure 8.10 in the appendix. The number of years (n) equals four since identical cash flows occur each year for four years. - Because the NPV is less than 0, the return generated by this investment is less than the company’s required rate of return of 15 percent. Thus Chip Manufacturing, Inc., should not purchase the specialized production machine.

- The net cash inflow, ignoring the time value of money, is $280,000, calculated as follows:

## Definitions

- A method used to evaluate long-term investments. It is calculated by adding the present value of all cash inflows and subtracting the present value of all cash outflows.
- The interest rate used for evaluating long-term investments; it represents the company’s minimum acceptable return (or discount rate; also called hurdle rate).
- The weighted average costs associated with debt and equity used to fund long-term investments.
- A term used to describe identical cash flows that occur in regular intervals.