## Boundless: Finance: "Chapter 11, Section 2: The Payback Method"

### Defining the Payback Method

The payback method is a method of evaluating a project by measuring the time it will take to recover the initial investment.

#### LEARNING OBJECTIVE

• Define the payback method

#### KEY POINTS

• The payback period is the number of months or years it takes to return the initial investment.
• To calculate a more exact payback period: payback period = amount to be invested / estimated annual net cash flow.
• The payback method also ignores the cash flows beyond the payback period; thus, it ignores the long-term profitability of a project.

#### TERMS

• Opportunity cost

The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity); the most valuable forgone alternative.

• time value of money

The value of money, figuring in a given amount of interest, earned over a given amount of time.

• cost of capital

the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

#### EXAMPLE

• A $1000 investment which returned$500 per year would have a two year payback period.

#### Defining the Payback Method

In capital budgeting, the payback period refers to the period of time required for the return on an investment to "repay" the sum of the original investment.

As a tool of analysis, the payback method is often used because it is easy to apply and understand for most individuals, regardless of academic training or field of endeavor. When used carefully to compare similar investments, it can be quite useful. As a stand-alone tool to compare an investment, the payback method has no explicit criteria for decision-making except, perhaps, that the payback period should be less than infinity.

The payback method is considered a method of analysis with serious limitations and qualifications for its use, because it does not account for the time value of money, risk,financing or other important considerations, such as opportunity cost. While the time value of money can be rectified by applying a weighted average cost of capital discount, it is generally agreed that this tool for investment decisions should not be used in isolation. Alternative measures of "return" preferred by economists are net present value and internal rate of return. An implicit assumption in the use of the payback method is that returns to the investment continue after the payback period. The payback method does not specify any required comparison to other investments or even to not making an investment .

Capital Investment in Plant and Property

The payback method is a simple way to evaluate the number of years or months it takes to return the

To calculate a more exact payback period: Payback Period = Amount to be initially invested / Estimated Annual Net Cash Inflow.initial investment.

The payback period is usually expressed in years. Start by calculating net cash flow for each year: net cash flow year one = cash inflow year one - cash outflow year one. The cumulative cash flow = (net cash flow year one + net cash flow year two + net cash flow year three). Accumulate by year until cumulative cash flow is a positive number, which will be the payback year.

### Calculating the Payback Period

#### LEARNING OBJECTIVE

• Calculate an investment's payback period

#### KEY POINTS

• Payback period is usually expressed in years. Start by calculating Net Cash Flow for each year, then accumulate by year until Cumulative Cash Flow is a positive number: that year is the payback year.
• Some businesses modified this method by adding the time value of money to get the discounted payback period. They discount the cash inflows of the project by the cost of capital, and then follow usual steps of calculating the payback period.
• Additional complexity arises when the cash flow changes sign several times (i.e., it contains outflows in the midst or at the end of the project lifetime). The modified payback period algorithm may be applied.

#### TERMS

• payback period

the amount of time required for the return on an investment to return the sum of the original investment

• cumulative

having priority rights to receive a dividend that accrue until paid

• discounted payback period

The discounted payback period is the amount of time that it takes to cover the cost of a project, by adding positive discounted cash flow coming from the profits of the project.

FULL TEXT

Payback period in capital budgeting refers to the period of time required for the returnon an investment to "repay" the sum of the original investment.

Payback period is usually expressed in years. Start by calculating Net Cash Flow for each year: Net Cash Flow Year 1 = Cash Inflow Year 1 - Cash Outflow Year 1. Then Cumulative Cash Flow = (Net Cash Flow Year 1 + Net Cash Flow Year 2 + Net Cash Flow Year 3 ... etc.) Accumulate by year until Cumulative Cash Flow is a positive number: that year is the payback year.

To calculate a more exact payback period:

Payback Period = Amount to be initially invested / Estimated Annual Net Cash Inflow.

Payback period method does not take into account the time value of money. Some businesses modified this method by adding the time value of money to get the discounted payback period. They discount the cash inflows of the project by a chosen discount rate (cost of capital), and then follow usual steps of calculating the payback period.

Discount rate

Discount rate set by Central Bank of Russia in 1992-2009.

Additional complexity arises when the cash flow changes sign several times (i.e., it contains outflows in the midst or at the end of the project lifetime). The modified payback period algorithm may be applied then. First, the sum of all of the cash outflows is calculated. Then the cumulative positive cash flows are determined for each period. The modified payback period is calculated as the moment in which the cumulative positive cash flow exceeds the total cash outflow.

Let's take a look at one example. Year 0: -1000, year 1: 4000, year 2: -5000, year 3: 6000, year 4: -6000, year 5: 7000. The sum of all cash outflows = 1000 + 5000 + 6000 = 12000.

The modified payback period is in year 5, since the cumulative positive cash flows (17000) exceeds the total cash outflows (12000) in year 5. To be more detailed, the payback period would be: 4 + 2/7 = 4.29 year.

### Discounted Payback

Discounted payback period is the amount of time to cover the cost, by adding positive discounted cash flow coming from the profits of the project.

#### LEARNING OBJECTIVE

• Calculate an investment's discounted payback period

#### KEY POINTS

• The payback period is considered a method of analysis with serious limitations and qualifications for its use, because it does not account for the time value of money.
• The discounted payback period takes the time value of money into consideration.
• Whilst the time value of money can be rectified by applying a weighted average cost of capital discount, it is generally agreed that this tool for investment decisions should not be used in isolation.

#### TERM

• Weighted average cost of capital

The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is the minimum return that a company must earn on an existing asset base to satisfy its creditors, owners, and other providers of capital, or they will invest elsewhere.

FULL TEXT

Payback period in capital budgeting refers to the period of time required for the returnon an investment to "repay" the sum of the original investment. The payback period is considered a method of analysis with serious limitations and qualifications for its use, because it does not account for the time value of money, risk, financing, or other important considerations, such as the opportunity cost.

Compared to payback period, the discounted payback period takes the time value of money into consideration. It is the amount of time that it takes to cover the cost of a project, by adding positive discounted cash flow coming from the profits of the project.

Discount rates

Bundesbank discount interest rates from 1948 to 1998. The vertical scale shows the interest rate in percent and the horizontal scale shows years.

That is, we want Net Present Value greater than 0. The income of the project will be discounted to assess the loss in value due to time (inflation or opportunity cost) to find how long it would take to recover the initially money invested.

Whilst the time value of money can be rectified by applying a weighted average cost of capital discount, it is generally agreed that this tool for investment decisions should not be used in isolation. An implicit assumption in the use of payback period is that returns to the investment continue after the payback period. Payback period does not specify any required comparison to other investments or even to not making an investment.

Let take a look at one example. In the following situation, the cash flows are as presented.

Year 0: -2000, year 1: 1000, year 2: 1000, year 3: 2000.

Assuming the discount rate is 10%, we would apply the following formula to each cash flow. Discounted Cash Flow at 10%: Year 0: -2000, year 1: 909, year 2: 827, year 3: 1503.

The next step is to compute the cumulative discounted cash flow, by summing the discounted cash flow for each year. Accumulated discounted cash flows: Year 0: -2000, year 1: -1091, year 2: -264, year 3: 1239.

We see that between years 2 and 3 we will recover our initial investment. To calculate specifically when we could see how long it took to recover the 264 remaining by end of year 2 as followed: 264/1503 = 0.1756 years. Thus, it will take a total of 2.1756 years to recover the initial investment.

Payback period as a tool of analysis is easy to apply and easy to understand, yet effective in measuring investment risk.

#### LEARNING OBJECTIVE

• Describe the advantages of using the payback method

#### KEY POINTS

• Payback period, as a tool of analysis, is often used because it is easy to apply and easy to understand for most individuals, regardless of academic training or field of endeavor.
• The payback period is an effective measure of investment risk. It is widely used when liquidity is an important criteria to choose a project.
• Payback period method is suitable for projects of small investments. It not worth spending much time and effort in sophisticated economic analysis in such projects.

#### TERMS

• time value of money

The value of money, figuring in a given amount of interest, earned over a given amount of time.

• cost of capital

the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

• Opportunity cost

The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity); the most valuable forgone alternative.

FULL TEXT

Payback period in capital budgeting refers to the period of time required for the returnon an investment to "repay" the sum of the original investment.

Payback period, as a tool of analysis, is often used because it is easy to apply and easy to understand for most individuals, regardless of academic training or field of endeavor. When used carefully or to compare similar investments, it can be quite useful. All else being equal, shorter payback periods are preferable to longer payback periods. As a stand-alone tool to compare an investment to "doing nothing," payback period has no explicit criteria for decision-making (except, perhaps, that the payback period should be less than infinity).

The term is also widely used in other types of investment areas, often with respect to energy efficiency technologies, maintenance, upgrades, or other changes. For example, a compact fluorescent light bulb may be described as having a payback period of a certain number of years or operating hours, assuming certain costs. Here, the return to the investment consists of reduced operating costs. Although primarily a financial term, the concept of a payback period is occasionally extended to other uses, such as energy payback period (the period of time over which the energy savings of a project equal the amount of energy expended since project inception). These other terms may not be standardized or widely used.

The payback period is an effective measure of investment risk. The project with a shortest payback period has less risk than with the project with longer payback period. The payback period is often used when liquidity is an important criteria to choose a project .

Monthly liquidity of an organic vegetable business

Cash demand is high from April to August. The business is more likely to use payback period to choose a project.

Payback period method is suitable for projects of small investments. It not worth spending much time and effort on sophisticated economic analysis in such projects.

Capital Investment in Plant and Property

The payback method is a simple way to evaluate the number of years or months it takes to return the initial investment.

### Disadvantages of the Payback Method

Payback period analysis ignores the time value of money and the value of cash flows in future periods.

#### LEARNING OBJECTIVE

• Explain the disadvantages of the Payback Method

#### KEY POINTS

• Payback ignores the time value of money.
• Payback ignores cash flows beyond the payback period, thereby ignoring the "profitability" of a project.
• To calculate a more exact payback period: Payback Period = Amount to be Invested/Estimated Annual Net Cash Flow.

#### TERMS

• return

Gain or loss from an investment.

• Opportunity cost

The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity); the most valuable forgone alternative.

• cost of capital

the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

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#### Disadvantages of the Payback Method

The payback period is considered a method of analysis with serious limitations and qualifications for its use, because it does not account for the time value of money, risk,financing, or other important considerations, such as the opportunity cost. While the time value of money can be rectified by applying a weighted average cost of capitaldiscount, it is generally agreed that this tool for investment decisions should not be used in isolation. Alternative measures of "return" preferred by economists are netpresent value and internal rate of return. An implicit assumption in the use of payback period is that returns to the investment continue after the payback period. Payback period does not specify any required comparison to other investments or even to not making an investment.

Zhuhai sea front development

Payback is the amount of time it takes to return an initial investment; however, it does not account for the time value of money, risk, financing, or other important considerations, such as the opportunity cost.

Payback ignores the time value of money. For example, two projects are viewed as equally attractive if they have the same payback regardless of when the payback occurs. If both project require an initial investment of \$300,000, but Project 1 has a payback of one year and Project two of three years, the projects are viewed equally, although Project 1 is more valuable because additional interest could be earned on the funds in year two and three.

Payback also ignores the cash flows beyond the payback period, thereby ignoring the profitability of the project. Thus, one project may be more valuable than another based on future cash flows, but the payback method does not capture this.

Additional complexity arises when the cash flow changes sign several times (i.e., it contains outflows in the midst or at the end of the project lifetime). The modified payback period algorithm may be applied then. First, the sum of all of the cash outflows is calculated. Then the cumulative positive cash flows are determined for each period. The modified payback period is calculated as the moment in which the cumulative positive cash flow exceeds the total cash outflow.