Investments with longer payback periods are more desirable

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Chapter 11

Capital Budgeting

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What is Capital Budgeting

The Goals of Capital Budgeting

Accounting Flows and Cash Flows

Ranking Investment Proposals

Reinvestment Assumptions

Long-Term vs. Short-Term Financing

Section 1

Introduction to Capital Budgeting

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What is Capital Budgeting Capital budgeting is the planning process used to determine which of an organization's long term investments are worth pursuing.

KEY POINTS

• Capital budgeting, which is also called investment appraisal, is the planning process used to determine whether an organization's long term investments, major capital, or expenditures are worth pursuing.

• Major methods for capital budgeting include Net present value, Internal rate of return, Payback period, Profitability index, Equivalent annuity and Real options analysis.

• The IRR method will result in the same decision as the NPV method for non-mutually exclusive projects in an unconstrained environment; Nevertheless, for mutually exclusive projects, the decision rule of taking the project with the highest IRR may select a project with a lower NPV.

Capital Budgeting

Capital budgeting, which is also called "investment appraisal," is the planning process used to determine which of an organization's long term investments such as new machinery, replacement machinery,

new plants, new products, and research development projects are worth pursuing. It is to budget for major capital investments or expenditures (Figure 11.1).

Major Methods

Many formal methods are used in capital budgeting, including the techniques as followed:

• Net present value

• Internal rate of return

• Payback period

• Profitability index

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Investment in real estate needs capital budgeting in advance.

Figure 11.1 Capital Budgeting

• Equivalent annuity

• Real options analysis

Net Present Value

Net present value (NPV) is used to estimate each potential project's value by using a discounted cash flow (DCF) valuation. This valuation requires estimating the size and timing of all the incremental cash flows from the project. The NPV is greatly affected by the discount rate, so selecting the proper rate– sometimes called the hurdle rate–is critical to making the right decision.

This should reflect the riskiness of the investment, typically measured by the volatility of cash flows, and must take into account the financing mix. Managers may use models, such as the CAPM or the APT, to estimate a discount rate appropriate for each particular project, and use the weighted average cost of capital(WACC) to reflect the financing mix selected. A common practice in choosing a discount rate for a project is to apply a WACC that applies to the entire firm, but a higher discount rate may be more appropriate when a project's risk is higher than the risk of the firm as a whole.

Internal Rate of Return

The internal rate of return (IRR) is defined as the discount rate that gives a net present value (NPV) of zero. It is a commonly used measure of investment efficiency.

The IRR method will result in the same decision as the NPV method for non-mutually exclusive projects in an unconstrained environment, in the usual cases where a negative cash flow occurs at the start of the project, followed by all positive cash flows. Nevertheless, for mutually exclusive projects, the decision rule of taking the project with the highest IRR, which is often used, may select a project with a lower NPV.

One shortcoming of the IRR method is that it is commonly misunderstood to convey the actual annual profitability of an investment. Accordingly, a measure called "Modified Internal Rate of Return (MIRR)" is often used.

Payback Period

Payback period in capital budgeting refers to the period of time required for the return on an investment to "repay" the sum of the original investment. Payback period intuitively measures how long something takes to "pay for itself." All else being equal, shorter payback periods are preferable to longer payback periods.

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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.

Profitability Index

Profitability index (PI), also known as profit investment ratio (PIR) and value investment ratio (VIR), is the ratio of payoff to investment of a proposed project. It is a useful tool for ranking projects, because it allows you to quantify the amount of value created per unit of investment.

Equivalent Annuity

The equivalent annuity method expresses the NPV as an annualized cash flow by dividing it by the present value of the annuity factor. It is often used when comparing investment projects of unequal lifespans. For example, if project A has an expected lifetime of seven years, and project B has an expected lifetime of 11 years, it would be improper to simply compare the net present values (NPVs) of the two projects, unless the projects could not be repeated.

Real Options Analysis

The discounted cash flow methods essentially value projects as if they were risky bonds, with the promised cash flows known. But

managers will have many choices of how to increase future cash inflows or to decrease future cash outflows. In other words, managers get to manage the projects, not simply accept or reject them. Real options analysis try to value the choices–the option value–that the managers will have in the future and adds these values to the NPV.

These methods use the incremental cash flows from each potential investment or project. Techniques based on accounting earnings and accounting rules are sometimes used. Simplified and hybrid methods are used as well, such as payback period and discounted payback period.

EXAMPLE

Payback period: For example, a $1000 investment which returned $500 per year would have a two year payback period. The time value of money is not taken into account.

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The Goals of Capital Budgeting The main goals of capital budgeting are not only to control resources and provide visibility, but also to rank projects and raise funds.

KEY POINTS

• Basically, the purpose of budgeting is to provide a forecast of revenues and expenditures and construct a model of how business might perform financially.

• Capital Budgeting is most involved in ranking projects and raising funds when long-term investment is taken into account.

• Capital budgeting is an important task as large sums of money are involved and a long-term investment, once made, can not be reversed without significant loss of invested capital.

The purpose of budgeting is to provide a forecast of revenues and expenditures. That is, to construct a model of how a business might perform financially if certain strategies, events, and plans are carried out. It enables the actual financial operation of the business

to be measured against the forecast, and it establishes the cost constraint for a project, program, or operation.

Budgeting helps to aid the planning of actual operations by forcing managers to consider how the conditions might change, and what steps should be taken in such an event. It encourages managers to consider problems before they arise. It also helps co-ordinate the activities of the organization by compelling managers to examine relationships between their own operation and those of other departments.

Other essential functions of a budget include:

• To control resources

• To communicate plans to various responsibility center managers

• To motivate managers to strive to achieve budget goals

• To evaluate the performance of managers

• To provide visibility into the company's performance

Capital Budgeting, as a part of budgeting, more specifically focuses on long-term investment, major capital and capital expenditures. The main goals of capital budgeting involve:

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Ranking Projects

The real value of capital budgeting is to rank projects. Most organizations have many projects that could potentially be financially rewarding. Once it has been determined that a particular project has exceeded its hurdle, then it should be ranked against peer projects (e.g. - highest Profitability index to lowest Profitability index). The highest ranking projects should be implemented until the budgeted capital has been expended (Figure 11.2).

Raising funds

When a corporation determines its capital budget, it must acquire funds. Three methods are generally available to publicly-traded corporations: corporate bonds, preferred stock, and common stock. The ideal mix of those funding sources is determined by the financial managers of the firm and is related to the amount of financial risk that the corporation is willing to undertake.

Corporate bonds entail the lowest financial risk and, therefore, generally have the lowest interest rate. Preferred stock have no financial risk but dividends, including all in arrears, must be paid to the preferred stockholders before any cash disbursements can be made to common stockholders; they generally have interest rates higher than those of corporate bonds. Finally, common stocks entail no financial risk but are the most expensive way to finance capital projects.The Internal Rate of Return is very important.

Capital budgeting is an important task as large sums of money are involved, which influences the profitability of the firm. Plus, a long- term investment, once made, cannot be reversed without significant loss of invested capital. The implication of long-term investment decisions are more extensive than those of short-run decisions because of the time factor involved; capital budgeting decisions are subject to a higher degree of risk and uncertainty than are short-run decisions.

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The main goal of capital budgeting is to rank projects.

Figure 11.2 Goals of capital budgeting

Accounting Flows and Cash Flows Accounting flows are used when transactions occur and documents are produced; Cash flow is the movement of money into or out of a business.

KEY POINTS

• Accounting flows involve Journal entries, Ledger accounts and Balancing to present a business's financial position in an Income statement, a Balance sheet and a Cash flow statement.

• Cash flow is the movement of money into or out of a business, project or financial product.

• Statement of cash flows includes three parts: Operational cash flows, Investment cash flows and Financing cash flows.

Accounting Flows

When a transaction occurs, a document is produced. Most of the time these documents are external to the business; however, they can also be internal documents, such as inter-office sales. These are referred to as source documents (Figure 11.3).

Basic accounting flows are as followed:

1. Identify the transaction through an original source document (such as an invoice, receipt, cancelled check, time card, deposit slip, purchase order) which provides the date, amount, description (account or business purpose), name and address of the other party.

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The basic cycle from open period to close period.

Figure 11.3 Accounting cycle

2. Analyze the transaction – determine which accounts are affected, how (increase or decrease), and by how much.

3. Make journal entries – record the transaction in the journal as both a debit and a credit. Journals are kept in chronological order and may include a sales journal, a purchases journal, a cash receipts journal, a cash payments journal and the general journal.

4. Post to ledger – transfer the journal entries to ledger accounts.

5. Trial Balance – a calculation to verify that the sum of the debits equals the sum of the credits. If they don’t balance, you have to fix the unbalanced trial balance before you go on to the rest of the accounting cycle.

6. Adjusting entries – prepare and post accrued and deferred items to journals and ledger T-accounts.

7. Adjusted trial balance – make sure the debits still equal the credits after making the period end adjustments.

8. Financial Statements – prepare income statement, balance sheet, statement of retained earnings and statement of cash flows.

9. Closing entries – prepare and post closing entries to transfer the balances from temporary accounts.

Cash flows

Cash flow is the movement of money into or out of a business, project or financial product. It is usually measured during a specified, finite period of time. Measurement of cash flow can be used for calculating other parameters that give information on a company's value and situation. Cash flow can be used, for example, for calculating parameters:

• To determine a project's rate of return or value. The time that cash flows into and out of projects is used as inputs in financial models such as internal rate of return and net present value.

• To determine problems with a business's liquidity. Being profitable does not necessarily mean being liquid. A company can fail because of a shortage of cash even while profitable.

• To be used as an alternative measure of a business's profits when it is believed that accrual accounting concepts do not represent economic realities.

• To evaluate the 'quality' of income generated by accrual accounting. When net income is composed of large non-cash items it is considered low quality.

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• To evaluate the risks within a financial product, e.g. matching cash requirements, evaluating default risk, re-investment requirements, etc.

Subsets of cash flow in a business's financials include:

• Operational cash flows: Cash received or expended as a result of the company's internal business activities. It includes cash earnings plus changes to working capital. Over the medium term, this must be net positive if the company is to remain solvent.

• Investment cash flows: Cash received from the sale of long-life assets, or spent on capital expenditure (investments, acquisitions and long-life assets).

• Financing cash flows: Cash received from the issue of debt and equity, or paid out as dividends, share repurchases or debt repayments.

Cash flow is a generic term used differently depending on the context. It may be defined by users for their own purposes. It can refer to actual past flows or projected future flows. It can refer to the total of all flows involved or a subset of those (Figure 11.4).

EXAMPLE

For example, a company may be notionally profitable but generating little operational cash (as may be the case for a company that barters its products rather than selling for cash). In such a case, the company may be deriving additional operating cash by issuing shares or raising additional debt finance.

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The movement of money into and out of a business, project or financial product.

Figure 11.4 Cash flow

Ranking Investment Proposals Several methods are commonly used to rank investment proposals, including NPV, IRR, PI, payback period, and ARR.

KEY POINTS

• The higher the NPV, the more attractive the investment proposal.

• The higher a project's IRR, the more desirable it is to undertake the project.

• As the value of the profitability index increases, so does the financial attractiveness of the proposed project.

• Shorter payback periods are preferable to longer payback periods.

• The higher the ARR, the more attractive the investment.

The most valuable aim of capital budgeting is to rank investment proposals. To choose the most valuable investment option, several methods are commonly used (Figure 11.5):

Net Present Value (NPV):

NPV can be described as the “difference amount” between the sums of discounted: cash inflows and cash outflows. In the case when all future cash flows are incoming, and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). The higher the NPV, the more attractive the investment proposal. NPV is a central tool in discounted cash flow (DCF) analysis and is a standard method for using the time value of money to appraise long-term projects. Used for capital budgeting and widely used throughout economics, finance, and accounting, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met (Figure 11.6).

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Choosing the best investment proposal for business

Figure 11.5 Investment Proposal

In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected. The rules of decision making are:

• When NPV > 0, the investment would add value to the firm so the project may be accepted

• When NPV < 0, the investment would subtract value from the firm so the project should be rejected

• When NPV = 0, the investment would neither gain nor lose value for the firm. We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria (e.g., strategic positioning or other factors not explicitly included in the calculation).

An NPV calculated using variable discount rates (if they are known for the duration of the investment) better reflects the situation than one calculated from a constant discount rate for the entire investment duration.

Internal Rate of Return (IRR)

The internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero.

IRR calculations are commonly used to evaluate the desirability of investments or projects. The higher a project's IRR, the more desirable it is to undertake the project. Assuming all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first.

Profitability Index (PI)

It is a useful tool for ranking projects, because it allows you to quantify the amount of value created per unit of investment. The ratio is calculated as follows:

Profitability index = PV of future cash flows / Initial investment

As the value of the profitability index increases, so does the financial attractiveness of the proposed project. Rules for selection or rejection of a project:

• If PI > 1 then accept the project

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Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore, NPV is the sum of all terms.

Figure 11.6 NPV formula

• If PI < 1 then reject the project

Payback Period

Payback period intuitively measures how long something takes to "pay for itself." All else being equal, shorter payback periods are preferable to longer payback periods. Payback period is widely used because of its ease of use despite the recognized limitations: The time value of money is not taken into account.

Accounting Rate of Return (ARR)

The ratio does not take into account the concept of time value of money. ARR calculates the return, generated from net income of the proposed capital investment. The ARR is a percentage return. Say, if ARR = 7%, then it means that the project is expected to earn seven cents out of each dollar invested. If the ARR is equal to or greater than the required rate of return, the project is acceptable. If it is less than the desired rate, it should be rejected. When comparing investments, the higher the ARR, the more attractive the investment. Basic formulae:

ARR = Average profit / Average investment

Where: Average investment = (Book value at beginning of year 1 + Book value at end of user life) / 2

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Reinvestment Assumptions NPV and PI assume reinvestment at the discount rate, while IRR assumes reinvestment at the internal rate of return.

KEY POINTS

• If trying to decide between alternative investments in order to maximize the value of the firm, the reinvestment rate would be a better choice.

• NPV and PI assume reinvestment at the discount rate.

• IRR assumes reinvestment at the internal rate of return.

Reinvestment Rate

To some extent, the selection of the discount rate is dependent on the use to which it will be put. If the intent is simply to determine whether a project will add value to the company, using the firm's weighted average cost of capital may be appropriate (Figure 11.7). If trying to decide between alternative investments in order to

maximize the value of the firm, the corporate reinvestment rate would probably be a better choice (Figure 11.8).

NPV Reinvestment Assumption

The rate used to discount future cash flows to the present value is a key variable of this process. A firm's weighted average cost of capital (after tax) is often used, but many people believe that it is appropriate to use higher discount rates to adjust for risk or other factors. A variable discount rate with higher rates applied to cash flows occurring further along the time span might be used to reflect the yield curve premium for long-term debt.

Another approach to choosing the discount rate factor is to decide the rate that the capital needed for the project could return if invested in an alternative venture. Related to this concept is to use the firm's reinvestment rate. Reinvestment rate can be defined as

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Describe how the reinvestment factors related to total return.

Figure 11.7 Reinvestment Factor

Reinvestment to expand business

Figure 11.8 Reinvestment

the rate of return for the firm's investments on average. When analyzing projects in a capital constrained environment, it may be appropriate to use the reinvestment rate, rather than the firm's weighted average cost of capital as the discount factor. It reflects opportunity cost of investment, rather than the possibly lower cost of capital.

PI Reinvestment Assumption

Profitability index assumes that the cash flow calculated does not include the investment made in the project, which means PI reinvestment at the discount rate as NPV method. A profitability index of 1 indicates break even. Any value lower than one would indicate that the project's PV is less than the initial investment. As the value of the profitability index increases, so does the financial attractiveness of the proposed project.

IRR Reinvestment Assumption

As an investment decision tool, the calculated IRR should not be used to rate mutually exclusive projects but only to decide whether a single project is worth the investment. In cases where one project has a higher initial investment than a second mutually exclusive project, the first project may have a lower IRR (expected return) but a higher NPV (increase in shareholders' wealth) and, thus, should

be accepted over the second project (assuming no capital constraints).

IRR assumes reinvestment of interim cash flows in projects with equal rates of return (the reinvestment can be the same project or a different project). Therefore, IRR overstates the annual equivalent rate of return for a project that has interim cash flows which are reinvested at a rate lower than the calculated IRR. This presents a problem, especially for high IRR projects, since there is frequently not another project available in the interim that can earn the same rate of return as the first project.

When the calculated IRR is higher than the true reinvestment rate for interim cash flows, the measure will overestimate–sometimes very significantly–the annual equivalent return from the project. This makes IRR a suitable (and popular) choice for analyzing venture capital and other private equity investments, as these strategies usually require several cash investments throughout the project, but only see one cash outflow at the end of the project (e.g., via IPO or M&A).

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MIRR is calculated as follows:

Figure 11.9 Calculation of the MIRR

When a project has multiple IRRs, it may be more convenient to compute the IRR of the project with the benefits reinvested. Accordingly, MIRR is used, which has an assumed reinvestment rate, usually equal to the project's cost of capital (Figure 11.9).

EXAMPLE

At the end of the first quarter, the investor had capital of $1,010.00, which then earned $10.10 during the second quarter. The extra dime was interest on his additional $10 investment.

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Long-Term vs. Short-Term Financing Long-term financing is generally for assets and projects and short term financing is typically for continuing operations.

KEY POINTS

• Management must match long-term financing or short-term financing mix to the assets being financed in terms of both timing and cash flow.

• Long-term financing includes equity issued, Corporate bond, Capital notes and so on.

• Short-term financing includes Commercial papers, Promissory notes, Asset-based loans, Repurchase agreements, letters of credit and so on.

Achieving the goals of corporate finance requires appropriate financing of any corporate investment. The sources of financing are, generically, capital that is self-generated by the firm and capital from external funders, obtained by issuing new debt and equity.

Management must attempt to match the long-term or short-term financing mix to the assets being financed as closely as possible, in terms of both timing and cash flows (Figure 11.10).

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Long-Term Financing

Businesses need long-term financing for acquiring new equipment, R&D, cash flow enhancement and company expansion. Major methods for long-term financing are as follows:

Equity Financing

This includes preferred stocks and common stocks and is less risky with respect to cash flow commitments. However, it does result in a dilution of share ownership, control and earnings. The cost of equity is also typically higher than the cost of debt - which is, additionally, a deductible expense - and so equity financing may result in an increased hurdle rate which may offset any reduction in cash flow risk.

Corporate Bond

A corporate bond is a bond issued by a corporation to raise money effectively so as to expand its business. The term is usually applied to longer-term debt instruments, generally with a maturity date falling at least a year after their issue date.

Some corporate bonds have an embedded call option that allows the issuer to redeem the debt before its maturity date. Other bonds, known as convertible bonds, allow investors to convert the bond into equity.

Capital Notes

Capital notes are a form of convertible security exercisable into shares. They are equity vehicles. Capital notes are similar to warrants, except that they often do not have an expiration date or an exercise price (hence, the entire consideration the company expects to receive, for its future issue of shares, is paid when the capital note is issued). Many times, capital notes are issued in connection with a debt-for-equity swap restructuring: instead of issuing the shares (that replace debt) in the present, the company gives creditors convertible securities – capital notes – so the dilution will occur later.

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To manage business often requires long-term and short-term financing.

Figure 11.10 Financing

Short-Term Financing

Short-term financing can be used over a period of up to a year to help corporations increase inventory orders, payrolls and daily supplies. Short-term financing includes the following financial instruments:

Commercial Paper

This is an unsecured promissory note with a fixed maturity of 1 to 364 days in the global money market. It is issued by large corporations to get financing to meet short-term debt obligations. It is only backed by an issuing bank or corporation's promise to pay the face amount on the maturity date specified on the note. Since it is not backed by collateral, only firms with excellent credit ratings from a recognized rating agency will be able to sell their commercial paper at a reasonable price.

Asset-backed commercial paper (ABCP) is a form of commercial paper that is collateralized by other financial assets. ABCP is typically a short-term instrument that matures between 1 and 180 days from issuance and is typically issued by a bank or other financial institution.

Promissory Note

This is a negotiable instrument, wherein one party (the maker or issuer) makes an unconditional promise in writing to pay a determinate sum of money to the other (the payee), either at a fixed or determinable future time or on demand of the payee, under specific terms.

Asset-based Loan

This type of loan, often short term, is secured by a company's assets. Real estate, accounts receivable (A/R), inventory and equipment are typical assets used to back the loan. The loan may be backed by a single category of assets or a combination of assets (for instance, a combination of A/R and equipment).

Repurchase Agreements

These are short-term loans (normally for less than two weeks and frequently for just one day) arranged by selling securities to an investor with an agreement to repurchase them at a fixed price on a fixed date.

Letter of Credit

This is a document that a financial institution or similar party issues to a seller of goods or services which provides that the issuer will

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pay the seller for goods or services the seller delivers to a third- party buyer. The issuer then seeks reimbursement from the buyer or from the buyer's bank. The document serves essentially as a guarantee to the seller that it will be paid by the issuer of the letter of credit, regardless of whether the buyer ultimately fails to pay.

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Defining the Payback Method

Calculating the Payback Period

Discounted Payback

Advantages of the Payback Method

Disadvantages of the Payback Method

Section 2

Payback Method

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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.

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.

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

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

Figure 11.11 Capital Investment in Plant and Property

comparison to other investments or even to not making an investment (Figure 11.11).

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. Then 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.

EXAMPLE

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

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

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.

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

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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 (Figure 11.12).

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.

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

Figure 11.12 Discount rate

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.

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.

Payback period in capital budgeting refers to the period of time required for the return on 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 (Figure 11.13).

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.

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

Figure 11.13 Discount rates

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.

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

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.

Payback period in capital budgeting refers to the period of time required for the return on 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

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used when liquidity is an important criteria to choose a project (Figure 11.14).

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.

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

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.

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 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

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

Figure 11.14 Capital Investment in Plant and Property

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 (Figure 11.15).

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 although 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.

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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.

Figure 11.15 Zhuhai sea front development

Defining the IRR

Calculating the IRR

Advantages of the IRR Method

Disadvantages of the IRR Method

Multiple IRRs

Modified IRR

Section 3

Internal Rate of Return

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Defining the IRR IRR is a rate of return used in capital budgeting to measure and compare the profitability of investments; the higher IRR, the more desirable the project.

KEY POINTS

• The IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment.

• The higher a project's IRR, the more desirable it is to undertake the project.

• A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital. Investment may be limited by availability of funds to the firm and/or by the firm's capacity or ability to manage numerous projects.

The internal rate of return (IRR) or economic rate of return (ERR) is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the "discounted cash flow rate of return" (DCFROR) or the rate of return (ROR). In the context of savings and loans the IRR is also called the "effective interest rate." The term "internal" refers to the fact that its

calculation does not incorporate environmental factors (e.g., the interest rate or inflation).

(Figure 11.16) The internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value (NPV as NET*1/ (1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero. In more specific terms, the IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment.