Discounted Payback Period

9 Key excerpts on "Discounted Payback Period"

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  eBook - PDF

  Capital Budgeting

  Theory and Practice

  • Pamela P. Peterson, Frank J. Fabozzi(Authors)
  • 2004(Publication Date)
  • Wiley

    (Publisher)

  61 Chapter 4 Payback and Discounted Payback Period Techniques n this chapter we will discuss the payback period technique and a variant of this technique, the Discounted Payback Period. PAYBACK PERIOD The payback period for a project is the length of time it takes to get your money back. It is the period from the initial cash outflow to the time when the project’s cash inflows add up to the initial cash out- flow. The payback period is also referred to as the payoff period or the capital recovery period . If you invest $10,000 today and are promised $5,000 one year from today and $5,000 two years from today, the payback period is two years — it takes two years to get your $10,000 investment back. Suppose you are considering investments A and B in Exhibit 1, each requiring an investment of $1,000,000 today (we’re consid- ering today to be the last day of the year 2000) and promising cash flows at the end of each of the following five years. How long does it take to get your $1,000,000 investment back? The payback period for investment A is three years: By the end of 2002, the full $1 million is not paid back, but by 2003, the accumulated cash flow exceeds $1 million. Therefore, the pay- End of Year Expected Cash Flow Accumulated Cash Flow 2001 $400,000 $400,000 2002 400,000 800,000 2003 400,000 1,200,000 $1,000,000 investment is paid back 2004 400,000 1,600,000 2005 400,000 2,000,000 I 62 Payback and Discounted Payback Period Techniques back period for investment A is three years. Using a similar approach of comparing the investment outlay with the accumulated cash flow, the payback period for investment B is four years — it is not until the end of 2004 that the $1,000,000 original investment (and more) is paid back. We have assumed that the cash flows are received at the end of the year. So we always arrive at a payback period in terms of a whole number of years.

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  Fundamentals of Corporate Finance

  • Robert Parrino, David S. Kidwell, Thomas Bates(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  The major advantage of the discounted payback is that it tells management how long it takes a project to reach an NPV of zero. Thus, any capital project that meets a firm’s decision rule must also have a positive NPV. This is an improvement over the standard payback calculation, which can accept projects with negative NPVs. Regardless of the improvement, the discounted Discounted Payback Period The length of time required to recover a project’s initial cost, accounting for the time value of money. Year A B C D E 0 − €500 − €500 − €500 − €500 − €500 1 200 300 250 500 200 2 300 100 250 0 200 3 400 50 − 250 0 200 4 500 0 250 − 5 000 5 000 Payback (years) 2.0 ∞ 2.0/4.0 ∞ 1.0 / 2.5 NPV €450 − €131 − €115 − €2 924 €2 815 = C ost of capital 15% EXHIBIT 10.6 Payback Period with Various Cash Flow Patterns Each of the five capital budgeting projects shown in the exhibit calls for an initial investment of $500, but all have different cash flow patterns. The bottom part of the exhibit shows each project’s payback period, along with its net present value for comparison. THE FUNDAMENTALS OF CAPITAL BUDGETING 340 payback method is not widely used by businesses and it still ignores all cash flows after the arbitrary cut-off period, which is a major flaw. To see how the Discounted Payback Period is calculated, turn to Exhibit 10.7. The exhibit shows the net cash flows for a proposed capital project along with both the cumulative and the discounted cumulative cash flows; thus, we can compute both the ordinary and the Discounted Payback Periods for the project and then compare them. The cost of capital is 10 per cent. The first two rows show the non-discounted cash flows, and we can see by inspection that the ordinary payback period is two years. We do not need to make any additional calculations because the cumulative cash flows equals zero at precisely two years.

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  Fundamentals of Corporate Finance

  • Robert Parrino, David S. Kidwell, Thomas Bates, Stuart L. Gillan(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  10.3 The Payback Period 10-17 The major advantage of the discounted payback approach is that it tells management how long it takes a project to reach an NPV of zero. This is an improvement over the standard payback calculation, which can lead to accepting projects with negative NPVs. Despite this improvement, the discounted payback method is not widely used by businesses, and it also ignores all cash flows after the arbitrary cutoff period, which is a major flaw. To see how the Discounted Payback Period is calculated, let’s take a look at Exhibit 10.7. The exhibit shows the net cash flows for a proposed capital project along with both the cumulative and discounted cumulative cash flows; thus, we can compute both the ordinary and the Discounted Payback Periods for the project and then compare them. The cost of capital is 10 percent. The first two rows show the nondiscounted cash flows, and we can see by inspection that the ordinary payback period is two years. We do not need to make any additional calculations because the cumulative cash flows equal zero at precisely two years. Now let’s turn our atten- tion to the lower two rows, which show the project’s discounted and cumulative discounted cash flows. Note that the first year’s cash flow is $20,000 and its discounted value is $18,182 ($20,000 × (1/1.1) = $18,182). The second year’s cash flow is also $20,000, and its discounted value is $16,529 ($20,000 × (1/(1.1) 2 ) = $16,529). Now, looking at the cumulative discounted NCF row, notice that it turns positive between two and three years. This means that the dis- counted payback period is two years plus some fraction of the third year’s discounted cash flow. The exact Discounted Payback Period computed value is 2 years + $5,289/$15,026 year = 2 years + 0.35 year = 2.35 years. As expected, the Discounted Payback Period is longer than the ordinary payback period (2 years < 2.35 years), and in 2.35 years the project will reach a NPV of $0.

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  Budgeting Basics and Beyond

  • Jae K. Shim, Joel G. Siegel, Allison I. Shim(Authors)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  The payback reciprocal is 20 percent as compared with the IRR of 18 percent when the life is 15 years, and 20 percent as compared with the IRR of 19 percent when the life is 20 years. This shows that the payback reciprocal gives a reasonable approximation of the IRR if the useful life of the project is at least twice the payback period.

  Discounted Payback Period

  Before looking at discounted cash flow methods, note that there is less reliability with discounted cash flow analysis where there is future uncertainty, the environment is changing, and cash flows themselves are hard to predict.

  Take into account the time value of money by using the discounted payback method. The payback period will be longer using this method because money is worth less over time.

  How to do it: Discounted payback is computed by adding the present value of each year's cash inflows until they equal the investment.

  Example 5 Assume the same facts as in Example 3 and a cost of capital of 10 percent. Net Present Value

  The NPV method compares the present value of future cash flows expected from an investment project with the initial cash outlay for the investment. Net cash flows are the difference between forecasted cash inflow received because of the investment and the expected cash outflow of the investment. Use as a discount rate the minimum rate of return earned by the company on its money. As reported in the June 2004 issue of Management Accounting, 45 percent of manufacturers used discount rates of between 13 percent and 17 percent, and more than 20 percent used discount rates of over 19 percent.

  A company should use as the discount rate its cost of capital.

  Rule of thumb: Considering inflation and the cost of debt, the anticipated return should be about 10 to 13 percent.

  Note: The net present value method discounts all cash flows at the cost of capital, thus implicitly assuming that these cash flows can be reinvested at this rate.

  An advantage of NPV is that it considers the time value of money. A disadvantage is the subjectivity in determining expected annual cash inflows and expected period of benefit.

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  Available until 25 Jan |Learn more

  Business Economics

  • Rob Dransfield(Author)
  • 2013(Publication Date)
  • Taylor & Francis

    (Publisher)

  A commonly used investment appraisal technique is the payback method. The payback period is the time required for a project to repay the initial investment. The calculation is based on cash flows and not profits. The annual cash flows are accumulated and the payback period is reached when the cumulative cash flow reaches zero.

  The formula for payback can thus be set out in the following way:

  We can illustrate this for an investment project (Project A) that costs £45,000 and where the project is expected to yield £15,000 in the first year, £25,000 in the second year and £20,000 in the third year. The column in Table 17.1 showing cumulative cash flow shows the net cash outflow or inflow in specific years.

  Table 17.1   Illustrating payback for Project A

  We use the term Year 0 to signify the start of the project (when there is the initial cash outlay). The payback period can then be calculated from these data in the following way. We know that the payback will take place between Year 2 and Year 3. Case Study  An alternative cash flow

  Analysts have identified an alternative way of investing the £45,000 outlined above (Project B). This will yield the following cash flows: £5,000 in Year 1, £40,000 in Year 2 and £10,000 in Year 3.

  • Which of the projects should the company invest in if it is going to use the payback method? Show your working.

  The payback will be particularly helpful in comparing the time taken to pay back alternative projects. The project with the shortest payback period is the best investment proposition, as the shorter timescale reduces the risk of unforeseen circumstances.

  Key Term

  Payback method – a way of appraising investment projects in terms of the amount of time that it takes to pay back an initial cash investment in terms of cash inflows from the project.

  17.4  Discounted cash flow to find net present value

  A second technique for appraising an investment is to use discounted cash flow. The discounted cash flow approach is a way of valuing the future returns on investment by assessing the value of these returns in terms of their present value. It places emphasis on the cost of funds tied up in a project by considering the timing of cash flows.

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  Making the Compelling Business Case

  Decision-Making Techniques for Successful Business Growth

  • W. Messner(Author)
  • 2013(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  NPV is always (!) the most appropriate approach to calculating business cases; Sections 2.3 – 2.6 describe the most common alternative methods, highlight their weaknesses (and strengths, if at all), and explain why they are always (!) inferior to the NPV method when making decisions on investment propositions. Sometimes they are indeed appropriate to use, but the same decision can always (!) be reached with the much more straightforward NPV method. Chapter 5 is dedicated to the practical application of the NPV method. 2.3 PAYBACK AND DISCOUNTED PAYBACK METHOD Some corporations require the initial investment on any of their projects (i.e. the cash outflow in year zero) to be recoverable within a specified period. Statements by executives like “The costs need to be recovered within the same financial year” or “The investment needs to show a leverage within the same quarter” are telling signs of this pre-set investment parameter. Other companies tend to compare and judge investment alternatives on how rapidly they can recover the cash outflow, obviously trying to impress shareholders and other stakeholders with quick results. And again, some business managers try to get their pet projects approved by promising “immediate returns” to their superiors. Such requirements and approaches all refer to the payback period, which can be found by calculating the time it takes before the cumulative forecasted net cash flows from year one onwards equal the initial investment in year zero. In simple terms, the payback period is the time it takes to recover the initial spending on the investment. Figure 2.7 looks at three different mutually exclusive project alternatives. All three projects initially invest $470,000, but differ in their cash flows in subsequent years. The first project reaps a positive cash flow of $25,000 in the first four years and then decommissions the investment with a positive cash flow of $470,000 in the fifth year

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  Hospitality Management Accounting

  • Martin G. Jagels(Author)
  • 2006(Publication Date)
  • Wiley

    (Publisher)

  It has a use in evaluating a number of proposals so that only those that fall within a predetermined payback period will be considered for further evaluation using other investment techniques. However, both the payback period and the ARR methods still suffer from a common fault: They ignore the time value of cash flows, or the concept that money now is worth more than the same amount of money at some time in the future. This concept will be discussed in the next section, after which we will explore the use of the net present value and internal rate of return methods. DISCOUNTED CASH FLOW The concept of discounted cash flow can probably best be understood by look- ing first at an example of compound interest. Exhibit 12.3 shows, year by year, what happens to $200 invested at a 10% compound interest rate. At the end of 4 years, the investment would be worth $292.82. A C C O U N T I N G R A T E O F R E T U R N 503 504 C H A P T E R 1 2 C A P I T A L B U D G E T I N G A N D T H E I N V E S T M E N T D E C I S I O N Discounting is simply the reverse of compounding interest. In other words, at a 10% interest rate, what is $292.82 4 years from now worth to me today? The solution could be worked out manually using the following equation: P  F  Where P is the present value, F is the future amount, I is the interest rate used as a decimal, and n is the number of years ahead for the future amount. For example, using the already illustrated figures, we have: P  $292.82   $292.82   $292.82  0.683  $200 Although a calculation can be made for any amount, any interest rate, and for any number of years into the future with this formula, it is much easier to use a table of discount factors. Exhibit 12.4 illustrates such a table. If we go to the number called a fac- tor that is opposite Year 4 and under the 10% column, we will see that it is 0.6830. This factor tells us that $1.00 received at the end of Year 4 is worth only $1.00  $0.683, or $0.683 right now.

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  Net Present Value and Risk Modelling for Projects

  • Martin Hopkinson(Author)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  Chapter 3 Discount Rates, Internal Rate of Return and Payback Periods      

  As we have seen in Chapter 1 , the selection of an appropriate discount rate is an important consideration, particularly in the case of longer projects. An organisation using inappropriately high discount rates risks rejecting viable projects and favouring short term projects over superior longer term projects. Conversely, an organisation using inappropriately low discount rates risks accepting projects with weak financial business cases. In practice, the exercise of prudence makes the former mistake more common than the latter. This chapter provides an overview of the issues associated with setting discount rates. It then concludes with short accounts of three other techniques associated with discounted cash flow models: internal rate of return, payback periods and present value cost (defined later in this chapter).

  Setting Discount Rates Using the Weighted Average Cost of Capital

  In principle, proceeding with a project is a good decision provided that it has a rate of return that exceeds the opportunity cost of capital. This opportunity cost is the rate of return that investors expect from other opportunities with an equivalent level of risk. If the project does not meet or exceed this hurdle, investors should decline it. This principle is called the Rate of Return Rule. If the discount rate used for Net Present Value (NPV) modelling reflects the cost of capital, the Rate of Return and Net Present Value Rules are equivalent.

  Companies fund projects with capital that could otherwise be returned to their owners. The opportunity cost of funding projects is thus equal to the cost of capital. This justifies the most common approach used by companies to setting discount rates, which is to calculate the weighted average cost of capital (WACC) after tax as a starting point. WACC sets a discount rate at nominal rates i.e. including the effects of inflation. The weighting in its calculation reflects the balance between the company’s use of equity and debt to sustain its capital. A company’s accounting function will be able to calculate the overall market values of equity (MVe ) and debt (MVd ) and the annual rate of cost of each ke and kd

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  Managerial Accounting

  Tools for Business Decision Making

  • Jerry J. Weygandt, Paul D. Kimmel, Donald E. Kieso(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  Discount rate The interest rate used in discounting the future net cash flows to determine present value. Internal rate of return (IRR) The interest rate that will cause the present value of the proposed capital expen-diture to equal the present value of the expected net annual cash flows. Internal rate of return (IRR) method A method used in capital budgeting that results in finding the interest yield of the potential investment. Net present value (NPV) The difference that results when the original capital outlay is subtracted from the discounted net cash flows. Net present value (NPV) method A method used in capital budgeting in which net cash flows are dis-counted to their present value and then compared to the capital outlay required by the investment. Post-audit A thorough evaluation of how well a project’s actual performance matches the original projections. Profitability index A method of comparing alternative projects that takes into account both the size of the investment and its discounted net cash flows. It is com-puted by dividing the present value of net cash flows by the initial investment. Required rate of return The rate of return manage-ment expects on investments, sometimes called the dis-count rate or cost of capital. GLOSSARY REVIEW 414 12 Planning for Capital Investments 1. BTMS Inc. wants to purchase a new machine for $30,000, excluding $1,500 of installa-tion costs. The old machine was bought five years ago and had an expected economic life of 10 years without salvage value. This old machine now has a book value of $2,000, and BTMS Inc. expects to sell it for that amount. The new machine would decrease operating costs by $8,000 each year of its economic life. The straight-line depreciation method would be used for the new machine, for a five-year period with no salvage value. Instructions (a) Determine the cash payback period. (b) Determine the approximate internal rate of return.

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