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Chapter 09 Capital Budgeting

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FINANCIAL MANAGEMENT PART 9

FINANCIAL MANAGEMENT PART 9


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  • 1. Capital Budgeting Chapter 9
  • 2. Introduction
    • Capital budgeting involves planning and justifying large expenditures on long-term projects
      • Projects can be classified as:
        • Replacement
        • New business ventures
  • 3. Characteristics of Business Projects
    • Project Types and Risk
      • Capital projects have increasing risk according to whether they are replacements, expansions or new ventures
    • Stand-Alone and Mutually Exclusive Projects
      • A stand-alone project has no competing alternatives
        • The project is judged on its own viability
      • Mutually exclusive projects are involved when selecting one project excludes selecting the other
  • 4. Characteristics of Business Projects
    • Project Cash Flows
      • The first and usually most difficult step in capital budgeting is reducing projects to a series of cash flows
      • Business projects involve early cash outflows and later inflows
        • The initial outlay is required to get started
    • The Cost of Capital
      • A firm’s cost of capital is the average rate it pays its investors for the use of their money
        • In general a firm can raise money from two sources: debt and equity
        • If a potential project is expected to generate a return greater than the cost of the money to finance it, it is a good investment
  • 5. Capital Budgeting Techniques
    • There are four basic techniques for determining a project’s financial viability:
      • Payback (determines how many years it takes to recover a project’s initial cost)
      • Net Present Value (determines by how much the present value of the project’s inflows exceeds the present value of its outflows)
      • Internal Rate of Return (determines the rate of return the project earns [internally])
      • Profitability Index (provides a ratio of a project’s inflows vs. outflows — in present value terms)
  • 6. Capital Budgeting Techniques—Payback
    • The payback period is the time it takes to recover early cash outflows
      • Shorter paybacks are better
    • Payback Decision Rules
      • Stand-alone projects
        • If the payback period < (>) policy maximum accept (reject)
      • Mutually Exclusive Projects
        • If Payback A < Payback B  choose Project A
    • Weaknesses of the Payback Method
      • Ignores the time value of money
      • Ignores the cash flows after the payback period
  • 7. Capital Budgeting Techniques—Payback
    • Consider the following cash flows
    Payback period occurs at 3.33 years.
    • Payback period is easily visualized by the cumulative cash flows
    $40,000 ($20,000) ($80,000) ($140,000) ($200,000) Cumulative cash flows $60,000 $60,000 $60,000 $60,000 ($200,000) Cash flow (C i ) 4 3 2 1 0 Year $60,000 $60,000 $60,000 $60,000 ($200,000) Cash flow (C i ) 4 3 2 1 0 Year
  • 8. Capital Budgeting Techniques—Payback—Example Q: Use the payback period technique to choose between mutually exclusive projects A and B. Example 800 200 C 5 800 200 C 4 350 400 C 3 400 400 C 2 400 400 C 1 ($1,200) ($1,200) C 0 Project B Project A A: Project A’s payback is 3 years as its initial outlay is fully recovered in that time. Project B doesn’t fully recover until sometime in the 4 th year. Thus, according to the payback method, Project A is better than B.
  • 9. Capital Budgeting Techniques—Payback
    • Why Use the Payback Method?
      • It’s quick and easy to apply
      • Serves as a rough screening device
    • The Present Value Payback Method
      • Involves finding the present value of the project’s cash flows then calculating the project’s payback
  • 10. Capital Budgeting Techniques—Net Present Value (NPV)
    • NPV is the sum of the present values of a project’s cash flows at the cost of capital
    • If PV inflows > PV outflows , NPV > 0
  • 11. Capital Budgeting Techniques—Net Present Value (NPV)
    • NPV and Shareholder Wealth
      • A project’s NPV is the net effect that undertaking a project is expected to have on the firm’s value
        • A project with an NPV > (<) 0 should increase (decrease) firm value
      • Since the firm desires to maximize shareholder wealth, it should select the capital spending program with the highest NPV
  • 12. Capital Budgeting Techniques—Net Present Value (NPV)
    • Decision Rules
      • Stand-alone Projects
        • NPV > 0  accept
        • NPV < 0  reject
      • Mutually Exclusive Projects
        • NPV A > NPV B  choose Project A over B
  • 13. Capital Budgeting Techniques—Net Present Value (NPV) Example Q: Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken? Example $3,000 C 3 $2,000 C 2 $1,000 C 1 ($5,000) C 0 A: The NPV is found by summing the present value of the cash flows when discounted at the firm’s cost of capital. Since Alpha’s NPV<0, it should not be undertaken.
  • 14. Techniques—Internal Rate of Return (IRR)
    • A project’s IRR is the return it generates on the investment of its cash outflows
      • For example, if a project has the following cash flows
        • The IRR is the interest rate at which the present value of the three inflows just equals the $5,000 outflow
    The “price” of receiving the inflows 3,000 2,000 1,000 -5,000 3 2 1 0
  • 15. Techniques—Internal Rate of Return (IRR)
    • Defining IRR Through the NPV Equation
      • The IRR is the interest rate that makes a project’s NPV zero
  • 16. Techniques—Internal Rate of Return (IRR)
    • Decision Rules
      • Stand-alone Projects
        • If IRR > cost of capital (or k)  accept
        • If IRR < cost of capital (or k)  reject
      • Mutually Exclusive Projects
        • IRR A > IRR B  choose Project A over Project B
  • 17. Techniques—Internal Rate of Return (IRR)
    • Calculating IRRs
      • Finding IRRs usually requires an iterative, trial-and-error technique
        • Guess at the project’s IRR
        • Calculate the project’s NPV using this interest rate
          • If NPV is zero, the guessed interest rate is the project’s IRR
          • If NPV > (<) 0, try a new, higher (lower) interest rate
  • 18. Techniques—Internal Rate of Return (IRR)—Example Q: Find the IRR for the following series of cash flows: If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of capital is 10%? Example $1,000 C 1 ($5,000) C 0 $2,000 C 2 $3,000 C 3 A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate. Since NPV<0, the project’s IRR must be < 12%.
  • 19. Techniques—Internal Rate of Return (IRR)—Example We’ll try a different, lower interest rate, say 10%. At 10%, the project’s NPV is ($184). Since the NPV is still less than zero, we need to try a still lower interest rate, say 9%. The following table lists the project’s NPV at different interest rates. Example Since NPV becomes positive somewhere between 8% and 9%, the project’s IRR must be between 8% and 9%. If the firm’s cost of capital is 8%, the project is marginal. If the firm’s cost of capital is 10%, the project is not a good idea. $130 7 $22 8 ($83) 9 ($184) 10 ($377) 12% Calculated NPV Interest Rate Guess The exact IRR can be calculated using a financial calculator. The financial calculator uses the iterative process just demonstrated; however it is capable of guessing and recalculating much more quickly.
  • 20. Techniques—Internal Rate of Return (IRR)
    • Technical Problems with IRR
      • Multiple Solutions
        • Unusual projects can have more than one IRR
          • Rarely presents practical difficulties
        • The number of positive IRRs to a project depends on the number of sign reversals to the project’s cash flows
          • Normal pattern involves only one sign change
      • The Reinvestment Assumption
        • IRR method implicitly assumes cash inflows will be reinvested at the project’s IRR
          • For projects with extremely high IRRs, this is unlikely
  • 21. NPV Profile
    • A project’s NPV profile is a graph of its NPV vs. the cost of capital
    • It crosses the horizontal axis at the IRR
  • 22. Figure 9.1: NPV Profile
  • 23. Comparing IRR and NPV
    • NPV and IRR do not always provide the same decision for a project’s acceptance
      • Occasionally give conflicting results in mutually exclusive decisions
    • If two projects’ NPV profiles cross it means below a certain cost of capital one project is acceptable over the other and above that cost of capital the other project is acceptable over the first
      • The NPV profiles have to cross in the first quadrant of the graph, where interest rates are of practical interest
    • The NPV method is the preferred decision-making criterion because the reinvestment interest rate assumption is more practical
  • 24. Figure 9.2: Projects for Which IRR and NPV Can Give Different Solutions At a cost of capital of k 1 , Project A is better than Project B, while at k 2 the opposite is true.
  • 25. NPV and IRR Solutions Using Financial Calculators
    • Modern financial calculators and spreadsheets remove the drudgery from calculating NPV and IRR
      • Especially IRR
    • The process involves inputting a project’s cash flows and then having the calculators calculate NPV and IRR
      • Note that a project’s interest rate is needed to calculate NPV
  • 26. Spreadsheets
    • NPV function in Microsoft Excel 
      • =NPV(interest rate, Cash Flow 1 :Cash Flow n ) + Cash Flow 0
        • Every cash flow within the parentheses is discounted at the interest rate
    • IRR function in Microsoft Excel 
      • =IRR(Cash Flow 0 :Cash Flow n )
  • 27. Projects with a Single Outflow and Regular Inflows
    • Many projects have one outflow at time 0 and inflows representing an annuity stream
    • For example, consider the following cash flows
      • In this case, the NPV formula can be rewritten as
        • NPV = C 0 + C[PVFA k, n ]
      • The IRR formula can be rewritten as
        • 0 = C 0 + C[PVFA IRR, n ]
    $2,000 C 1 ($5,000) C 0 $2,000 C 2 $2,000 C 3
  • 28. Projects with a Single Outflow and Regular Inflows—Example Q: Find the NPV and IRR for the following series of cash flows: Example A: Substituting the cash flows into the NPV equation with annuity inflows we have: NPV = -$5,000 + $2,000[PVFA 12, 3 ] NPV = -$5,000 + $2,000[2.4018] = -$196.40 Substituting the cash flows into the IRR equation with annuity inflows we have: 0 = -$5,000 + $2,000[PVFA IRR, 3 ] Solving for the factor gives us: $5,000  $2,000 = [PVFA IRR, 3 ] The interest factor is 2.5 which equates to an interest rate between 9% and 10%. $2,000 C 1 ($5,000) C 0 $2,000 C 2 $2,000 C 3
  • 29. Profitability Index (PI)
    • The profitability index is a variation on the NPV method
    • It is a ratio of the present value of a project’s inflows to the present value of a project’s outflows
    • Projects are acceptable if PI>1
      • Larger PIs are preferred
  • 30. Profitability Index (PI)
    • Also known as the benefit/cost ratio
      • Positive future cash flows are the benefit
      • Negative initial outlay is the cost
  • 31. Profitability Index (PI)
    • Decision Rules
      • Stand-alone Projects
        • If PI > 1.0  accept
        • If PI < 1.0  reject
      • Mutually Exclusive Projects
        • PI A > PI B choose Project A over Project B
    • Comparison with NPV
      • With mutually exclusive projects the two methods may not lead to the same choices
  • 32. Comparing Projects with Unequal Lives
    • If a significant difference exists between mutually exclusive projects’ lives, a direct comparison of the projects is meaningless
    • The problem arises due to the NPV method
      • Longer lived projects almost always have higher NPVs
  • 33. Comparing Projects with Unequal Lives
    • Two solutions exist
      • Replacement Chain Method
        • Extends projects until a common time horizon is reached
          • For example, if mutually exclusive Projects A (with a life of 3 years) and B (with a life of 5 years) are being compared, both projects will be replicated so that they each last 15 years
      • Equivalent Annual Annuity (EAA) Method
        • Replaces each project with an equivalent perpetuity that equates to the project’s original NPV
  • 34. Comparing Projects with Unequal Lives—Example Q: Which of the two following mutually exclusive projects should a firm purchase? Example Short-Lived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%) $750 $750 $750 $750 $750 $750 ($2,600) - C 5 - C 4 $750 C 3 Long-Lived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%) $750 C 1 ($1,500) C 0 $750 C 2 - C 6 A: The IRR method argues for undertaking the Short-Lived Project while the NPV method argues for the Long-Lived Project. We’ll correct for the unequal life problem by using both the Replacement Chain Method and the EAA Method. Both methods will lead to the same decision.
  • 35. Comparing Projects with Unequal Lives—Example The Replacement Chain Method involves replicating all projects (if needed) until each project being evaluated has a common time horizon. If the Short-Lived Project is replicated for a total of two times, it will have the same life (6 years) as the Long-Lived Project. This involves buying the Short-Lived Project again in year 3 and receiving the same stream of cash flows as originally expected for the following three years. This stream of cash flows is represented in the table below. Example ($750) Short-Lived Project replicated for a total of two times $750 $750 $750 ($1,500) - C 5 - C 4 $750 C 3 $750 C 1 ($1,500) C 0 $750 C 2 - C 6 Thus, buying the Long-Lived Project is a better decision than buying the Short-Lived Project twice. The NPV of this stream of cash flows is $776.41.
  • 36. Comparing Projects with Unequal Lives—Example The EAA Method equates each project’s original NPV to an equivalent annual annuity. For the Short-Lived Project the EAA is $167.95 (the equivalent of receiving $432.82 spread out over 3 years at 8%); while the Long-Lived Project has an EAA of $187.58 (the equivalent of receiving $867.16 spread out over 6 years at 8%). Since the Long-Lived Project has the higher EAA, it should be chosen. This is the same decision reached by the Replacement Chain Method. Example
  • 37. Capital Rationing
    • Capital rationing exists when there is a limit (cap) to the amount of funds available for investment in new projects
    • Thus, there may be some projects with +NPVs, IRRs > discount rate or PIs >1 that will be rejected, simply because there isn’t enough money available
    • How do you choose the set of projects in which to invest?
      • Use complex mathematical process called constrained maximization
  • 38. Figure 9.6: Capital Rationing