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The first and most difficult step in capital budgeting is reducing projects to a series of cash flows
C 0 $(50,000)
C 1 (10,000)
C 2 15,000
C 3 15,000
C 4 15,000
C 5 15,000
Business projects: early cash outflows and later inflows
C 0 is the Initial Outlay and is usually required to get started
The Cost of Capital
The average rate a firm pays investors for use of its long term money
Firms raise money from two sources: debt and equity
A project is a good investment if it is expected to generate a return that’s greater than the rate that must be paid to finance it
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Capital Budgeting Techniques
Payback
How many years to recover initial cost
Net Present Value
Present value of inflows less outflows
Internal Rate of Return
Project’s return on investment
Profitability Index
Ratio of present value of inflows to outflows
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Capital Budgeting Techniques—Payback
Payback period is the time it takes to recover early cash outflows
Shorter paybacks are better
Payback Decision Rules
Stand-alone projects
payback period < policy maximum accept
Payback period > policy maximum reject
Mutually Exclusive Projects
If Payback A < Payback B choose Project A
Weaknesses of the Payback Method
Ignores time value of money
Ignores cash flows after payback period
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Capital Budgeting Techniques—Payback
Consider the following cash flows
7 Payback period occurs at 3.33 years.
Payback period is easily visualized by the cumulative cash flows
Year 0 1 2 3 4 Cash flow (C i ) ($200,000) $60,000 $60,000 $60,000 $60,000 Cumulative cash flows ($200,000) ($140,000) ($80,000) ($20,000) $40,000 Year 0 1 2 3 4 Cash flow (C i ) ($200,000) $60,000 $60,000 $60,000 $60,000
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Capital Budgeting Techniques—Payback Example 10.1 8 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. But project B is clearly better because of the large inflows in the last two years
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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
Calculate payback period using the present value of project cash flows
Not widely used
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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
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If PV inflows > PV outflows => NPV > 0
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Capital Budgeting Techniques Net Present Value (NPV)
NPV and Shareholder Wealth
A project’s NPV is the net effect that it is expected to have on the firm’s value
To maximize shareholder wealth, select the capital spending program with the highest NPV
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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
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Capital Budgeting Techniques Net Present Value (NPV) Example 10.2 13 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.
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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
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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 0 1 2 3 -5,000 1,000 2,000 3,000
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Internal Rate of Return (IRR)
Defining IRR Through the NPV Equation
The IRR is the interest rate that makes a project’s NPV zero
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Internal Rate of Return (IRR)
Decision Rules
Stand-alone Projects
If IRR > cost of capital (k) accept
If IRR < cost of capital (k) reject
Mutually Exclusive Projects
IRR A > IRR B choose Project A over Project B
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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 = zero, the guessed interest rate is the project’s IRR
If NPV > 0, try a higher interest rate
If NPV < 0, try a lower interest rate
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Internal Rate of Return (IRR) Example 10.4 18 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
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Techniques Internal Rate of Return (IRR)
Technical Problems with IRR
Multiple Solutions
Unusual projects can have more than one IRR
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
These are rarely of practical concern
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Comparing IRR and NPV
NPV and IRR do not always select the same project in mutually exclusive decisions
A conflict can arise if NPV profiles cross in the first quadrant
In the event of a conflict The selection of the NPV method is preferred
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NPV and IRR Solutions Using Financial Calculators and Spreadsheets
Financial calculators and spreadsheets make calculating NPV and IRR easy
Input a project’s cash flows, the calculator or spreadsheet calculates NPV and IRR
An interest rate is needed to calculate NPV
The calculator procedure is tricky
Cash Flow (CF) mode
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Comparing Projects with Unequal Lives
If a significant difference exists between mutually exclusive projects’ lives, a direct comparison is meaningless
The problem arises due to the NPV method
Longer lived projects almost always have higher NPVs
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Comparing Projects with Unequal Lives
Two solutions exist
Replacement Chain Method
Extends projects until a common time horizon is reached
If mutually exclusive Projects A (with a life of 3 years) and B (with a life of 5 years) are compared, both projects will be replicated so that they last 15 years
Equivalent Annual Annuity (EAA) Method
Replaces each project with an equivalent perpetuity that equates to the project’s original NPV
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Comparing Projects with Unequal Lives - Example 24 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.
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Replacement Chain Method Figure 10.3 25 Thus, buying the Long-Lived Project is a better decision than buying the Short-Lived Project twice.
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A Three-Year Project Chained into Six Years Figure 10.4 26
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Capital Rationing
Used when capital funds for new projects are limited
Generally rank projects in descending order of IRR and cut off at the cost of capital
However this doesn’t always make the best use of capital so a complex mathematical process called constrained maximization can be used