1. 12 Capital Budgeting Chapter Terry Fegarty Seneca College
Slides Developed by:
Terry Fegarty
Seneca College

2. Chapter 12 – Outline (1) Capital Budgeting
Characteristics of Business Projects
Capital Budgeting Techniques
Capital Budgeting Techniques—Payback
Capital Budgeting Techniques—Net Present Value (NPV)
Capital Budgeting Techniques—Internal Rate of Return (IRR)
NPV Profile
Conflicting Results Between IRR and NPV
NPV and IRR Solutions Using Spreadsheets
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3. Chapter 12 – Outline (2)
Projects with a Single Outflow and Regular Inflows
Profitability Index (PI)
Comparing Projects with Unequal Lives
Capital Rationing
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4. Capital Budgeting
Capital budgeting involves planning and justifying large expenditures on long-term projects
Projects can be classified as:
Replacements
Expansions
New business ventures
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5. 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—when selecting one project excludes selecting the other
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6. Characteristics of Business Projects
Project Cash Flows
First and usually most difficult step in capital budgeting is reducing projects to series of cash flows
Business projects involve early cash outflows and later inflows
Initial outlay is required to get started
Annual net inflows, after tax, generated by project
Terminal value from sale or salvage of project
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7. Characteristics of Business Projects
Cost of Capital
Firm’s cost of capital is average rate it pays its investors for use of their money
In general, firm can raise money from two sources: debt and equity
If potential project is expected to generate return greater than cost of money to finance it, it is a good investment
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8. Capital Budgeting Techniques
Four techniques for determining a project’s financial viability:
Payback—how many years to recover project’s initial cost
Net Present Value—how much the present value of project’s inflows exceeds present value of its outflows
Internal Rate of Return—return on investment in the project
Profitability Index—ratio of project’s inflows vs. outflows—in present value terms)
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9. Capital Budgeting Techniques—Payback
Payback period—time to recover early cash outflows
Shorter paybacks are better
Payback Decision Rules
Stand-alone projects
If payback period < (>) policy maximum accept (reject)
Mutually Exclusive Projects
If PaybackA < PaybackB  choose Project A
Weaknesses of the Payback Method
Ignores time value of money
Ignores cash flows after the payback period
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10. Capital Budgeting Techniques—Payback—Example
Consider the following cash flows
Example
Year 1 2 3 4
Cash flow (Cn)
($200,000)
$60,000
Payback period is easy to see by the cumulative cash flows
Year 1 2 3 4
Cash flow (Cn)
($200,000)
$60,000
Cumulative cash flows
($140,000)
($80,000)
($20,000)
$40,000
Payback period occurs at 3.33 years
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11. Example 12.1: Capital Budgeting Techniques—Payback
Q: Use the payback period technique to choose between mutually exclusive projects A and B.
Example
800
200 C5 C4
350
400 C3 C2 C1
($1,200) C0
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 4th year. Thus, according to the payback method, Project A is better than B.
Example
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12. Capital Budgeting Techniques—Payback
Why Use the Payback Method?
Quick and easy to apply
Serves as rough screening device
The Present Value Payback Method
Involves finding present value of project’s cash flows, then calculating project’s payback
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13. Capital Budgeting Techniques—Net Present Value (NPV)
NPV—sum of present values of project’s cash flows, discounted at cost of capital
PVoutflows
PVinflows
If PVinflows > PVoutflows, NPV > 0
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14. Capital Budgeting Techniques—Net Present Value (NPV)
NPV and Shareholder Wealth
Project’s NPV is net effect that undertaking project is expected to have on firm’s value
A project with NPV > (<) 0 should increase (decrease) firm value
Since firm desires to maximize shareholder wealth, it should select capital spending program with highest total NPV
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15. Capital Budgeting Techniques—Net Present Value (NPV)
NPV Decision Rules
Stand-alone Projects
NPV > 0  accept
NPV < 0  reject
Mutually Exclusive Projects
NPVA > NPVB  choose Project A over B
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16. Example 12.2: Capital Budgeting Techniques—Net Present Value
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 C3
$2,000 C2
$1,000 C1
($5,000) C0
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
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17. Example 12.2: Capital Budgeting Techniques—Net Present Value1 2 3
-$5,000
$1,000
$2,000
$3,000
$892.90
$1,594.40
$2,135.40
-$377.30
Solution is calculated by discount each of the cash flows back to time period zero using a discount rate of 12%.
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18. Capital Budgeting Techniques—Internal Rate of Return (IRR)
Project’s IRR is return it generates on investment of its cash outflows
For example, if a project has the following cash flows 1 2 3
-5,000
1,000
2,000
3,000
The “price” of receiving
the inflows
The IRR is the interest rate at which the present value of the three inflows just equals the $5,000 outflow
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19. Capital Budgeting 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 —
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20. 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
IRRA > IRRB  choose Project A over Project B
If NPV > 0, IRR > k
If NPV < 0, IRR < k
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21. Techniques—Internal Rate of Return
Calculating IRRs
Finding IRRs usually requires an iterative, trial-and-error technique
Guess at project’s IRR
Calculate 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
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22. Example 12.3: Capital Budgeting Techniques—Internal Rate of Return
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 C1
($5,000) C0
$2,000 C2
$3,000 C3
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%.
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23. Example 12.3: Capital Budgeting Techniques—Internal Rate of Return
A: 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 9%, 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
or spreadsheet
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24. NPV Profile
Project’s NPV Profile—graph of its NPV vs. the cost of capital
It crosses the horizontal axis at the IRR
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25. Figure 12.1: NPV Profile
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26. Techniques—Internal Rate of Return (IRR)
Technical Problems with IRR
Multiple Solutions
If some future cash flows are negative, project can have more than one IRR solution
Normal pattern involves negative initial outlay and positive future cash flows
Rarely presents practical difficulties
The Reinvestment Assumption
IRR method assumes cash inflows will be reinvested at project’s IRR
For projects with extremely high IRRs, this is unlikely
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27. Conflicting Results Between 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:
one project is accepted below a certain cost of capital
the other project is accepted above that cost of capital
The NPV profiles have to cross in the first quadrant of the graph, where interest rates are practical
NPV method is the preferred over IRR method because the reinvestment interest rate assumption is more practical
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28. Figure 12.2: Projects for Which IRR and NPV Can Give Different Solutions
At a cost of capital of k1, Project A is better than Project B, while at k2 the opposite is true.
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29. NPV and IRR Solutions Using Spreadsheets
NPV function in Microsoft® Excel®
=Cash Flow0 + NPV(interest rate, Cash Flow1:Cash Flown)
Every cash flow within the parentheses is discounted at the interest rate
IRR function in Excel®
=IRR (interest rate, Cash Flow0:Cash Flown)
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30. Example 12.3: Spreadsheet Solution
Formula in B6:
=B2 + NPV(C4,C2:E2)
Formula in B8:
=IRR(B2:E2,C4)
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31. 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 C0 C1 C2 C3
($5,000)
$2,000
In this case, the NPV formula can be rewritten as
NPV = -C0 + C[PVFAk, n]
The IRR formula can be rewritten as
0 = C0 + C[PVFAIRR, n]
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32. Example 12.5: Projects with a Single Outflow and Regular Inflows
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[PVFA12, 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[PVFAIRR, 3]
Solving for the factor gives us:
$5,000  $2,000 = [PVFAIRR, 3]
The interest factor is 2.5 which equates to an interest rate between 9% and 10%.
$2,000 C1
($5,000) C0 C2 C3
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33. Example 12.5: Spreadsheet Solution
Formula in B6:
=B2 + NPV(C4,C2:E2)
Formula in B8:
=IRR(B2:E2,C4)
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34. Profitability Index (PI)
Profitability Index—ratio of the present value of a project’s inflows to the present value of a project’s outflows
a variation on the NPV method
Projects are acceptable if PI>1
Larger PIs are preferred
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35. Profitability Index (PI)
Also known as the benefit/cost ratio
Positive future cash flows are the benefit
Negative initial outlay is the cost
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36. Profitability Index (PI)
PI Decision Rules
Stand-alone Projects
If PI > 1.0  accept
If PI < 1.0  reject
Mutually Exclusive Projects
PIA > PIB choose Project A over Project B
Comparison with NPV
With mutually exclusive projects, two methods may not lead to same choice
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37. Comparing Projects with Unequal Lives
If significant difference exists between lives of mutually exclusive projects, direct comparison of the projects is meaningless
Problem arises due to the NPV method
Longer lived projects almost always have higher NPVs
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38. Figure 12.3: Comparing Projects with Unequal Lives
Example
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39. Comparing Projects with Unequal Lives—Example
Q: Which of the two following mutually exclusive projects should a firm purchase?
Example
Short-Lived Project (NPV = $ at an 8% discount rate; IRR = 23.4%)
$750
($2,600) - C5 C4 C3
Long-Lived Project (NPV = $ at an 8% discount rate; IRR = 18.3%) C1
($1,500) C0 C2 C6
A: The IRR method favours the Short-Lived Project while the NPV method favours the Long-Lived Project. We’ll correct for the unequal life problem by using the EAA Method.
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40. Comparing Projects with Unequal Lives
Equivalent Annual Annuity (EAA) Method
Replaces each project with an equivalent perpetuity that equates to the project’s original NPV
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41. Comparing Projects with Unequal Lives—Example
A: The EAA Method equates each project’s original NPV to an equivalent annual annuity.
For the Short-Lived Project the EAA is $ (the equivalent of receiving $ spread out over 3 years at 8%).
The Long-Lived Project has an EAA of $ (the equivalent of receiving $ spread out over 6 years at 8%).
Since the Long-Lived Project has the higher EAA, it should be chosen.
Example
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42. Figure 12.4: Comparing Projects with Unequal Lives
Example
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43. Capital Rationing
Capital rationing— exists when there is limit (maximum) to amount of funds available for new projects
Thus, there may be some projects with +NPVs, IRRs > discount rate or PIs >1 that will be rejected, because not enough money available
How do you choose the set of projects in which to invest?
Use complex mathematical process called constrained maximization
Use intuition and judgment
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44. Figure 12.5: Capital Rationing
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