1. Chapter 9 Capital Budgeting © 2000 South-Western College Publishing

2. Capital Budgeting A major part of the financial management of the firm Kinds Of Spending In Business Short term - to support day to day operations Long term - to support long lived equipment and projects Long term spending is called Capital Capital Budgeting Planning and Justifying How Capital Dollars Are Spent On Long Term Projects Provides methods for evaluating whether projects make financial sense and for choosing among them TM 9-1 Slide 1 of 2

3. Project Types and Risk Projects fall into three general categories characterized by increasing risk: Replacement Expansion New Venture STAND-ALONE AND MUTUALLY EXCLUSIVE PROJECTS The Stand-Alone Decision Is the project a good idea if there's no competition for the resources to do it The Mutually Exclusive Decision Selecting either project excludes the other Choosing among different ways to do something or among separate projects competing for limited resources TM 9-1 Slide 2 of 2

4. PROJECT CASH FLOWS The first step in capital budgeting is to represent all projects as a series of incremental cash flows Example: A new venture takes an initial investment of $50,000, will lose $10,000 in the first year, and earn $15,000 per year for five years C 0 ($50,000) C 1 ($10,000) C 2 $15,000 C 3 $15,000 C 4 $15,000 C 5 $15,000 C 6 $15,000 TM 9-2 Slide 1 of 2

5. PROJECT CASH FLOWS (cont.) The typical pattern involves outflows first and inflows later C 0, the Initial Outlay, is virtually always negative (A few of the later flows may also be negative) Estimating cash flows is the most difficult part of capital budgeting (Chapter 10) For now, we'll take them as given TM 9-2 Slide 2 of 2

6. THE COST OF CAPITAL The average rate of return the firm pays to its long term investors for the use of their money. Intuitive Purpose : An investment makes sense only if it earns more than the cost of funds put into it. A weighted average concept where the weights are the proportionate amounts invested in each kind of capital PortionReturn Equity.75 x 10% = 7.5% Debt.25 x 8% = 2.0% Weighted Average Cost of Capital 9.5% TM 9-3

7. CAPITAL BUDGETING TECHNIQUES Payback period Net Present Value (NPV) Internal Rate of Return (IRR) Profitability Index (PI) Each involves calculating a number for every project under consideration and applying decision rules to those numbers to make accept or reject choices TM 9-4 Slide 1 of 4

8. PAYBACK PERIOD Measure the time it takes for the project to "break even" in terms of undiscounted cash flows Example: Year 0 1 2 3 4 Cash Flow (C i ) ($200,000) $60,000 $60,000 $60,000 $60,000 Cumulative Cash Flow ($200,000) ($140,000) ($80,000) ($20,000) $40,000 Payback Period = 3.33 years TM 9-4 Slide 2 of 4

9. Payback Decision Rules It's better to recover invested money sooner than later Stand-alone Projects: Businesses generally have stated policies as to the maximum time allowable for capital recovery Accept Payback period < Policy Maximum Accept Reject Payback Period > Policy Maximum Reject TM 9-4 Slide 3 of 4

10. Mutually Exclusive Projects Shorter Is Better: A P/B A < P/B B Choose Project A over Project B Weaknesses of the Payback Method Ignores the time value of money Ignores cash flows after the payback period TM 9-4 Slide 4 of 4

11. Example 9-1 Choose between mutually exclusive projects A and B: Project A Project B C 0 ($1,200) ($1,200) C 1 $400 $400 C 2 $400 $400 C 3 $400 $350 C 4 $200 $800 C 5 $200 $800 Solution: P/B A = 3 years P/B B = slightly more than 3 years Therefore, Payback chooses Project A, but Project B is better because of years 4 and 5 Why Use the Payback Method? Quick and easy to apply serves as a rough screening device before more sophisticated methods TM 9-5

12. NET PRESENT VALUE (NPV) The present value of future cash flows is what counts when making decisions based on value. The Net Present Value of all of a project's cash flows is its expected contribution to the firm's value and shareholder wealth PVs are taken at k, the cost of capital Outflows are C i with negative values and tend to occur first NPV is the difference between the present values of all the positives and all the negatives TM 9-6 Slide 1 of 2

13. NPV DECISION RULES Stand-alone Projects: NPV > 0 Accept NPV < 0 Reject Example 9-2: Should project Alpha be undertaken if the cost of capital is 12%? C 0 C 1 C 2 C 3 ($5,000) $1,000 $2,000 $3,000 Solution: Year Cash Flow PV Factor PV of Cash Flow 0 ($5,000) - ($5,000.00) 1 $1,000.8929 $892.90 2 $2,000.7972 $1,594.40 3 $3,000.7118 $2,135.40 NPV = ($377.30) Project Alpha's negative NPV REJECT TM 9-6 Slide 2 of 2

14. Mutually Exclusive Projects: A bigger NPV is better NPV A > NPV B Choose Project A over B The idea is straightforward, but a number of practical questions arise Example 9-3: Xavier makes outdoor power equipment and is considering two projects: 1) making larger tractors and 2) making snowblowers (snowblowers use similar technology, but are a new product for Xavier). Management wants to base the decision on only 5 years of estimated cash flow as follows ($000): Year Tractor Snowblower 0 ($3,000) ($3,500) 1 ($250) ($700) 2 $500 $800 3 $1,000 $1,200 4 $1,500 $2,000 5 $1,500 $2,000 Evaluate each project as a stand alone and if only $5M in capital is available TM 9-7 Slide 1 of 2

15. Solution: Cash Flows PV of Cash Flows Year Factor Tractor Snowblower Tractor Snowblower 0 ($3,000) ($3,500) ($3,000) ($3,500) 1.9174 ($250) ($700) ($229) ($642) 2.8417 $500 $800 $421 $673 3.7722 $1,000 $1,200 $772 $927 4.7084 $1,500 $2,000 $1,063 $1,417 5.6499 $1,500 $2,000 $975 $1,300 NPV's $2 $175 Stand-alone: Both are marginally acceptable Mutually Exclusive: Snowblower is marginally better (Both NPVs are small relative to C 0 s) TM 9-7 Slide 2 of 2

16. Reevaluate if management considers two more years of cash flow at the level of 5th year Cash Flows PV of Cash Flows Year Factor Tractor Snowblower Tractor Snowblower 6.5963 $1,500 $2,000 $894 $1,193 7.5470 $1,500 $2,000 $821 $1,094 Addition to NPVs $1,715 $2,287 Previous NPV s $2 $175 New NPVs $1,717 $2,462 Notice the change in the complexion of the problem. Stand-alone: Both projects clearly favorable Mutually exclusive: Snowblower seems the obvious choice However, cash flows become less certain as they are further into the future TM 9-8 Slide 1 of 2

17. Are Other Risk Considerations Relevant? Yes!!! Tractors are an expansion - Snowblowers are a new venture Risks are unlikely to be the same Is a straight comparison of NPVs appropriate??? Probably not - Stay tuned until Chapter 10 TM 9-8 Slide 2 of 2

18. INTERNAL RATE OF RETURN (IRR) Define IRR in two ways: The return a project earns on invested funds or In terms of the NPV equation The Project as an Investment View a project as an investment similar to the purchase of a financial asset The initial outlay is the "price" of receiving the future inflows IRR is the return on the investment (equates the PV of future cash flows to the price today) Finding a project's IRR is analogous to finding a bond's yield at a given price TM 9-9 Slide 1 of 2

19. Defining IRR Through the NPV Equation At the IRR the PVs of project inflows and outflows are equal, so NPV = 0 A project's IRR is the solution to this equation for a given set of C i TM 9-9 Slide 2 of 2

20. IRR Decision Rules Follow from thinking in terms of a return on investment Stand-alone Projects: Invest only if IRR exceeds k, the cost of capital IRR > k Accept IRR < k Reject Mutually Exclusive Projects: a bigger IRR is better IRR A > IRR B Choose Project A over Project B Calculating IRRs IRR equation is an nth order polynomial in the unknown IRR Can't generally be solved algebraically Use an iterative approach in the NPV equation starting with a guess at k Calculate NPV, if not zero guess again moving closer to solution TM 9-10

21. Example 9-4 Find IRR for cash flows of Example 9-2: C 0 C 1 C 2 C 3 ($5,000) $1,000 $2,000 $3,000 Is the project acceptable if k = 8%, 10%? Solution: Use NPV equation and find value of k where NPV = 0 TM 9-11 Slide 1 of 3

22. Rationale: Larger interest rates shrink positive C i in the distant future more than early negative C i, especially C 0 Hence NPV for normal projects decreases as k increases NPV k IRR Figure 9-1 NPV Profile TM 9-11 Slide 2 of 3

23. Finding an IRR is equivalent to locating the crossover point of the NPV Profile by testing points on either side Set up a two column table and calculate as in Example 9-2 Interest Calculated Rate Guess NPV 12% ($377) 10% ($184) 9% ($83) 8% $22 7% $130 IRR is between 8% and 9% (where NPV changes sign) k = 8% project is marginally favorable k = 9% project is unfavorable (Technique is similar to finding bond yields) TM 9-11 Slide 3of 3

24. TECHNICAL PROBLEMS WITH IRR Multiple Solutions IRR equation can have as many as n solutions (positive, negative, or imaginary) Only as many positive solutions as sign reversals Only one is generally reasonable The Reinvestment Assumption Implicitly assumes reinvestment of inflows at the IRR Unlikely to be possible if IRR very high Overstates calculated IRR somewhat Rarely affects acceptance or ranking (Note: NPV's reinvestment assumption is usually easily satisfied) Technical problems rarely present practical difficulties TM 9-12

25. COMPARING IRR AND NPV NPV and IRR May Occasionally Give Conflicting Results in Mutually Exclusive Decisions NPV NPV B k 2 NPV A k 1 A NPV B B k 2 k 1 IRR B IRR A Figure 9-2 Projects For Which IRR and NPV Can Give Different Solutions TM 9-13 Slide 1 of 2 k

26. In Case of Conflict The NPV Method is Preferred Reinvestment assumption is more easily satisfied. Direct link to shareholder wealth Businesspeople Tend to Prefer IRR Over NPV More used to working with rates of return PV'd dollars are a little abstract TM 9-13 Slide 2 of 2

27. PROJECTS WITH A SINGLE OUTFLOW AND REGULAR INFLOWS Many projects are characterized by an initial outflow and equal regular inflows: PV of annuity formula makes pattern easy to work with NPV: NPV = C 0 + C [PVFA k,n ] IRR: 0 = C 0 + C [PVFA IRR,n ] TM 9-14

28. PROFITABILITY INDEX A variation on the NPV method Compares PV of future cash flows with initial outlay in a ratio (NPV works with the difference between inflows and outflows) (Also known as the Benefit/Cost Ratio ) Concept poorly defined if some early Cs after C 0 are negative TM 9-15 Slide 1 of 2

29. DECISION RULES Stand-alone Projects: Accept PI > 1.0 Accept Reject PI < 1.0 Reject Mutually Exclusive Projects: PI A > PI B Choose Project A over Project B TM 9-15 Slide 2 of 2

30. COMPARING PROJECTS WITH UNEQUAL LIVES C 0 C 1 C 2 C 3 C 4 C 5 C 6 Short Lived Project ($1,500) $750 $750 $750 IRR = 23.4% NPV = $432.82 Long Lived Project ($2,600) $750 $750 $750 $750 $750 $750 IRR = 18.3% NPV = $867.16 Figure 9-3 Comparing Projects with Different Lives NPV method adds up six years of benefits for one project and three years for the other. Hence longer lived machine gets a higher NPV. TM 9-16 Slide 1 of 2

31. The Replacement Chain Method Chain short projects to cover the time span of the longer project. Two Short-Lived Projects Back-to-Back ($1,500) $750 $750 $750 ($750) NPV = $776.41 Figure 9-4 A Three-Year Project Chained into Six Years A problem exists if a large number of replacements are necessary. TM 9-16 Slide 2 of 2

32. The Equivalent Annual Annuity (EAA) Method Replace each link in the chain by its NPV Then replace each NPV with an annuity of the same length and equal NPV Example: Shorter project has n = 3 yrs and NPV = $432.82. PVA = PMT [PVFA k,n ] $432.82= PMT [PVFA 8,3 ] $432.82 = PMT (2.5771) PMT= $167.95 = EAA TM 9-17 Slide 1 of 3

33. First link Second link 0123456 (1,500) $750 $750 $750 PROJECTS ($1,500) $750 $750 $750 NPVs $432.82 $432.82 EAA $167.95 $167.95 $167.95 $167.95 $167.95 $167.95 Figure 9-5 Replacing a Project with its NPV and EAA TM 9-17 Slide 2 of 3

34. Since the project can be chained forward indefinitely, it can be represented by an indefinitely long EAA. Can calculate an EAA for any project For the longer project: PVA= PMT [PVFA k,n ] $867.16= PMT [PVFA 8,6 ] $867.16= PMT (4.6229) PMT= $187.58 = EAA So choose the longer project since it has the larger EAA TM 9-17 Slide 3 of 3

35. CAPITAL RATIONING k% Possible $16M Funds Limitation 15% 10% Cost of Capital 5% $8$13$19$22$28$35$ Cumulative Capital Investment (for the year in $M) Capital Budget The Capital Budget is generally less than the total of projects available Requires selecting projects to maximize total NPV TM 9-18 A B C D E F