CHAPTER 9Capital Budgeting • PV of Cash Flows • Payback • NPV • IRR • EAA • NPV profiles
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
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
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]) • Equivalent annual annuity (EAA)
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 PaybackA < PaybackB choose Project A • Weaknesses of the Payback Method • Ignores the time value of money • Ignores the cash flows after the payback period
Relevant Cash Flows • Cash Flow (vs. Accounting Income) • Incremental Cash Flows • Partial budget concept
0 1 2 3 CFt 10 60 80 -90 Cumul -100 -30 50 PaybackL 2 + 30/80 = 2.375 years Payback for Project L(Long: Most CFs in out years) 2.4 -100 0 =
0 1 2 3 70 50 20 CFt -30 Cumul -100 20 40 PaybackL 1 + 30/50 = 1.6 years Project S (Short: CFs come quickly) 1.6 -100 0 =
0 1 2 3 10 60 80 Discounted Payback: Uses discounted rather than raw CFs. Project L 10% CFt -100 9.09 49.59 60.11 PVCFt -100 -100 -90.91 -41.32 18.79 Cumul(PV) Disc. payback 2 + 41.32/60.11 = 2.7 yrs = Recover invest + cap costs in 2.7 yrs.
Capital Budgeting Techniques—Payback: another example • Consider the following cash flows • Payback period is easily visualized by the cumulative cash flows Payback period occurs at 3.33 years.
Q: Use the payback period technique to choose between mutually exclusive projects A and B. Project A Project B C0 ($1,200) ($1,200) C1 400 400 C2 400 400 Example C3 400 350 C4 200 800 C5 200 800 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. Capital Budgeting Techniques—Payback— yet another example
Capital Budgeting Techniques—Payback • Why Use the Payback Method? • It’s quick and easy to apply • Serves as a rough screening device • Indicates how long to resolve uncertainty • The Present Value Payback Method • Involves finding the present value of the project’s cash flows then calculating the project’s payback
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 PVinflows > PVoutflows, NPV > 0
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 • NPV is the PV of economic profit
Capital Budgeting Techniques—Net Present Value (NPV) • Decision Rules • Stand-alone Projects • NPV > 0 accept • NPV < 0 reject • Mutually Exclusive Projects • NPVA > NPVB choose Project A over B
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? C0 ($5,000) C1 $1,000 C2 $2,000 C3 $3,000 Example 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. Capital Budgeting Techniques—Net Present Value (NPV) Example
Use CFj on the cash flow • Show on the board
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 “price” of receiving the inflows • Literally the IRR is the interest rate at which the present value of the three inflows just equals the $5,000 outflow • If you lend yourself the money to make the investment, the IRR is the highest interest rate you could charge and the investment pay off the loan
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 • Solve for IRR • one equation, one unknown, but usually impossible to solve with algebra Project cost
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 (but don’t use IRR to rank mutually exclusive projects)
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
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%? C0 C1 C2 C3 ($5,000) $1,000 $2,000 $3,000 A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate. Example Since NPV<0, the project’s IRR must be < 12%. 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. 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. Interest Rate Guess Calculated NPV 12% ($377) 10 ($184) Example 9 ($83) 8 $22 7 $130 The exact IRR can be calculated using a financial calculator. The financial calculator uses the iterative process just demonstrated; however it is capable of guessing and recalculating much more quickly. Techniques—Internal Rate of Return (IRR)—Example
Okay, if you haven’t already pointed it out by now, there is really no reason to do the trial and error yourself! • Use the CFjcalculator function (IRR key) • Cash flows • -5000 • 1000 • 2000 • 3000
Techniques—Internal Rate of Return (IRR) • Technical Problems with IRR • Multiple Solutions • Unusual projects can have more than one IRR • Rarely presents practical difficulties • The number of positive IRRs to a project depends on the number of sign reversals to the project’s cash flows • Normal pattern involves only one sign change • The Reinvestment Assumption • IRR method implicitly assumes cash inflows will be reinvested at the project’s IRR • For projects with extremely high IRRs, this is unlikely
When NPV and IRR disagree • Only when comparisons must be made • Not stand alone analysis • Use the NPV rankings, not the IRR rankings
NPV Profile • A project’s NPV profile is a graph of its NPV vs. the cost of capital • It crosses the horizontal axis at the IRR
Construct NPV Profiles Enter CFs in CFLO and find NPVL and NPVS at several discount rates: k 0 5 10 15 20 NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5
k 0 5 10 15 20 NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5 NPV ($) Crossover Point = 8.7% S IRRS = 23.6% L Discount Rate (%) IRRL = 18.1%
Mutually Exclusive Projects NPV k< 8.7: NPVL> NPVS , IRRS > IRRL CONFLICT L k> 8.7: NPVS> NPVL , IRRS > IRRL NO CONFLICT S IRRs Rankings of S and L were consistent because K was 10% % k 8.7 k IRRL Crossover rate = 8.7%
To find the crossover rate: 1. Find cash flow differences between the projects. Project L minus Project S CashL (100) 10 60 80 CashS (100) 70 50 20 Difference 0 -60 10 60
2. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68, rounded to 8.7%. 3. Can subtract S from L or vice versa, but better to have first CF negative. 4. If profiles don’t cross, one project dominates the other.
Two reasons NPV profiles cross: 1) Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the discount rate, the more valuable these funds, so high k favors small projects. 2) Timing differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPVS > NPVL.
Reinvestment Rate Assumptions • NPV assumes reinvest at k. • IRR assumes reinvest at a rate greater than the crossover rate. • Reinvest at opp. cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.
Comparing Projects with Unequal Lives • If a significant difference exists between mutually exclusive projects’ lives, a direct comparison of the projects can be in error • The problem arises using the NPV method • Longer lived projects often have higher NPVs • Or shorter projects lower net present cost • Must consider if the investments are really a sequence • If not a sequence then NPV is correct.
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 annuity (PMT) that equates to the project’s original NPV • That is, annualize the NPV (or net present cost) • Both methods give the same conclusion so I only use EAA
Q: Which of the two following mutually exclusive projects should a firm purchase? C0 C1 C2 C3 C4 C5 C6 Short-Lived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%) ($1,500) $750 $750 $750 - - - Long-Lived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%) Example ($2,600) $750 $750 $750 $750 $750 $750 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 the EAA Method. Both the EAA and Replacement Chain methods will lead to the same decision. 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 Comparing Projects with Unequal Lives—Example
Review Steps: • 1. Create ideas for capital investment • 2. Estimate CFs (inflows & outflows). • 3. Assess riskiness of CFs. • 4. Determine k = WACC (adj. for risk). • 5. Find NPV and/or IRR. • Accept if NPV > 0 and/or IRR > WACC. • If mutually exclusive, take the highest NPV • If mutu. excl. & lives differ take highest EAA