Corporate Finance Fundamentals FN1 Module 6 Strategic Decisions: Capital Budgeting Criteria Lectures and handouts by: Ruth Heathcote 1
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FN1 Module 6 • • • • • •
Part 1: Part 2: Part 3: Part 4: Part 5: Part 6:
Net Present Value Risk-adjusted discount rates Internal Rate of Return (IRR) Payback and Discounted payback method Profitability Index Past exam questions
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Evaluation of Investment Alternatives • Net Present Value (NPV) • Internal Rate of Return (IRR) • Payback Period and Discounted Payback Period • Profitability Index (PI)
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Project Evaluation Techniques • The following evaluation approaches (NPV, IRR, Discounted payback and PI) require the same data: – Estimate of initial cost (CF0 ) – Net incremental after-tax cash flows CFBT(1-T) – Cost of Capital (k) – Estimate of useful life (n) – Ending Cash flows (ECFn) – Corporate tax rate (T) – Capital Cost Allowance Rate (d) 4
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Project Evaluation Techniques • The payback method evaluation approach requires the following data only: – Estimate of initial cost (CF0 ) – Net incremental after-tax cash flows CFBT(1-T) – Estimate of useful life (n) – Ending Cash flows (ECFn) – Corporate tax rate (T) – Capital Cost Allowance Rate (d) – DISCOUNT RATE NOT USED 5
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Part 1
Net Present Value
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Net Present Value (NPV) Formula
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Evaluating Investment Alternatives Net Present Value (NPV) Analysis NPV = the sum of the present value of all benefits minus the present value of costs
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Net Present Value (NPV) Analysis • If benefits > cost, NPV will be positive and the project is acceptable and will add value to the firm. • If benefits = cost, NPV will be equal to zero, and the project is acceptable, but will not add value to the firm. • If benefits < cost, NPV will be negative and the project is unacceptable because it destroys firm value. 9
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Net Present Value (NPV) Analysis Decision Rule • Accept all projects that generate a NPV > 0 • Reject all projects that generate a NPV < 0
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Net Present Value Interpreted NPV is an absolute measure (expressed in present dollars) of the net incremental benefits the project is forecast to bring to the shareholders. In a perfectly efficient market, the total value of the firm should rise by the value of the NPV if the project is undertaken. Remember – it is the manager’s responsibility to maximize shareholder wealth 11
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Net Present Value We have identified that there are several long-term decision criteria, but the use of the Net Present Value method ensures that our focus is on building shareholder value. The Net Present value method has the fewest limiting assumptions
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Example If NPV is forecast to be + $250,000, then the PV of incremental benefits exceeds the present value of costs today by $250,000. Remember the PV is determined by discounting the forecast cash flows by the investor’s required return. A positive NPV indicates that returns are greater than what investors require. This means a positive NPV adds value to the firm.
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Net Present Value Interpreted In this case, if there were 1,000,000 shares outstanding, acceptance of a $250,000 NPV project in an efficient market means that the market price of each share should rise by:
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NPV Example Problem: • Initial outlay = $12,000 • After-tax cash flow benefits:
– Year 1 = $5,000 – Year 2 = $5,000 – Year 3 = $8,000 • Discount rate (k) = 15%
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NPV Example The Formula-based Approach Solution:
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NPV Example The Spreadsheet Approach Solution:
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The Financial Calculator Approach CF
-12000 5000 5000 8000 NPV
CLR WORK
2ND ENTER ENTER ENTER ENTER
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ENTER
CPT
gives $1,388.67 18
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Template
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Initial Cost (Co) Working capital Opportunity cost PV of operating benefits PVTS – PVTSL PV of Sn PV of Release of WCn
+ + + +
NPV
? FN1 Module 6
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Example 1
See Handout #1, Example 1
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Example 2
See Handout #1, Example 2
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• • • •
Part 1: Net Present Value Part 2: Risk-adjusted discount rates Part 3: Internal Rate of Return (IRR) Part 4: Payback and Discounted payback method • Part 5: Profitability Index • Part 6: Past exam questions
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Part 2
Risk-adjusted discount rates
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Firm’s Cost of Capital (WACC = k) • The weighted average cost of capital (WACC) is the relevant discount rate for NPV analysis only if the risk of the project being evaluated is similar to the risk of the overall firm • If the risk of the project differs from the risk of the overall firm a risk-adjusted discount rate (RADR) should be used.
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Risk-Adjusted Discount Rates • Remember that the discount rate applied to a project represents the return required by our providers of capital (investors). • We know that investors are risk averse, and require a higher return for higher risk. • This means that the correct discount rate for any project should be adjusted for risk. 25
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Required Rates of Return (RADR) Components • The risk-free rate is equal to the real rate of return plus expected inflation (Fisher Equation) • The risk premium is based on an estimate of the risk associated with the project.
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Risk-Adjusted Discount Rates (RADRs = k) •
RADRs can be estimated using a number of alternative techniques: 1. Use the CAPM formula after determining the project beta and using the current risk-free rate (RF) and an estimate of the market risk premium 2. Pure play approach where you find the cost of capital of a firm in the industry associated with the project.
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Risk-Adjusted Discount Rates • For financial assets, we could measure the investor’s reaction to risk by analyzing how share prices change as risk changes, and determine the relationship between risk and return, using the short term risk free interest rate, and the return on the market in our model (CAPM). •
Market risk, as measured by beta, may be an appropriate risk measure for capital investments for well-diversified investors.
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RADR • RADR = RF + beta * (RM – RF) • In this application, beta represents the risk of the project. • We can determine RF and RM. • Have to estimate project beta.
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Estimating project beta • Analyze historical holding-period returns for past similar projects against the returns on the market portfolio. • Use holding-period returns for comparable companies in the same line of business as the proposed project. (Pure play method)
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Project beta Problems: • Project betas can shift over time • Some projects are safer at start up, others are riskier • The CAPM looks one period into the future • How accurate is it to use this 1 period rate for a capital budgeting proposal that has a 5 year life?
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Difficulties in estimating project betas • Incomplete or unreliable data • Difficulty in estimating periodic returns • No historical data
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Difficulties in estimating project betas • Unpredictable outcomes • CAPM is a one period model – projects are multiperiod • Historical data may not predict future risk.
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Pure Play Approach • This method is used to estimate a project’s beta by analysis of comparable companies. • In this approach, a firm would identify several publicly traded companies in the same or similar line of business as the proposed project, and determine the beta of this other firm. • After making appropriate adjustments for risk (operating and financial leverage adjustments) a beta for the proposed project can be estimated.
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Pure Play Approach Problems: • Difficult to find firms that are similar in risk to the proposed project • If we want to determine the appropriate beta for this project, we want to measure project risk only. • Must adjust the beta of a similar firm to remove financial risk, due to financial leverage
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Project risk and Financial risk Project risk = business risk • The risk in the normal operations of the firm • Factors affecting business risk include – Variability of sales and operating costs – Measured by analyzing earnings before interest and taxes.
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Project risk and Financial risk Financial risk – The risk that a firm faces due to debt financing. – Measured by analyzing variability in Net Income
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Importance of using correct discount rate • Using a RADR adjusted for the uncertainty of timing and amount of a project’s cash flows is consistent with the fact that our providers of capital do just that. • If we use a lower discount rate than our investors require, then we will accept projects that would decrease the value of the firm • If we use a higher discount rate than our investors require, then we will reject projects that would add value to the firm. 38
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Example 3
See Handout #1, Example 3
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• • • •
Part 1: Net Present Value Part 2: Risk-adjusted discount rates Part 3: Internal Rate of Return (IRR) Part 4: Payback and Discounted payback method • Part 5: Profitability Index • Part 6: Past exam questions
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Part 3
Internal Rate of Return (IRR)
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IRR • The IRR is the same as the YTM for a bond. • The IRR determines the economic rate of return for a given project.
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IRR • The internal rate of return (IRR) is that discount rate that causes the NPV of the project to equal zero. • If IRR > WACC (for a project in the same risk class as the firm), then the project is acceptable because it will return a rate of return on invested capital that is likely to be greater than the cost of funds used to invest in the project.
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IRR Decision Rule: • Accept the project if the IRR > the risk adjusted discount rate for the project.
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Formula to Calculate IRR
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IRR Example Problem: • Initial outlay = $12,000 • After-tax cash flow benefits: – Year 1 = $5,000 – Year 2 = $5,000 – Year 3 = $8,000 • Cost of Capital = 15%
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Solution Using a Financial Calculator (TI BA II Plus) CF
2ND
IRR
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CLR WORK
ENTER
-12,000 5,000 5,000 8,000
ENTER ENTER ENTER
CPT
gives 21.31%
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IRR versus NPV • Both methods use the same basic decision inputs. • The only difference is the assumed discount rate. • The IRR assumes intermediate cashflows are reinvested at IRR…NPV assumes they are reinvested at WACC – This difference, however, can produce conflicting decision results under specific conditions
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Comparing NPV and IRR • If there is more than one change in sign for the stream of cash flows in a project, for example cash outflow at time 0 (CFo), following by four years of cash inflows, then one year of cash outflows, then multiple IRR values may result – in this case the IRR cannot be used for accept/reject, or ranking decisions. • The NPV decision rule for accept/reject still works
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Example • The CEO of BigCo has just bought a fancy financial calculator and calculated the IRR and NPV of a project: His calculator is telling him that the IRR is 26 percent, but when he uses a cost of capital of 1 percent, the NPV is negative. The CEO expects that if the IRR is greater than the cost of capital then the NPV should be positive. How are the CEO’s observations possible? • Hint: Construct the NPV profile of this project.
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Example Cash flows: • C0 = -5,000 • CF1 = 4,800 • CF2 = 1,000 • CF3 = 6,000 • CF4 = -3,000 • CF5 = -4,000
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Example
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Example • The NPV profile is constructed by determining the NPV of the cash flows at different discount rates.
• This is an example of a project with more than one change of sign so we can have multiple IRR’s implying that we can’t rely on the standard result of decreasing the discount rate will increase the NPV
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Comparing NPV and IRR • For ranking projects, the NPV decision rule will always result in the best decision. WHY? Because higher NPV implies greater contribution to firm wealth – it is an absolute measure of wealth • The higher IRR project may have a lower NPV, depending on the size of the project. EG. – a 20% return on an initial investment of $1,000 would be ranked higher than a 15% return on a $1,000,000 project. 54
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Comparing NPV and IRR • The NPV method assumes all future cash flows are re-invested at the discount rate. This is appropriate because it treats the reinvestment of all future cash flows consistently, and k is the investor’s opportunity cost. • The IRR method assumes cash flows from each project are reinvested at the project’s IRR. This is inappropriate particularly when the IRR is high.
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NPV and IRR Compared Which method should be relied upon? – It depends on which reinvestment assumption is most realistic. – Most often, the NPV assumption of reinvestment at WACC is the most realistic because no rational manager would reinvest cash flows at rates lower than the firm’s cost of capital. – Projects with high IRRs are not common – to assume that future cash flows will be reinvested at the inflated IRR rate is probably wrong. 56
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Limitations of IRR Method • IRR can favor small projects with high rates of return but low NPV • IRR can give misleading results when comparing mutually exclusive projects with different lives • IRR cannot handle multiple cash flows in and out, as it gives multiple rates of return.
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Example • The cash flows for a project proposal are provided below: Determine the NPV and IRR for this project, assuming the cost of capital for the firm is 7%, and the risk of this project is similar to the risk of the company. – – – – 58
Co -5,000 Incremental after tax cash flows $1,500 N= 4 years ECF = 0 FN1 Module 6
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Solution: NPV • You can determine the PV of the benefits by using the annuity end function on your calculator: – PMT = 1,500 – N=4 – FV = 0 – I/Y = 7 – CPT PV = 5,080.82 • NPV = -5,000 + 5,080.82 = +80.82 • Conclusion: Accept project, as NPV>0 59
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Solution: IRR • We can also solve this using the annuity function: – PV = -5,000 – PMT = +1,500 – N=4 – FV = 0 – CPT I/Y = 7.71% • Conclusion: IRR > WACC Accept project
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Solution: IRR • CF 2nd clr work • • • • • •
at CFo prompt -5,000 enter down at C01 prompt + 1,500 enter down At F01 prompt 4 enter IRR CPT Answer = 7.71% Decision: Accept project as IRR > WACC
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Example • A firm is analyzing 2 mutually exclusive projects. The appropriate discount rate is 12%
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» Project A Project B Co -10,000 -10,000 CF1 +2,000 +10,000 CF2 +4,000 +3,000 CF3 +12,000 +3,000 Determine the NPV and IRR
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Project A Solution NPV NPV = -10,000 + 2,000 + 4,000 + 12,000 (1.12) (1.12)2 (1.12)3 = 3,516
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Project A Solution IRR CF 2nd clr work At Co -10,000 enter down At C01 +2,000 enter down down At C02 +4,000 enter down down At C03 +12,000 enter down down IRR CPT 26.5%
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Project B Solution NPV NPV = -10,000 + 10,000 + 3,000 + 3,000 (1.12) (1.12)2 (1.12)3 = 3,455
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Project B Solution IRR CF 2nd clr work At Co -10,000 enter down At C01 +10,000 enter down down At C02 +3,000 enter down down At C03 +3,000 enter down down IRR CPT 37.6
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Summary
Project A
NPV 3,516
IRR 26.5%
Project B
3,455
37.6%
Conflicting results!! NPV choose Project A IRR choose Project B 67
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NPV vs IRR In this example, project B yields a higher IRR because the highest cash flows are received in the early years. Remember, that the IRR method assumes that all cash flows can be invested at the IRR.
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Example • A firm is analyzing the following project: – Co -22,000 – CF1 +15,000 – CF2 +15,000 – CF3 +15,000 – CF4 +15,000 – CF5 -40,000 • Determine the NPV and IRR • The firm’s cost of capital is 10% 69
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Solution NPV NPV; Using the CF function on our calculator : NPV = +711 Conclusion: Accept project
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Solution IRR IRR: Using the IRR function on our calculator: IRR = 5.6% BUT… if we determine the PV of all of the cash flows in years 1 – 5 inclusive, discounted at 27.7%, we get a PV of $22,009. IRR = 27.7% Why do we get 2 IRR’s? There are 2 changes of signs in the cash flows (- + -) 71
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Conclusion When there are multiple changes in the sign of the cash flows, the IRR rule does not work. The NPV rule always works.
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• • • •
Part 1: Net Present Value Part 2: Risk-adjusted discount rates Part 3: Internal Rate of Return (IRR) Part 4: Payback and Discounted payback method • Part 5: Profitability Index • Part 6: Past exam questions
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Part 4
Payback and Discounted payback method
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Payback Method • The payback period is defined as the number of years required to fully recover the initial cash outlays associated with the project. • Firms will choose an arbitrary cut-off period.
Decision rule: • Reject projects whose payback period is longer than the cut-off period. 75
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Payback Method • It is often used by financial managers as one of a set of investment screens, because it gives the manager an intuitive sense of the project’s risk. • How does this method provide a measure of risk? • Projects that pay for themselves quickly are viewed as less risky.
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Payback Method • Use after tax, actual, incremental, nominal cash flows in analysis • Ignore cash flows after cut-off period • Ignore time value of money.
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Simple Payback Example • A project is under consideration with the following cash flows: – – – – –
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Initial investment = -100,000 Annual after tax cash flow benefits = 60,000 Useful life = 5 years CCA = N/A Cost of capital = 10%
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Payback Method
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Payback Method How did we determine the answer 1.7 years? After year one cash flows of 60,000 are received, there is still $40,000 of the initial $100,000 to recover. The second year expected cash flows are $60,000 for the entire year, so 40,000 should be recovered after 40,000/60,000 of the year =.6667 = .7 rounded.
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Limitations of payback period • The cash flows beyond the payback period are not considered • The payback method ignores the risk of the project cash flows and the rate of return the investors require (no discounting – no adjustment for project risk) • Choice of cut-off date is arbitrary 81
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Discounted payback Period • Defined as the number of years to fully recover the initial cash outlay in terms of discounted cash flows. • Firms will choose an arbitrary cut-off period.
Decision rule: • Reject projects whose discounted payback period is longer than the cut-off period.
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Discounted payback Period • Does consider the time value of money. • Ignores cash flows beyond the cut off date • Cutoff date is arbitrary
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Discounted Payback Example • A project is under consideration with the following cash flows: – Initial investment = -100,000 – Annual after tax cash flow benefits = 60,000 – Useful life = 5 years – CCA = N/A – Cost of capital = 10%
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Discounted Payback Example
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Discounted Payback Method • How did we come to the answer 1.9 years? • After one year, discounted cash flows of $54,545 are recovered. • Discounted cash flows of $45,455 are still required. • In year 2, discounted cash flows of $49,587 are expected. • If we expect to recover 49,587 in one year, then we expect to recover 45,455 in (45,455/49,587) years = 0.9 year • Total = 1.9 years 86
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• • • •
Part 1: Net Present Value Part 2: Risk-adjusted discount rates Part 3: Internal Rate of Return (IRR) Part 4: Payback and Discounted payback method • Part 5: Profitability Index • Part 6: Past exam questions
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Part 5
Profitability Index
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Profitability Index • Uses exactly the same decision inputs as NPV • simply expresses the relative profitability of the project’s incremental after-tax cashflow benefits as a ratio to the project’s initial cost. PI =
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PV of incremental ATCF benefits PV of initial cost of project
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Profitability Index Decision Rule
Accept all projects if PI > 1
WHY? because the PV of benefits exceeds the PV of costs. 90
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Profitability Index Advantages of this method: • Provides the dollar-to-dollar return you obtain on a project Disadvantages: • May provide no help for selecting projects under capital rationing conditions. 91
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Profitability Index (PI)
• PI is a ratio of the present value of benefits to costs. • As a pure coefficient, as long as it exceeds 1.00 the project will increase the value of the firm if accepted. • A PI of more than 1.0 indicates that the project is expected to earn a return greater than the required return. 92
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Capital Rationing • The corporate practice of limiting the amount of funds dedicated to capital investments in any one year. • Is academically illogical. – Why would a manager not invest in a project that will offer a greater return than the cost of capital used to finance it? • In the long-run could threaten a firm’s continuing existence through erosion of its competitive position.
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Capital Rationing • Practical Reasons for This Practice • The firm may have owners who do not want to raise additional external equity because it will mean ownership dilution to them • The firm may have so many great investment projects that they exceed the firm’s short-term managerial capacity to take advantage of them. 94
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Example Consider a firm that has six different capital investment proposals this year. Each project has it’s own IRR, NPV, PI and capital cost. Each project has the same risk as the firm as a whole. Assume the firm’s cost of capital is 10%. Determine which projects should be chosen based on NPV, IRR, PI assuming no capital rationing. See Example 5 in Handout #1
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Example
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Projects Ranked by NPV • Assume no capital rationing
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Projects Ranked by IRR • Assume no capital rationing
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Projects Ranked by PI • Assume no capital rationing
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Ranking of Projects In the Absence of Capital Rationing • • • • • •
Project 1 2 3 4 5
NPV C F E B D
IRR D C E F B
PI D C F E B
Capital Budget $9,369,000 $9,369,000 $9,369,000 Total NPV $679,803 $679,803 $679,803 • Clearly, in the absence of capital rationing, all three methods choose value maximizing projects and reject value-destroying projects. 100
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Example Consider a firm that has six different capital investment proposals this year. Each project has it’s own IRR, NPV, PI and capital cost. Each project has the same risk as the firm as a whole. Assume the firm’s cost of capital is 10%. The firm has a capital budget of $6,000,000. Determine which projects should be chosen based on NPV, IRR, PI See Example 6 in Handout #1 101
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Projects Ranked by NPV • Assume a capital budget of $6,000,000
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Projects Ranked by IRR • Assume a capital budget of $6,000,000
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Projects Ranked by PI • Assume a budget of $6,000,000
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Ranking of Projects Assuming a Limit on Capital Expenditures to $6,000,000 • • • •
Project PI 1 2 3
NPV
IRR
C F E
D C E
Capital Budget $5,960,000 Total NPV $735,785 •
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D C F
$5,070,000 5,030,000 $656,168 $663,824
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Conclusion • The NPV criterion produces the optimal combination of projects, when there is capital rationing.
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Part 1: Net Present Value Part 2: Risk-adjusted discount rates Part 3: Internal Rate of Return (IRR) Part 4: Payback and Discounted payback method • Part 5: Profitability Index • Part 6: Past exam questions
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Part 6
Past exam questions
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Past Exam Questions
Please note that past exam questions are to be used as a guideline and they are not updated to the newest materials.
I have not seen your exam.
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Past exam questions
Question 1
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Question 2
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Past exam questions
Question 6
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Part 1: Net Present Value Part 2: Risk-adjusted discount rates Part 3: Internal Rate of Return (IRR) Part 4: Payback and Discounted payback method • Part 5: Profitability Index • Part 6: Past exam questions
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