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Chapter 9 - Capital Budgeting Decision Criteria

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Capital Budgeting: The process of planning for purchases of long- term assets. For example: Suppose our firm must decide whether to purchase a new plastic molding machine for $125,000. How do we decide? Will the machine be profitable? Will our firm earn a high rate of return on the investment?

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Decision-making Criteria in Capital Budgeting How do we decide if a capital investment project should be accepted or rejected?

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The ideal evaluation method should: a) include all cash flows that occur during the life of the project, b) consider the time value of money, and c) incorporate the required rate of return on the project. Decision-making Criteria in Capital Budgeting

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Payback Period How long will it take for the project to generate enough cash to pay for itself? Payback period = 3.33 years 012345 8 6 7 (500) 150 150 150 150 150 150 150 150

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Is a 3.33 year payback period good? Is it acceptable? Firms that use this method will compare the payback calculation to some standard set by the firm. If our senior management had set a cut- off of 5 years for projects like ours, what would be our decision? Accept the project. Payback Period

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Drawbacks of Payback Period Projects A B Cash outlay -10,000 -10,000 Annual CF Year 1 6,000 5,000 Year 2 4,000 5,000 Year 3 3,000 0 Year 4 2,000 0 Year 5 1,000 0

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Drawbacks of Payback Period Firm cutoffs are subjective. Does not consider time value of money. Does not consider any required rate of return. Does not consider all of the project’s cash flows.

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Discounted Payback Discounts the cash flows at the firm’s required rate of return. Payback period is calculated using these discounted net cash flows. Problems: Cutoffs are still subjective. Still does not examine all cash flows.

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Discounted Payback 0 123 45 (500) 250 250 250 250 250 Discounted Discounted Year Cash FlowCF (14%) 0-500-500.00 0-500-500.00 1 250 219.30 1 year 1 250 219.30 1 year 280.70 280.70 2 250 192.37 2 years 2 250 192.37 2 years 88.33 88.33 3 250 168.74.52 years 3 250 168.74.52 years

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Discounted Payback 0 123 45 (500) 250 250 250 250 250 Discounted Discounted Year Cash FlowCF (14%) 0-500-500.00 0-500-500.00 1 250 219.30 1 year 1 250 219.30 1 year 280.70 280.70 2 250 192.37 2 years 2 250 192.37 2 years 88.33 88.33 3 250 168.74.52 years 3 250 168.74.52 years The Discounted Payback is 2.52 years

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Advantages of Payback Use free cash flow, not accounting profits Easy understood and calculate Often used as a rough screening device

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Other Methods 1) Net Present Value (NPV) 2) Profitability Index (PI) 3) Internal Rate of Return (IRR) Consider each of these decision-making criteria: All net cash flows. The time value of money. The required rate of return.

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NPV = the total PV of the annual net cash flows - the initial outlay. NPV = - IO FCF t FCF t (1 + k) t nt=1 Net Present Value

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Decision Rule: If NPV is >=0, accept. If NPV is negative, reject.

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NPV Example 0 1 2 3 4 5 (250,000) 100,000 100,000 100,000 100,000 100,000 Suppose we are considering a capital investment that costs $250,000 and provides annual net cash flows of $100,000 for five years. The firm’s required rate of return is 15%.

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Net Present Value NPV is just the PV of the annual cash flows minus the initial outflow. N = 5 I = 15 PMT = 100,000 PV of cash flows = $335,216 PV of cash flows = $335,216 - Initial outflow: ($250,000) - Initial outflow: ($250,000) = Net PV $85,216 = Net PV $85,216

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NPV with the TI BAII Plus: Select CF mode. CFo=? -250,000 ENTER C01=? 100,000 ENTER F01= 1 5 ENTER NPV I= 15 ENTER CPT You should get NPV = 85,215.51

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NPV Example Free Cash Flow Free Cash Flow Initial outlay -40,000 Year 1 15,000 Year 2 14,000 Year 3 13,000 Year 4 12,000 Year 5 11,000 12% required rate of return, what is NPV?

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NPV Example Free Cash Flow Discount Factor PV Free Cash Flow Discount Factor PV Year 1 $15,000.893 $13,395 Year 2 14,000.797 11,158 Year 3 13,000.712 9,256 Year 4 12,000.636 7,632 Year 5 11,000.567 6,237 Present Value of free cash flow $47,678 Initial outlay -40,000 Net present value $7,678

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NPV Example Financial calculator: select CF mode Enter CF0 – CF5 one by one Fre = 1 I = 12 NPV = $7,678

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Features of NPV Deals with free cash flow Consider the time value of money Acceptance of a project using this criterion increases the value of firm

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Profitability Index PI = IO FCF t (1 + k) n t=1 t NPV = - IO FCF t (1 + k) t n t=1

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Decision Rule: If PI is greater than or equal to 1, accept. If PI is less than 1, reject. Profitability Index

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PI Example Free Cash Flow Free Cash Flow Initial outlay -40,000 Year 1 15,000 Year 2 14,000 Year 3 13,000 Year 4 12,000 Year 5 11,000 12% required rate of return, what is PI?

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PI Example Free Cash Flow Discount Factor PV Free Cash Flow Discount Factor PV Year 1 $15,000.893 $13,395 Year 2 14,000.797 11,158 Year 3 13,000.712 9,256 Year 4 12,000.636 7,632 Year 5 11,000.567 6,237 Present Value of free cash flow $47,678 Initial outlay -40,000 PI = 47,678 / 40,000 = 1.19 PI = 47,678 / 40,000 = 1.19

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Yield the same accept-reject decision NPV: absolute dollar PI: relative measure Compare NPV and PI

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Example: Project A: NPV = $10 Project B: NPV = $20 Which one is relatively better from the perspective of profitability? Compare NPV and PI

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Example: It depends on your initial outlay. Suppose initial outlay of A = $50 Suppose initial outlay of B = $150 PI of A = (10 + 50) / 50 = 1.2 PI of B = (20 + 150) / 150 = 1.13 A’s profitability is higher Compare NPV and PI

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Internal Rate of Return (IRR) IRR: The return on the firm’s invested capital. IRR is simply the rate of return that the firm earns on its capital budgeting projects.

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Internal Rate of Return (IRR) NPV = - IO FCF t (1 + k) t n t=1 n t=1 IRR: = IO FCF t (1 + IRR) t

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Internal Rate of Return (IRR) IRR is the rate of return that makes the PV of the cash flows equal to the initial outlay. This looks very similar to our Yield to Maturity formula for bonds. In fact, YTM is the IRR of a bond. n t=1 IRR: = IO FCF t (1 + IRR) t

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Calculating IRR Looking again at our problem: The IRR is the discount rate that makes the PV of the projected cash flows equal to the initial outlay. 0 1 2 3 4 5 (250,000) 100,000 100,000 100,000 100,000 100,000

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IRR with your Calculator IRR is easy to find with your financial calculator. Just enter the cash flows as you did with the NPV problem and solve for IRR. You should get IRR = 28.65%!

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IRR Decision Rule: If IRR is greater than or equal to the required rate of return, accept. If IRR is less than the required rate of return, reject.

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Example A B C A B C Initial outlay -10,000 -10,000 -10,000 FCF year 1 3,362 0 1,000 FCF year 2 3,362 0 3,000 FCF year 3 3,362 0 6,000 FCF year 4 3,362 13,605 7,000 Required rate of return = 10% Will we accept these projects?

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Example IRR for A = 13% >10% accept IRR for A = 13% >10% accept IRR for B = 8% < 10% reject IRR for B = 8% < 10% reject IRR for C = 19.04% > 10% accept IRR for C = 19.04% > 10% accept

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Summary Problem Enter the cash flows only once. Find the IRR. Using a discount rate of 15%, find NPV. Add back IO and divide by IO to get PI. 0 1 2 3 4 5 (900) 300 400 400 500 600

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Summary Problem IRR = 34.37%. Using a discount rate of 15%, NPV = $510.52. NPV = $510.52. PI = 1.57. 0 1 2 3 4 5 (900) 300 400 400 500 600

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Relationships of Methods If NPV is “+”, IRR must be greater than the required rate of return. Also, PI is >1. All three discounted cash flow criteria are consistent and give similar accept-reject decision.

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Relationships of Methods NPV: assumes cash flow can be reinvested at the project’s required rate of return IRR: assumes cash flow can be reinvested at the project’s IRR NPV is superior to IRR As discount rate increases, PNV drops

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One Drawback of IRR IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +) Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +)

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IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +) Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +) 0 1 2 3 4 5 (500) 200 100 (200) 400 300 1 2 3

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Modified Internal Rate of Return (MIRR) IRR assumes that all cash flows are reinvested at the IRR. MIRR provides a rate of return measure that assumes cash flows are reinvested at the required rate of return.

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MIRR Steps: Calculate the PV of the cash outflows. Using the required rate of return. Calculate the FV of the cash inflows at the last year of the project’s time line. This is called the terminal value (TV). Using the required rate of return. MIRR: the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes: PV outflows = PV inflows

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MIRR Using our time line and a 15% rate: PV outflows = (900). FV inflows (at the end of year 5) = 2,837. MIRR: FV = 2837, PV = (900), N = 5. Solve: I = 25.81%. 0 1 2 3 4 5 (900) 300 400 400 500 600

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Using our time line and a 15% rate: PV outflows = (900). FV inflows (at the end of year 5) = 2,837. MIRR: FV = 2837, PV = (900), N = 5. Solve: I = 25.81%. Conclusion: The project’s IRR of 34.37% assumes that cash flows are reinvested at 34.37%. Assuming a reinvestment rate of 15%, the project’s MIRR is 25.81%. MIRR

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Decision rule: If MIRR is greater than or equal to the required rate of return, accept. If MIRR is less than the required rate of return, reject. MIRR

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Find profitable projects, and make accurate cash flow forecasting Correctly evaluate them Choose one as main criterion Use others as robustness check How to Use Evaluating Criteria

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