Capital Budgeting Decision-making Criteria Payback Period Discounted Payback Net Present Value (NPV) Internal Rate of Return (IRR) Modified Internal Rate of Return (MIRR)

Capital Budgeting: the process of planning for purchases of long-term assets 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?

Decision-making Criteria in Capital Budgeting The Ideal Evaluation Method should: Include all cash flows that occur during the life of the project Consider the time value of money Incorporate the required rate of return on the project

Payback Period How long will it take for the project to generate enough cash to pay for itself? 1 2 3 4 5 8 6 7 (500) 150 150 150 150 150 150 150 150

It takes more than 3, but less than 4 years Payback Period (PB) Cumulative Years Cash Flow Cash Flow -500 1 150 150 2 150 300 3 150 450 4 150 600 5 150 750 6 150 900 7 150 1050 8 150 1200 It takes more than 3, but less than 4 years

Payback Period (Continued) To find the fraction of the 4th year, we first assume that cash flows are evenly distributed throughout the year Payback = Number of Full Years + [(Initial Investment – Cumulative Cash Flow at the end of Last Full Year) / The Next Year’s Cash Flow] Payback = 3 + (500 – 450) / 150 = 3.33 years

Payback Period (Continued) 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

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

Drawbacks of Payback Period (Continued) Does not consider all of the project’s cash flows. This project is clearly unprofitable, but we would accept it based on a 4-year payback criterion! 1 2 3 4 5 8 6 7 (500) 150 150 150 150 150 (300) 0 0

Discounted Payback (DPB) 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

Discounted Payback – Example 1 2 3 4 5 (500) 250 250 250 250 250 Cumulative Year Cash Flow PVCIF (14%) PVCIF 0 -500 -500.00 0.00 1 250 219.30 219.30 2 250 192.37 411.67 3 250 168.74 580.41 Payback = 2 + [(500 – 411.67) / 168.74] = 2.52 years

Net Present Value (NPV) Profitability Index (PI) Other Methods Net Present Value (NPV) Profitability Index (PI) Internal Rate of Return (IRR) Each of these decision-making criteria: Examines all net cash flows Considers the time value of money Considers the required rate of return

Net Present Value (NPV) NPV = the total PV of the annual net cash flows – the initial outlay. Where, FCF is the Free Cash Flow k is the required return t is the time subscript Decision Rule: If NPV is positive, accept If NPV is negative, reject

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

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 IRR is the rate of return that makes the PV of the cash flows equal to the initial outlay or NPV = 0 This looks very similar to our Yield to Maturity formula for bonds. In fact, YTM is the IRR of a bond

Internal Rate of Return (IRR) (Continued) 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

Internal Rate of Return (IRR) (Continued) 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

Internal Rate of Return (IRR) (Continued) We know that the IRR is the discount rate that makes the PV of the projected cash flows equal to the initial outlay or NPV = 0 Above table shows a trial and error procedure is applied to determine the IRR. Using different discount rates we check if NPV = 0

Internal Rate of Return (IRR) (Continued)

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

Modified Internal Rate of Return (MIRR) Calculate the PV of the cash outflows (PVCOF) using the required rate of return – this is usually the investment amount Calculate the FV of the cash inflows (FVCIF) at the last year of the project’s time line. This is also called the terminal value (TV) Using the required rate of return MIRR is the growth rate of money from initial investment to terminal value over the life of the investment N I/Y P/Y PV PMT FV MODE Project Life MIRR 1 -Investment (PVCOF) Terminal Value (FVCIF)

Modified Internal Rate of Return (MIRR) (Continued) Finding FV of Uneven Cash Flows: Cumulate CF one year at a time taking FV into account Find FV of each CF at the end of project life and then sum FVs Use of NPV function (faster): First, find the PVCIF (NPV) (exclude initial investment) using required return. Second, change the sign of NPV and store it in PV (now a single cash flow as PV of all cash inflows) to find FV at the end of project life