Capital Budgeting Decision Methods

Capital Budgeting Decision Methods 1

Learning Objectives The capital budgeting process. Calculation of payback, NPV, IRR, and MIRR for proposed projects. Capital rationing. Measurement of risk in capital budgeting and how to deal with it. 2

The Capital Budgeting Process Capital Budgeting is the process of evaluating proposed investment projects for a firm. Managers must determine which projects are acceptable and must rank mutually exclusive projects by order of desirability to the firm. 3

The Accept/Reject Decision Four methods: Payback Period years to recoup the initial investment Net Present Value (NPV) change in value of firm if project is under taken Internal Rate of Return (IRR) projected percent rate of return project will earn Modified Internal Rate of Return (MIRR) 4

Capital Budgeting Methods Consider Projects A and B that have the following expected cashflows? P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 5

Capital Budgeting Methods What is the payback for Project A? P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 6

Capital Budgeting Methods What is the payback for Project A? P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) Cumulative CF 3,500-6,500 3,500-3,000 3,500 +500 3,500 7

Capital Budgeting Methods What is the payback for Project A? P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 Payback in 2.9 years 0 1 2 3 4 (10,000) Cumulative CF 3,500-6,500 3,500-3,000 3,500 +500 3,500 8

Capital Budgeting Methods What is the payback for Project B? P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 (10,000) 0 1 2 3 4 500 500 4,600 10,000 9

Capital Budgeting Methods What is the payback for Project B? P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 Payback in 3.4 years 0 1 2 3 4 (10,000) Cumulative CF 500-9,500 500-9,000 4,600-4,400 10,000 +5,600 10

Payback Decision Rule Accept project if payback is less than the company s predetermined maximum. If company has determined that it requires payback in three years or less, then you would: accept Project A reject Project B 11

Capital Budgeting Methods Net Present Value Present Value of all costs and benefits (measured in terms of incremental cash flows) of a project. Concept is similar to Discounted Cashflow model for valuing securities but subtracts the cost of the project. 12

What is the NPV for Project B? k=10% P R O J E C T Time A B 0 (10,000) (10,000) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) 500 500 4,600 10,000 14

What is the NPV for Project B? k=10% P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) 455 500 500 4,600 10,000 $500 (1.10) 1 15

What is the NPV for Project B? k=10% P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) 455 413 500 500 4,600 10,000 $500 (1.10) 2 16

What is the NPV for Project B? k=10% P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) 455 413 3,456 500 500 4,600 10,000 $500 (1.10) 2 $4,600 (1.10) 3 17

What is the NPV for Project B? k=10% P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) 455 413 3,456 6,830 500 500 4,600 10,000 $500 (1.10) 2 $4,600 (1.10) 3 $10,000 (1.10) 4 18

What is the NPV for Project B? k=10% P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) 455 413 3,456 6,830 $11,154 500 500 4,600 10,000 PV Benefits > PV Costs $11,154 > $ 10,000 20

What is the NPV for Project B? k=10% P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) 500 500 4,600 10,000 455 413 3,456 6,830 $11,154 PV Benefits > PV Costs $11,154 > $ 10,000 - $10,000 = $1,154 = NPV NPV > $0 $1,154 > $0 21

Financial Calculator: Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV) 22

Financial Calculator: Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV) CF NPV P/YR IRR N I/Y PV PMT FV Key used to enter expected cash flows in order of their receipt. Note: the initial investment (CF 0 ) must be entered as a negative number since it is anoutflow. 23

Financial Calculator: Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV) CF NPV P/YR IRR N I/Y PV PMT FV Key used to calculate the net present value of the cashflows that have been entered in the calculator. 24

Financial Calculator: Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV) CF NPV P/YR IRR N I/Y PV PMT FV Key used to calculate the internal rate of return for the cashflows that have been entered in the calculator. 25

Calculate the NPV for Project B with calculator. CF NPV P/YR IRR N I/Y PV PMT FV P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 26

Calculate the NPV for Project B with calculator. CF 0 = -10,000 Keystrokes for TI BAII PLUS: CF 10000 +/- ENTER CF NPV P/YR IRR N I/Y PV PMT FV 27

Calculate the NPV for Project B with calculator. C01 = 500 CF NPV P/YR IRR N I/Y PV PMT FV 500 ENTER Keystrokes for TI BAII PLUS: CF 10000 +/- ENTER 28

Calculate the NPV for Project B with calculator. F01 = 2 CF NPV P/YR IRR N I/Y PV PMT FV Keystrokes for TI BAII PLUS: CF 10000 +/- ENTER 500 ENTER 2 ENTER F stands for frequency. Enter 2 since there are two adjacent payments of 500 in periods 1 and 2. 29

Calculate the NPV for Project B with calculator. Keystrokes for TI BAII PLUS: C02 = 4600 CF NPV P/YR IRR CF 10000 +/- ENTER 500 ENTER 2 ENTER 4600 ENTER N I/Y PV PMT FV 30

Calculate the NPV for Project B with calculator. Keystrokes for TI BAII PLUS: F02 = 1 CF 10000 +/- ENTER CF NPV P/YR IRR N I/Y PV PMT FV 500 ENTER 2 ENTER 4600 ENTER 1 ENTER 31

Calculate the NPV for Project B with calculator. Keystrokes for TI BAII PLUS: C03 = 10000 CF NPV P/YR IRR N I/Y PV PMT FV CF 10000 +/- ENTER 500 ENTER 2 ENTER 4600 ENTER 1 ENTER 10000 ENTER 32

Calculate the NPV for Project B with calculator. Keystrokes for TI BAII PLUS: F03 = 1 CF NPV P/YR IRR N I/Y PV PMT FV CF 10000 +/- ENTER 500 ENTER 2 ENTER 4600 ENTER 1 ENTER 10000 ENTER 1 ENTER 33

Calculate the NPV for Project B with calculator. I = 10 Keystrokes for TI BAII PLUS: NPV 10 ENTER CF NPV P/YR IRR N I/Y PV PMT FV k = 10% 34

Calculate the NPV for Project B with calculator. NPV = 1,153.95 Keystrokes for TI BAII PLUS: NPV 10 ENTER CF NPV P/YR IRR CPT N I/Y PV PMT FV The net present value of Project B = $1,154 as we calculated previously. 35

NPV Decision Rule Accept the project if the NPV is greater than or equal to 0. Example: NPV A = $1,095 NPV B = $1,154 > 0 > 0 Accept Accept If projects are independent, accept both projects. If projects are mutually exclusive, accept the project with the higher NPV. 36

Capital Budgeting Methods IRR (Internal Rate of Return) IRR is the discount rate that forces the NPV to equal zero. It is the rate of return on the project given its initial investment and future cash flows. The IRR is the rate earned only if all CFs are reinvested at the IRR rate. 37

Calculate the IRR (through trial and error) IRR A 1 - k 1 (1 + k) 4 NPV A = 0 =(3,500 x ) - 10,000 IRR B 500 k =.1496 = 14.96% = IRR A NPV B = 0 = + 500 + 4600 + 10000-10,000 (1+k) 1 (1+k) 2 (1+k) 3 (1+k) 4 k =.135 = 13.5% = IRR B 38

Calculate the IRR for Project B with calculator. CF NPV P/YR IRR N I/Y PV PMT FV P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 39

Calculate the IRR for Project B with calculator. IRR = 13.5% CF NPV P/YR IRR N I/Y PV PMT FV P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 Enter CFs as for NPV IRR CPT 40

IRR Decision Rule Accept the project if the IRR is greater than or equal to the required rate of return (k). Reject the project if the IRR is less than the required rate of return (k). Example: k = 10% IRR A = 14.96% > 10% > 10% Accept Accept 41 IRR B = 13.50%

Capital Budgeting Methods MIRR (Modified Internal Rate of Return) This is the discount rate which causes the project s PV of the outflows to equal the project s TV (terminal value) of the inflows. PV outflow = TV inflows (1 + MIRR) n Assumes cash inflows are reinvested at k, the cost of capital. MIRR avoids the problem of multiple IRRs (described later). 42

What is the MIRR for Project B? k=10% P R O J E C T Time A B 0 (10,000.) (10,000.) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 1 2 3 4 (10,000) (10,000)/(1.10) 0 500 500 4,600 10,000 500(1.10) 3 500(1.10) 2 4,600(1.10) 1 10,000(1.10) 0 10,000 5,060 (10,000) 10,000 = 16,331 (1 + MIRR) 4 605 666 16,331 43 MIRR =.1305 = 13.05%

Calculate the MIRR for Project B with calculator. Step 1. Calculate NPV using cash inflows Keystrokes for TI BAII PLUS: CF 0 +/- ENTER 500 ENTER 2 ENTER 4600 ENTER CF NPV P/YR IRR 1 ENTER N I/Y PV PMT FV 10000 ENTER 1 ENTER 44

Calculate the MIRR for Project B with calculator. Step 1. Calculate NPV using cash inflows Keystrokes for TI BAII PLUS: NPV = 11,154 NPV 10 ENTER CF NPV P/YR IRR CPT N I/Y PV PMT FV The net present value of Project B cash inflows = $11,154 (use as PV) 45

Calculate the MIRR for Project B with calculator. Step 2. Calculate FV of cash inflows using previous NPV This is the Terminal Value Calculator Enter: N = 4 I/YR = 10 PV = -11154 PMT = 0 CPT FV =? FV = 16,331 CF NPV P/YR IRR N I/Y PV PMT FV 46

Calculate the MIRR for Project B with calculator. Step 3. Calculate MIRR using PV of outflows and calculated Terminal Value. Calculator Enter: N = 4 PV = -10000 PMT = 0 FV = 16331 CPT I/YR =?? MIRR 13.05 CF NPV P/YR IRR N I/Y PV PMT FV 47

Calculate NPV and IRR for Project A NPV = $1,094.53 IRR = 14.96% Which project(s) should the firm accept? NPV IRR A $1,095 14.96% B $1,154 13.5% 48

NPV/IRR Decision Rules IRR Project A > IRR Project B NPV Project B > NPV Project A If projects A & B are independent, accept both projects If projects A & B are mutually exclusive, there is a ranking conflict. 49

Net Present Value Profile Graphs the Net Present Value of the project with different required rates 6,000 N P V 3,000 Project A P R O J E C T Time A B 0 (10,000) (10,000) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 5% Cost of Capital 10% 15% 20% Intersects the X axis at the IRR 50

Risk in Capital Budgeting Project risk needs to be considered in comparing projects with different levels of risk. The discount rate can be adjusted for risk when NPV is used to evaluate projects. The hurdle rate can be adjusted when IRR is used to evaluate projects. 51

Net Present Value Profile Graphs the Net Present Value of the project with different required rates 6,000 N P V 3,000 Project B P R O J E C T Time A B 0 (10,000) (10,000) 1 3,500 500 2 3,500 500 3 3,500 4,600 4 3,500 10,000 0 5% 10% 15% Cost of Capital 20% Intersects the X axis at the IRR 52

Crossover Point There is a ranking conflict between NPV and IRR to the left of the crossover point. N P V 6,000 Project B Crossover point 3,000 Project A 0 Cost of Capital 5% 10% 15% 20% 53

What is capital rationing? Capital rationing is the practice of placing a dollar limit on the total size of the capital budget. This practice may not be consistent with maximizing shareholder value but may be necessary for other reasons. Choose between projects by selecting the combination of projects that yields the highest total NPV without 54 exceeding the capital budget limit.

Measurement of Project Risk Calculate the coefficient of variation of returns of the firm s asset portfolio with the project and without it. This can be done by following a five step process. Observe the following example. 55

Measurement of Project Risk Step 1: Find the CV of the Existing Portfolio Assume Company X has an existing rate of return of 6% and standard deviation of 2%. CV= Standard Deviation Mean, or expected value =.02.06 =.3333, or 33.33% 56

Measurement of Project Risk Step 2: Find the Expected return of the New Portfolio (Existing plus Proposed) Assume the New Project (Y) has an IRR of 5.71% and a Standard Deviation of 2.89% Assume further that Project Y will account for 10% of X s overall investment. E(R p ) = (w x x E(R x )) + (w y x E(R y )) = (.10 x.0571) + (.90 x.06) =.00571 +.05400 =.05971, or 5.971% 57

Measurement of Project Risk Step 3: Find the Standard Deviation of the New Portfolio (Existing plus Proposed). Assume the proposed is uncorrelated with the existing project. r xy = 0 σ [w x2 σ x2 + w y2 σ y2 + 2w x w y r xy σ x σ y ] 1/2 p = = [(.10 2 )(.0289 2 ) + (.90 2 )(.02 2 ) + (2)(.10)(.90)(0.0)(.0289)(02)] 1/2 = [(.01)(.000835) + (.81)(.0004) + 0] 1/2 = [.00000835 +.000324] 1/2 = [.00033235] 1/2 =.0182, or 1.82% 58

Measurement of Project Risk Step 4: Find the CV of the New Portfolio (Existing plus Proposed) CV= Standard Deviation Mean, or expected value =.0182.05971 =.3048, or 30.48% 59

Measurement of Project Risk Step 5: Compare the CV of the portfolio with and without the Proposed Project. The difference between the two coefficients of variation is the measure of risk of the capital budgeting project. CV without Y CV with Y Change in CV 33.33% 30.48% -2.85 60

Comparing risky projects using risk adjusted discount rates (RADRs) Firms often compensate for risk by adjusting the discount rate used to calculate NPV. Higher risk, use a higher discount rate. Lower risk, use a lower discount rate The risk adjusted discount rate (RADR) can also be used as a risk adjusted hurdle rate for IRR comparisons. 61

Non-simple Projects Non-simple projects have one or more negative future cash flows after the initial investment. 62

Non-simple projects How would a negative cash flow in year 4 affect Project Z s NPV? k=10% 0 1 2 3 4 (10,000) 5,000 5,000 5,000-6,000 4,545 4,132 3,757-4,098 8,336 - $10,000 = -$1,664 NPV Project Z should be rejected in this case. 63

Multiple IRRs Some non-simple projects may have more than one discount rate that results in an NPV of zero (IRRs). Example: Cash Flows: t o : (160,000) t 1 : 1,000,000 t 2 : (1,000,000) 64

Multiple IRRs When k=25% $1,000,000 - $1,000,000 - $160,000 (1+.25) 1 (1+.25) 2 = $800,000 - $640,000 - $160,000 NPV= $0 Note: When k =.25, the NPV = 0 65

Multiple IRRs When k=400% $1,000,000 - $1,000,000 - $160,000 (1+4.00) 1 (1+4.00) 2 = $200,000 - $40,000 - $160,000 NPV = 0 Note: When k = 4.00, the NPV also = 0 THIS PROJECT HAS TWO IRRS!!! 66

Multiple IRRs Non-simple projects may have, but do not have to have, as many IRRs as there are sign changes. If a project has more than one IRR, use the NPV method for project accept/reject decisions. 67

Mutually Exclusive Projects With Unequal Lives Mutually exclusive projects with unequal project lives can be compared by using two methods: Replacement Chain Equivalent Annual Annuity 68

Replacement Chain Approach Assumes each project can be replicated until a common period of time has passed, allowing the projects to be compared. Example Project Cheap Talk has a 3-year life, with an NPV of $4,424. Project Rolles Voice has a 12-year life, 69 with an NPV of $4,510.

Replacement Chain Approach Project Cheap Talk could be repeated four times during the life of Project Rolles Voice. The NPVs of Project Cheap Talk, in years t 3, t 6, and t 9,are discounted back to year t 0. 70

Replacement Chain Approach The NPVs of Project Cheap Talk, in years t 3, t 6, and t 9, are discounted back to year t 0, which results in an NPV of $12,121. k=10% 0 3 6 9 4,424 4,424 4,424 4,424 3,324 2,497 1,876 12,121 71

Equivalent Annual Annuity Amount of the annuity payment that would equal the same NPV as the actual future cash flows of a project. EAA = NPV PVIFA k,n 72

Equivalent Annual Annuity Project Cheap Talk $4,244 ((1-(1.1) -3 ) /.1) = $1778.96 Project Rolles Voice $4,510 ((1-(1.1) -12 ) /.1) = $661.90 73