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? 5 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000

Capital Budgeting Methods What is the payback for Project A? 6 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000

Capital Budgeting Methods ,500 -6,500 3,500 -3,000 3, ,500(10,000) Cumulative CF What is the payback for Project A? 7 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000

Capital Budgeting Methods Payback in 2.9 years 2.9 years What is the payback for Project A? P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010, ,500 -6,500 3,500 -3,000 3, ,500(10,000) Cumulative CF ,500 -6,500 3,500 -3,000 3, ,500(10,000) Cumulative CF

Capital Budgeting Methods What is the payback for Project B? ,500 (10,000) P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000

Payback in 3.4 years 3.4 years Capital Budgeting Methods What is the payback for Project B? ,500 -6,500 3,500 -3,000 3, ,500(10,000) Cumulative CF P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000

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

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. Net Present Value Capital Budgeting Methods 12

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 of cost of project. Net Present Value NPV = PV of Inflows - Initial Investment NPV = + + – Initial Investment CF 1 (1+ k) 1 CF 2 (1+ k) 2 …. CF n (1+ k ) n Capital Budgeting Methods 13

What is the NPV for Project B? 14 P R O J E C T Time A B 0(10,000) (10,000) 13, , ,5004,600 43,50010,000 k=10% ,60010,000(10,000)

455 $500 (1.10) 1 What is the NPV for Project B? 15 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000 k=10% ,60010,000(10,000)

413 $500 (1.10) 2 What is the NPV for Project B? 16 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010, k=10% ,60010,000(10,000)

3,456 $4,600 (1.10) 3 What is the NPV for Project B? 17 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010, $500 (1.10) k=10% ,60010,000(10,000)

6,830 $10,000 (1.10) 4 What is the NPV for Project B? 18 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000 3,456 $4,600 (1.10) $500 (1.10) k=10% ,60010,000(10,000)

$11,154 What is the NPV for Project B? 19 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000 6,830 3, k=10% ,60010,000(10,000)

PV Benefits > PV Costs $11,154 > $ 10,000 What is the NPV for Project B? 20 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000 $11,154 6,830 3, k=10% ,60010,000(10,000)

NPV > $0 $1,154 > $0 - $10,000 = $1,154 = NPV What is the NPV for Project B? 21 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000 PV Benefits > PV Costs $11,154 > $ 10,000 $11,154 6,830 3, k=10% ,60010,000(10,000)

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

NPVIRR P/YR CF N I/Y PV PMT FV Key used to enter expected cash flows in order of their receipt. Note: 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)

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

NPVIRR P/YR CF N I/Y PV PMT FV Financial Calculator: Additional Keys used to enter Cash Flows and compute the Net Present Value (NPV) 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. 26 NPVIRR P/YR CF N I/Y PV PMT FV P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000

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

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

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

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

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

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

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

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

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

NPV Decision Rule Accept the project if the NPV is greater than or equal to 0. Example: A = NPV A = $1,095 B = NPV B = $1,154 > 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 A IRR A B IRR B 500 (1+k) 1 NPV B = 0 = (1+k) (1+k) (1+k) ,000 k =.135 = 13.5% = IRR B 38 NPV A = 0 =(3,500 x ) - 10,000 1 (1 + k) k k =.1496 = 14.96% = IRR A

Calculate the IRR for Project B with calculator. 39 NPVIRR P/YR CF N I/Y PV PMT FV P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000

Enter CFs as for NPV NPVIRR P/YR CF N I/Y PV PMT FV Calculate the IRR for Project B with calculator. IRR = 13.5% 40 P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000 IRR CPT

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% A = 14.96% IRR A = 14.96% B = 13.50% IRR B = 13.50% > 10% Accept Accept 41

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. –Assumes cash inflows are reinvested at k. –MIRR avoids the problem of multiple IRRs (described later). PV outflow = TV inflows (1 + MIRR) n 42

What is the MIRR for Project B? P R O J E C T Time A B 0(10,000.) (10,000.) 13, , ,5004,600 43,50010,000 k=10% ,600 10,000 (10,000) 10,000 10,000(1.10) 0 10,000 4,600(1.10) 1 500(1.10) 2 500(1.10) 3 5, ,331 10,000 = 16,331 (1 + MIRR) 4 10,000/(1.10) 0 MIRR =.1305 = 13.05% 43

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

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

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

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

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

NPV/IRR Decision Rules 49 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.

10%5% 0 Cost of Capital NPVNPV 6,000 3,000 20%15% Net Present Value Profile Graphs the Net Present Value of the project with different required rates Intersects the X axis at the IRR Project A 50 P R O J E C T Time A B 0(10,000) (10,000) 13, , ,5004,600 43,50010,000

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

10%5% 0 Cost of Capital NPVNPV 6,000 3,000 20%15% Net Present Value Profile Graphs the Net Present Value of the project with different required rates Intersects the X axis at the IRR P R O J E C T Time A B 0(10,000) (10,000) 13, , ,5004,600 43,50010,000 Project B 52

10%5% 0 Cost of Capital NPVNPV 6,000 3,000 20%15% Project B Crossover point Project A There is a ranking conflict between NPV and IRR to the left of the crossover point. Crossover Point 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 exceeding the capital budget limit. 54

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 56 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%. Standard Deviation Mean, or expected value CV= = =.3333, or 33.33%

Measurement of Project Risk 57 Step 2: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. (w x x E(R x )) + (w y x E(R y )) = (.10 x.0571) + (.90 x.06) = =.05971, or 5.971% E(R p ) =

Measurement of Project Risk 58 Step 3: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 [w x 2 σ x 2 + w y 2 σ y 2 + 2w x w y r xy σ x σ y ] 1/2 = [(.10 2 )( ) + (.90 2 )(.02 2 ) + (2)(.10)(.90)(0.0)(.0289)(02)] 1/2 = [(.01)( ) + (.81)(.0004) + 0] 1/2 =.0182, or 1.82% = [ ] 1/2 = [ ] 1/2 σ p =

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

Measurement of Project Risk Step 5: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. 60 CV without YChange in CVCV with Y 33.33% %

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 negative cash flows, in years 1 and 2, affect Project B’s NPV? Project B should be rejected in this case. 63 (582) 6,830 3, k=10% ,500 (10,000)

Multiple IRRs Some 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 65 Note: When k =.25, the NPV = 0

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 66 Note: When k = 4.00, the NPV also = 0 THIS PROJECT HAS TWO IRRS!!!

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 pp –Project Cheap Talk has a 3-year life, with an NPV of $4,424. –Project Rolles Voice has a 12-year life, with an NPV of $4,

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. 3,324 12,121 2,497 1, ,424 k=10% 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 73 Project Rolles VoiceProject Rolles Voice – $4,510 ((1-(1.1) -12 ) /.1) –= $ Project Cheap TalkProject Cheap Talk – $4,244 ((1-(1.1) -3 ) /.1) –= $