3 Recall the Flows of funds and decisions important to the financial manager Financing Decision Investment Decision Reinvestment Refinancing Financial Manager Financial Markets Real Assets Returns from Investment Returns to Security Holders Capital Budgeting is used to make the Investment Decision 4 Introduction
Capital Budgeting is the process of determining which real investment projects should be accepted and given an allocation of funds from the firm.
To evaluate capital budgeting processes their consistency with the goal of shareholder wealth maximization is of utmost importance.
5 Capital Budgeting Mutually Exclusive versus Independent Project
Mutually Exclusive Projects only ONE of several potential projects can be chosen e.g. acquiring an accounting system.
RANK all alternatives and select the best one.
Independent Projects accepting or rejecting one project does not affect the decision of the other projects.
Must exceed a MINIMUM acceptance criteria.
6 The Net Present Value (NPV) Rule
Net Present Value (NPV)
Total PV of future CFs - Initial Investment
1. Estimate future cash flows how much and when
2. Estimate discount rate
3. Estimate initial costs
Minimum Acceptance Criteria
Accept if NPV gt 0
Ranking Criteria Choose the highest NPV
7 NPV - An Example
Assume you have the following information on
Initial outlay -1100 Required return 10
Annual cash revenues and expenses are as follows
Year Revenues Expenses
1 1000 500
2 2000 1300
3 2200 2700
4 2600 1400
Draw a time line and compute the NPV of project X.
8 The Time Line NPV of Project X 0 1 2 3 4 Initial outlay (1100) Revenues 2000 Expenses 1300 Cash flow 700 Revenues 1000 Expenses 500 Cash flow 500 Revenues 2200 Expenses 2700 Cash flow (500) Revenues 2600 Expenses 1400 Cash flow 1200 1100.00 454.54 578.51 -375.66 819.62 377. 02 1 500 x 1.10 1 700 x 1.10 2 1 - 500 x 1.10 3 1 1200 x 1.10 4 NPV NPV -C0 PV0(Future CFs) -C0 C1/(1r) C2/(1r)2 C3/(1r)3 C4/(1r)4 ______ ______ ______ _______ _______ 377.02 gt 0 9 NPV in your HP 10B Calculator First clear previous data and check that your calculator is set to 1 P/YR CLEAR ALL The display should show 1 P_Yr Input data (based on above NPV example) INPUT Yellow Display should show CF 0 /- CFj 1100 Key in CF0 Display should show CF 1 CFj 500 Key in CF1 Display should show CF 2 CFj 700 Key in CF2 Display should show CF 3 Key in CF3 /- CFj 500 Display should show CF 4 CFj 1200 Key in CF4 I/YR Key in r 10 NPV Display should show 377.01659723 Compute NPV PRC Yellow 10 NPV Strengths and Weaknesses
Resulting number is easy to interpret shows how wealth will change if the project is accepted.
Acceptance criteria is consistent with shareholder wealth maximization.
Relatively straightforward to calculate
An improper NPV analysis may lead to the wrong choices of projects when the firm has capital rationing this will be discussed later.
11 The Payback Period Rule
How long does it take the project to pay back its initial investment
Payback Period of years to recover costs of project
Minimum Acceptance Criteria set by management
Ranking Criteria set by management
12 Discounted Payback - An Example
Initial outlay -1000
Year Cash flow Cash flow
1 200 182
2 400 331
3 700 526
4 300 205
Year discounted cash flow
Discounted payback period is just under 3 years
13 Average Accounting Return (AAR)
Also known as Accounting Rate of Return (ARR)
Method using accounting data on profits and book value of the investment
AAR Average Net Income / Average Book Value
If AAR gt some target book rate of return then accept the project
14 Average Accounting Return (AAR)
You want to invest in a machine that produces squash balls.
The machine costs 90000.
The machine will die after 3 years (assume straight line depreciation the annual depreciation is 30000).
You estimate for the life of the project
Year 1 Year 2 Year 3
Sales 140 160 200
Expenses 120 100 90
EBD 20 60 110
15 Calculating Projected NI Year 1 Year 2 Year 3 Sales 140 160 200 Expenses 120 100 90 E.B.D. Depreciation E.B.T. Taxes (40) NI 16 We calculate (i) Average NI (ii) Average book value (BV) of the investment (machine) time-0 time-1 time-2 time-3 BV of investment 90 60 30 0 gt Average BV (divide by 4 - not 3) (iii) The Average Accounting Return AAR 44.44 Conclusion If target AAR lt 44.44 gt accept If target AAR gt 44.44 gt reject 17 The Internal Rate of Return (IRR) Rule
IRR the discount rate that sets the NPV to zero
Minimum Acceptance Criteria
Accept if IRR gt required return
Ranking Criteria Select alternative with the highest IRR
Reinvestment assumption the IRR calculation assumes that all future cash flows are reinvested at the IRR
18 Internal Rate of Return - An Example Initial outlay -2200 Year Cash flow 1 800 2 900 3 500 4 1600 Find the IRR such that NPV 0 ______ _______ ______ _______ 0
(1IRR)1 (1IRR)2 (1IRR)3 (1IRR)4 19 IRR in your HP 10B Calculator First clear previous data and check that your calculator is set to 1 P/YR CLEAR ALL The display should show 1 P_Yr Input data (based on above NPV example) INPUT Yellow Display should show CF 0 /- CFj 2200 Key in CF0 Display should show CF 1 CFj 800 Key in CF1 Display should show CF 2 CFj 900 Key in CF2 Display should show CF 3 CFj 500 Key in CF3 Display should show CF 4 CFj 1600 Key in CF4 IRR/YR Display should show 23.29565668 Compute IRR CST Yellow 20 Internal Rate of Return and the NPV Profile
The NPV Profile
Discount rates NPV
IRR is between 20 and 25 -- about 23.30
If required rate of return (r) is lower than IRR gt accept the project (e.g. r 15)
If required rate of return (r) is higher than IRR gt reject the project (e.g. r 25)
21 The Net Present Value Profile Net present value Year Cash flow 0 2200 1 800 2 900 3 500 4 1600 1600.00 1126.47 739.55 419.74 159.62 Discount rate 0 72.64 2 6 10 14 18 22 IRR23.30 22 IRR Strengths and Weaknesses
IRR number is easy to interpret shows the return the project generates.
Acceptance criteria is generally consistent with shareholder wealth maximization.
Does not distinguish between investing and financing scenarios
IRR may not exist or there may be multiple IRR
Problems with mutually exclusive investments
23 IRR for Investment and Financing Projects Initial outlay 4000 Year Cash flow 1 -1200 2 -800 3 -3500 Find the IRR such that NPV 0 _______ _______ _______ 0
(1IRR)1 (1IRR)2 (1IRR)3 -1200 -800 -3500 - 4000
(1IRR)1 (1IRR)2 (1IRR)3 24 Internal Rate of Return and the NPV Profile for a Financing Project
The NPV Profile of a Financing Project
Discount rates NPV
IRR is between 10 and 15 -- about 14.37
For a Financing Project the required rate of return is the cost of financing thus
If required rate of return (r) is lower than IRR gt reject the project (e.g. r 10)
If required rate of return (r) is higher than IRR gt accept the project (e.g. r 15)
25 The NPV Profile for a Financing Project 26 Multiple Internal Rates of Return Example 1 Assume you are considering a project for which the cash flows are as follows Year Cash flows 0 -900 1 1200 2 1300 3 -1200 27 Multiple IRRs and the NPV Profile - Example 1 IRR272.25 IRR1-29.35 28 Multiple IRRs in your HP 10B Calculator First clear previous data and check that your calculator is set to 1 P/YR CLEAR ALL The display should show 1 P_Yr Input data (based on above NPV example) INPUT Yellow Display should show CF 0 /- CFj 900 Key in CF0 Display should show CF 1 CFj 1200 Key in CF1 Display should show CF 2 CFj 1300 Key in CF2 Display should show CF 3 CFj /- 1200 Key in CF3 IRR/YR Display should show 72.252175 CST Yellow Compute 1st IRR IRR/YR STO CST Yellow /- RCL Yellow 30 Compute 2nd IRR by guessing it first Display should show -29.352494 29 No or Multiple IRR Problem What to do
IRR cannot be used in this circumstance the only solution is to revert to another method of analysis. NPV can handle these problems.
How to recognize when this IRR problem can occur
When changes in the signs of cash flows happen more than once the problem may occur (depending on the relative sizes of the individual cash flows).
Examples - -- -- ---
30 Multiple Internal Rates of Return Example 2 Assume you are considering a project for which the cash flows are as follows Year Cash flows 0 -260 1 250 2 300 3 20 4 -340 31 Multiple IRRs and the NPV Profile - Example 2 IRR229.84 IRR111.52 32 Multiple Internal Rates of Return Example 3 Assume you are considering a project for which the cash flows are as follows Year Cash flows 0 660 1 -650 2 -750 3 -50 4 850 33 Multiple IRRs and the NPV Profile - Example 3 IRR18.05 IRR233.96 34 The Profitability Index (PI) Rule
Total Present Value of future CFs / Initial Investment
Minimum Acceptance Criteria Accept if PI gt 1
Ranking Criteria Select alternative with highest PI
Problems with mutually exclusive investments (to be discussed later)
May be useful when available investment funds are limited (to be discussed later).
Easy to understand and communicate
Correct decision when evaluating independent projects
38 Special situations
When projects are independent and the firm has few constraints on capital then we check to ensure that projects at least meet a minimum criteria if they do they are accepted.
NPV0 IRRhurdle rate PI1
Sometimes a firm will have plenty of funds to invest but it must choose between projects that are mutually exclusive. This means that the acceptance of one project precludes the acceptance of any others. In this case we seek to choose the one highest ranked of the acceptable projects.
If the firm has capital rationing then its funds are limited and not all independent projects may be accepted. In this case we seek to choose those projects that best use the firms available funds. PI is especially useful here.
39 Using IRR and PI correctly when projects are mutually exclusive and are of differing scales
Consider the following two mutually exclusive projects. Assume the opportunity cost of capital is 12
40 Incremental Cash Flows Solving the Problem with IRR and PI
As you can see individual IRRs and PIs are not good for comparing between two mutually exclusive projects.
However we know IRR and PI are good for evaluating whether one project is acceptable.
Therefore consider one project that involves switching from the smaller project to the larger project. If IRR or PI indicate that this is worthwhile then we will know which of the two projects is better.
Incremental cash flow analysis looks at how the cash flows change by taking a particular project instead of another project.
41 Using IRR and PI correctly when projects are mutually exclusive and are of differing scales 42 Using IRR and PI correctly when projects are mutually exclusive and are of differing scales
IRR and PI analysis of incremental cash flows tells us which of two projects are better.
Beware before accepting the better project you should always check to see that the better project is good on its own (i.e. is it better than do nothing).
43 IRR NPV and Mutually Exclusive Projects Year 0 1 2 3 4 Project A 350 50 100 150 200 Project B 250 125 100 75 50 44 IRR NPV and the Incremental Project Year 0 1 2 3 4 Project A 350 50 100 150 200 Project B 250 125 100 75 50 (A-B) The Crossover Rate IRRA-B 8.07 45 Capital Rationing
Recall If the firm has capital rationing then its funds are limited and not all independent projects may be accepted. In this case we seek to choose those projects that best use the firms available funds. PI is especially useful here.
Note capital rationing is a different problem than mutually exclusive investments because if the capital constraint is removed then all projects can be accepted together.
Analyze the projects on the next page with NPV IRR and PI assuming the opportunity cost of capital is 10 and the firm is constrained to only invest 50000 now (and no constraint is expected in future years).
46 Capital Rationing Example(All numbers are in thousands) 47 Capital Rationing Example Comparison of Rankings
NPV rankings (best to worst)
A D C B E
A uses up the available capital
Overall NPV 4545.45
IRR rankings (best to worst)
E D B A C
E D B use up the available capital
Overall NPV NPVEDB6181.82
PI rankings (best to worst)
E D C B A
E D C use up the available capital
Overall NPV NPVEDC6381.82
The PI rankings produce the best set of investments to accept given the capital rationing constraint.
48 Capital Rationing Conclusions
PI is best for initial ranking of independent projects under capital rationing.
Comparing NPVs of feasible combinations of projects would also work.
IRR may be useful if the capital rationing constraint extends over multiple periods (see project C).
49 Summary and Conclusions
Discounted Cash Flow (DCF) techniques are the best of the methods we have presented.
In some cases the DCF techniques need to be modified in order to obtain a correct decision. It is important to completely understand these cases and have an appreciation of which technique is best given the situation.
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