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**B280F Introduction to Financial Management**

Lecture 6 Capital-Budgeting Decision Criteria By Charles Chiu, PhD, CFA

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**What is Capital Budgeting?**

The list of planned investment projects. Capital budgeting is the process of analyzing alternative long term investments and making long-term investment decisions.

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**About Capital Budgeting Decisions**

Outcome is uncertain. Large amounts of money are usually involved. Investment involves a long-term commitment. Decision may be difficult or impossible to reverse. Capital budgeting: Analyzing alternative long- term investments and deciding which assets to acquire or sell.

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**Types of Investment Decisions**

Selection decisions concerning proposed projects such as investments in long-term assets. i.e., property, plant, and equipment, or resource commitments in the form of new product development, market research, re-funding of long-term debt, and introduction of a computer. Replacement decisions such as replacement of existing facilities with new facilities.

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**Limited Investment Funds**

I will choose the project with the most profitable return on available funds. ? Plant Expansion New Equipment Office Renovation Limited Investment Funds

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**Decision Process Develop and rank all investment projects**

Authorize projects based on: Government regulation Production efficiency Capacity requirements NPV 4

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**Nonfinancial Considerations**

Employee working conditions Environmental concerns Corporate image Employee morale Product quality

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**How do we decide if a capital investment project should be accepted or rejected?**

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**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, and incorporate the required rate of return on the project.

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**Decision-making Criteria in Capital Budgeting**

Payback Period Discounted Payback Period Net Present Value (NPV) Profitability Index (PI) Internal Rate of Return (IRR) Modified Internal Rate of Return (MIRR)

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Decision Rule All of these techniques attempt to compare the costs and benefits of a project The over-riding rule of capital budgeting is to accept all projects for which the cost is less than, or equal to, the benefit: Accept if: Cost £ Benefit Reject if: Cost > Benefit

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Payback Period How long will it take for the project to generate enough cash to pay for itself? The payback period measures the length of time to recover the amount of initial investment. It is computed by dividing the initial investment by the cash inflows through increased revenues or cost savings.

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**Example initial investment cost $18,000**

Assume: Cost of investment $18,000 Annual free cash flows $ 3,000 Payback period = initial investment cost $18,000 increased revenues or cost savings $ 3,000 = = 6 years Decision rule: Choose the project with the shorter payback period, because the shorter the payback period, the less risky the project, and the greater the liquidity.

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**Consider two projects whose free cash inflows are not even**

Consider two projects whose free cash inflows are not even. Assume each project costs $1,000. When cash inflows are not even, the payback period has to be found by trial and error.

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**The payback period of project A is 4 years. **

($1,000 = $100 + $200 + $300 + $400 ) The payback period of project B is: ($1000 = $500 + $400 + $100) or The payback period of project B is 2.33 years. $100 $300 = 0.33 years. Project B is the project of choice in this case, since it has the shorter payback period.

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**Advantages Shortcomings**

It deals with cash flows rather than accounting profits and therefore focuses on the true timing of the project’s benefits and costs. It is simple to compute and easy to understand. It can be used as a rough screening device, eliminating projects whose returns do not materialize until later years. Shortcomings It ignores the time value of money. It does not consider any required rate of return It ignores the impact of cash inflows received after the payback period

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**Discounted Payback Period**

Discounts the cash flows at the firm’s required rate of return. Payback period is calculated using these discounted net cash flows.

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**Discounted Payback Period**

1 2 3 4 5 (500) Discounted Year Cash Flow CF (14%) year 280.70 years 88.33 years

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Net Present Value Net present value (NPV) is the excess of the present value (PV) of cash inflows generated by the project over the amount of the initial outlay (IO): Advantages It recognizes the time value of money. It is easy to compute whether the cash flows form an annuity or vary from period to period

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Computation Choose a discount rate – the minimum required rate of return. Calculate the present value of cash inflows. Calculate the present value of cash outflows. NPV = -

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Decision Rule General decision rule . . .

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**Foundation of the NPV Approach**

The market value of the firm is based on the present value of the cash flows it is expected to generate. Additional investments are “good” if the present value of the incremental expected cash inflows exceeds their cost. Thus, “good” projects are those which increase firm value - or, good projects are those projects that have positive NPVs! Conclusion - Invest only in projects with non-negative NPV.

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**Sources of NPV Economies of Scale Cost Advantages**

Product differentiation Distribution Advantage Regulatory Protection

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**Profitability Index (Benefit/Cost Ratio)**

The profitability index is the ratio of the total PV of future cash inflows to the initial investment This index is used as a means of ranking projects in descending order of attractiveness. Decision rule: If the profitability index is greater than or equal to 1.00, then accept the project.

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**Internal Rate of Return**

Internal rate of return (IRR) is defined as the rate of interest that equates I with the PV of future cash inflows. At IRR: NPV = 0 Decision rule: Accept the project if the IRR is greater than or equal to the required rate of return or hurdle rate. Otherwise, reject it.

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**1 2 3 (500) 200 100 (200) 400 300 0 1 2 3 4 5 Advantage Shortcoming**

IRR is a good decision-making tool as long as cash flows are conventional. ( ) Shortcoming If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. ( ) (500) (200)

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**Mutually Exclusive Investments**

A project is said to be mutually exclusive if the acceptance of one project automatically excludes the acceptance of one or more other projects. In the case where one must choose between mutually exclusive investments, the NPV and IRR methods may result in contradictory indications.

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**Contradictions May Occur When**

Projects that have different life expectancies. Projects that have different sizes of investment. Projects whose cash flows differ over time. For example, the cash flows of one project increase over time, while those of another decrease.

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**Causes for Contradiction**

The contradictions result from different assumptions with respect to the reinvestment rate on cash flows from the projects. The NPV method discounts all cash flows at the cost of capital, thus implicitly assuming that these cash flows can be reinvested at this rate. The IRR method implies a reinvestment rate at IRR. Thus, the implied reinvestment rate will differ from project to project. The NPV method generally gives correct ranking, since the cost of capital is a more realistic reinvestment rate.

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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). MIRR: the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes: PVoutflows = PVinflows

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Example Suppose we are considering investing in an asset that yields $1000 in year one, $1100 in year two, $1500 in year three and $3200 in year four. If your required rate of return is 12%, and the asset costs $5000, determine the IRR and MIRR. $4000 = $1000/(1+IRR) + $1100/(1+IRR)2 + $1500/(1+IRR)3 + $3200/(1+IRR)4 IRR = 20.09%

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**To find the Modified IRR**

$4000 = [$1000(1.12)3 + $1100(1.12)2 + $1500(1.12) + $3200]/(1 + MIRR)4 $4000 = [$ $ $1680 +$3200] /(1 + MIRR)4 $4000(1 + MIRR)4 = $7665 (1 + MIRR) = MIRR = 17.66%

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**Importance of Capital Budgeting**

Capital budgeting is probably the most important issues in corporate finance Identifying investment opportunities which offer more value to the firm than their cost - the value of the future cash flows need to be greater than the investment required estimating the size, timing and risk of future cash flows is the most challenging aspect of capital budgeting

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End of Lecture 6

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