Fin M12 Project Evaluation—Cash Flows and Capital Budgeting Techniques

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Chapter 10

Capital-Budgeting Techniques and Practice

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Learning Objectives

Discuss the difficulty encountered in finding profitable projects in competitive markets and the importance of the search.

Determine whether a new project should be accepted or rejected using the payback period, net present value, the profitability index, and the internal rate of return.

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Learning Objectives

Explain how the capital-budgeting decision process changes when a dollar limit is placed on the capital budget.

Discuss the problems encountered when deciding among mutually exclusive projects.

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FINDING PROFITABLE PROJECTS

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Capital Budgeting

Meaning: The process of decision making with respect to investments in fixed assets—that is, should a proposed project be accepted or rejected.

It is easier to “evaluate” profitable projects than to “find them.”

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Source of Ideas for Projects

R&D: Typically, a firm has a research & development (R&D) department that searches for ways of improving existing products or finding new projects.

Other sources: Employees, Competition, Suppliers, Customers.

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CAPITAL-BUDGETING DECISION CRITERIA

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Capital-Budgeting Decision Criteria

The Payback Period

Net Present Value

Profitability Index

Internal Rate of Return

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The Payback Period

Meaning: Number of years needed to recover the initial cash outlay related to an investment.

Decision Rule: Project is considered feasible or desirable if the payback period is less than or equal to the firm’s maximum desired payback period. In general, shorter payback period is preferred while comparing two projects.

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Payback Period Example

Example: Project with an initial cash outlay of $10,000 with following free cash flows for 5 years.

Payback is 2 years.

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Trade-Offs

Benefits:

Uses cash flows rather than accounting profits

Easy to compute and understand

Useful for firms that have capital constraints

Drawbacks:

Ignores the time value of money

Does not consider cash flows beyond the payback period

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Discounted Payback Period

The discounted payback period is similar to the traditional payback period except that it uses discounted free cash flows rather than actual undiscounted cash flows.

The discounted payback period is defined as the number of years needed to recover the initial cash outlay from the discounted free cash flows.

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Discounted Payback Period

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Payback Period Example

Table 10-2 shows the difference between traditional payback and discounted payback methods.

With undiscounted free cash flows, the payback period is only 2 years, while with discounted free cash flows (at 17%), the discounted payback period is 3.07 years.

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Net Present Value (NPV)

NPV is equal to the present value of all future free cash flows less the investment’s initial outlay. It measures the net value of a project in today’s dollars.

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NPV Example

Example: Project with an initial cash outlay of $40,000 with following free cash flows for 5 years and a required rate of return of 12%.

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NPV Example

PV of FCF = $47,675

Subtracting the initial cash outlay of $40,000 leaves an NPV of $7,675.

Since NPV > 0, project is feasible.

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NPV Trade-Offs

Benefits

Considers all cash flows

Recognizes time value of money

Drawbacks

Requires detailed long-term forecast of cash flows

NPV is generally considered to be the most theoretically correct criterion for evaluating capital budgeting projects.

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The Profitability Index (PI) (Benefit-Cost Ratio)

The profitability index (PI) is the ratio of the present value of the future free cash flows (FCF) to the initial outlay.

It yields the same accept/reject decision as NPV.

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Profitability Index

Decision Rule:

PI ≥ 1 = accept;

PI < 1 = reject

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Profitability Index Example

A firm with a 10% required rate of return is considering investing in a new machine with an expected life of six years. The initial cash outlay is $50,000.

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Profitability Index Example

PI = ($13,636 + $6,612 + $7,513 + $8,196 + $8,693 + $9,032) / $50,000

= $53,682/$50,000

= 1.0736

Project’s PI is greater than 1. Therefore, accept.

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NPV and PI

When the present value of a project’s free cash inflows are greater than the initial cash outlay, the project NPV will be positive. PI will also be greater than 1.

NPV and PI will always yield the same decision.

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Internal Rate of Return (IRR)

IRR is the discount rate that equates the present value of a project’s future net cash flows with the project’s initial cash outlay (IO).

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Internal Rate of Return

Decision Rule:

If IRR ≥ Required Rate of Return, accept

If IRR < Required Rate of Return, reject

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IRR and NPV

If NPV is positive, IRR will be greater than the required rate of return

If NPV is negative, IRR will be less than required rate of return

If NPV = 0, IRR is the required rate of return.

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IRR Example

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Multiple IRRs

A normal cash flow pattern for project is negative initial outlay followed by positive cash flows (–, +, +, + …)

However, if the cash flow pattern is not normal (such as –, +, –) there can be more than one IRR.

Figure 10-2 is based on cash flows of –1,600, +10,000, –10,000 in years 0, 1, 2.

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Modified IRR (MIRR)

Primary drawback of the IRR relative to the net present value is the reinvestment rate assumption made by the internal rate of return. Modified IRR allows the decision maker to directly specify the appropriate reinvestment rate.

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Modified IRR

Accept if MIRR ≥ required rate of return

Reject if MIRR < required rate of return

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MIRR Example

Project having a 3-year life and a required rate of return of 10% with the following free cash flows:

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MIRR Example

Step 1: Determine the PV of the project’s free cash outflows. $6,000 is already at the present.

Step 2: Determine the terminal value of the project’s free cash inflows. To do this use the project’s required rate of return to calculate the FV of the project’s three cash inflows. They turn out to be $2,420 + $3,300 + $4,000 = $9,720 for the terminal value.

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MIRR Example

Step 3: Determine the discount rate that equates the PV of the terminal value and the PV of the project’s cash outflows. MIRR = 17.446%.

Decision: MIRR is greater than required rate of return, so accept.

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CAPITAL RATIONING

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Capital Rationing

Capital rationing refers to situation where there is a limit on the dollar size of the capital budget. This may be due to:

temporary adverse conditions in the market;

shortage of qualified personnel to direct new projects; and/or

other factors such as not being willing to take on excess debt to finance new projects.

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Capital Rationing

How to select? Select a set of projects with the highest NPV—subject to the capital constraint.

Note, using NPV may preclude accepting the highest ranked project in terms of PI or IRR.

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RANKING MUTUALLY EXCLUSIVE PROJECTS

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Ranking Mutually Exclusive Projects

Size Disparity

Time Disparity

Unequal Life

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Size Disparity

This occurs when we examine mutually exclusive projects of unequal size.

Example: Consider the following cash flows for one-year Project A and B, with required rates of return of 10%.

Initial Outlay: A = $200; B = $1,500

Inflow: A = $300; B = $1,900

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Size-Disparity Ranking Problem

Ranking Conflict:

Using NPV, Project B is better;

Using PI and IRR, Project A is better.

	Project A	Project B
NPV	$72.73	$227.28
PI	1.36	1.15
IRR	50%	27%

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Size-Disparity Ranking Problem

Which technique to use to select the project?

Use NPV whenever there is size disparity. If there is no capital rationing, project with the largest NPV will be selected. When capital rationing exists, rank and select set of projects based on NPV.

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The Time-Disparity Problem

Time-disparity problem arises because of differing reinvestment assumptions made by the NPV and IRR decision criteria.

How are cash flows reinvested?

According to NPV: Required rate of return

According to IRR: IRR

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The Time-Disparity Problem

Example: Consider two projects, A and B, with initial outlay of $1,000, cost of capital of 10%, and following cash flows in years 1, 2, and 3:

A: $100 $200 $2,000

B: $650 $650 $650

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The Time-Disparity Problem

Ranking Conflict:

Using NPV or PI, A is better

Using IRR, B is better

Which technique to use to select the superior project?

Use NPV

	Project A	Project B
NPV	$758.83	$616.45
PI	1.759	1.616
IRR	35%	43%

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Unequal-Lives Problem

This occurs when we are comparing two mutually exclusive projects with different life spans.

To compare projects, we compute the Equivalent Annual Annuity (EAA).

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Unequal-Lives Problem

Example: If you have two projects, A and B, with equal investment of $1,000, required rate of return of 10%, and following cash flows in years 1-3 (for project A) and 1-6 (for project B)

Project A = $500 each in years 1-3

Project B = $300 each in years 1-6

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Computing EAA

Calculate the project’s NPV: A = $243.43 and B = $306.58

Calculate EAA = NPV/annual annuity factor A = $97.89 B = $70.39

Project A is better

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Key Terms

Capital budgeting

Capital rationing

Discounted payback period

Equivalent annual annuity (EAA)

Internal rate of return (IRR)

Modified internal rate of return (MIRR)

Mutually exclusive projects

Net present value (NPV)

Net present value profile

Payback period

Profitability index (PI) or benefit-cost ratio

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