capital budgeting

Slide 1

Introduction

Welcome to Financial Management. In this lesson we will discuss the basics of capital budgeting: evaluating cash flows.

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Slide 2

Topics

The following topics will be covered in this lesson:

An overview of capital budgeting;

Net present value;

Internal rate of return;

Multiple internal rates of return;

Reinvestment rate assumptions;

Modified internal rate of return;

NPV profiles;

Profitability index;

Payback period;

Conclusions on capital budgeting methods;

Decision criteria used in practice; and

Other issues in capital budgeting.

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Slide 3

An Overview of Capital Budgeting

Unlike stocks and bonds which are part of the securities market where investors choose from the available set, capital budgeting involves project creation because firms create capital budgeting projects. Provide the company executes its plans well their capital budgeting projects will be successful. As we do when we analyze a security we must forecast cash flows, calculate the present value of the cash flows associated with each investment opportunity and make the investment if and only if the present value of the future expected cash flows is greater than the project’s cost. The firm has available several methods with which to evaluate projects and decide whether to accept or reject them. Specifically, the project evaluation methods are:

Net present value also known called NPV;

Internal rate of return, also known called IRR;

Modified internal rate of return, also known called MIRR;

Profitability index, also known called PI; and

The payback period.

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Slide 4

Net present value (NPV)

The NPV method for project evaluation is defined as the present value of a project’s cash flows minus the present value of its costs. It tells the firm how much the project contributes to shareholder wealth. Higher NPVs mean a higher stock price for the firm because the project increases to shareholder wealth. The NPV method is considered the best project evaluation method because it is directly related to the objective of maximizing the firm’s intrinsic value. To determine the NPV using Excel we use the following procedure:

First, determine the present value of each cash flow which is net of depreciation, taxes, and salvage value and is discounted at the project’s risk adjusted cost of capital;

Next, add discounted cash flows to obtain the project’s NPV. In general the NPV of a project is given by:

NPV equals summation t equals zero through N CF sub t divided by the quantity one plus r raised to the tth power;

Where CF sub t is the expected net cash flow at time T;

R is the project’s risk adjusted cost of capital or the WACC; and

N is the project’s life.

Any project usually requires an initial investment which is entered as a negative number in Excel and is not discounted because it occurs at times zero. When we use the NPV method it is important that we know whether or not the projects in question are independent or mutually exclusive. Independent projects have cash flows that are not impacted by other projects. If projects are mutually exclusive all the projects can be rejected but not all of them can be accepted at the same time. According to the NPV method, if NPV is greater than zero we accept the projects if they are independent, but if the projects are mutually exclusive the firm must accept the project with the highest NPV. To use the NPV method all projects under consideration must be either independent or mutually exclusive.

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Slide 5

Internal rate of return (IRR)

Recall, the YTM is the discount rate that equates the present value of a bond’s cash inflows to the price of the bond. The IRR is analogous to the yield to maturity for a bond because the IRR is the rate of return that sets the present value of cash inflows equal to the cost of the proposed project. This is the same as determining the rate of return that equates the NPV of a project to zero.

To calculate the IRR we can solve the equation given by:

NPV equals summation T equals zero through N CF sub T divided by the quantity one plus IRR raised to the tth power equals zero.

For IRR, use a financial calculator to solve the problem, or use the IRR in function in Excel. Then, if the IRR is greater than zero the cost of funds to finance the project the difference is a bonus to the stockholders and the firm’s stock price rises because the IRR is an estimate of the project’s rate of return. If the firm uses the IRR method to rank projects, it uses the following decision rule:

If the projects are independent and the IRR is greater than the WACC the project should be accepted otherwise they should be rejected;

If the projects are mutually exclusive the firm should accept the project with the highest IRR and reject any project if its IRR is less than or equal to its WACC. However, if the projects are mutually exclusive the NPV and IRR methods yield conflicting results. In the case of a conflict, the NPV method is better.

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Slide 6

Multiple internal rates of return

When a project has a cash outflow that occurs after the inflows have started the project may have more than one IRR and the cash flows are said to be non-normal. It is difficult to determine multiple internal rates of return since it must be done using trial and error procedure. If however the number of years ranges from zero to two we can use the quadratic formula, from algebra, to solve for the two internal rates of return.

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Slide 7

Reinvestment rate assumptions

The NPV method assumes that cash inflows are reinvested at the risk adjusted rate of return or WACC, and the IRR method assumes the cash flows are reinvested at the IRR itself. For most firms the assumption of reinvestment at the WACC is better for several reasons.

First, if the firm has fairly good access to the capital markets it can raise the capital it needs at the going rate.

Then, assuming the firm can obtain capital at its WACC the firm should accept those investment opportunities with positive NPVs and finance them at its weighted average cost of capital. If the firm operates in a competitive environment its return on investment opportunities is probably close to its cost of capital.

Finally, if the firm uses retained earnings from past projects rather than external capital its weighted average cost of capital is the opportunity cost of the cash flows and hence is the effective rate of return on reinvested funds.

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Slide 8

Modified internal rate of return (MIRR)

Usually cash flows cannot be reinvested at the IRR and for this reason the IRR usually overstates the expected return for accepted projects. This upward bias is a fundamental flaw in the IRR method. Therefore, we calculate the MIRR in which we assume that the cash flows are reinvested at the weighted average cost of capital or some other reasonable rate.

Mathematically, the MIRR method is given by summation T equals zero through N COF sub T divided by the quantity one plus R raised to the tth power equals summation T equals zero through N CIF sub T times the quantity one plus R raised to the N minus tth power divided by the quantity one plus MIRR raised to the Nth power;

Where COF sub T is expected cash outflow at time T;

CIF sub T is the expected cash inflow at time T;

R is the project’s risk-adjusted cost of capital or WACC; and

N is the life of the project.

By using the MIRR method we eliminate the problem of multiple IRRs and therefore the results can be compared with the cost of capital when deciding to accept or reject projects. If projects are independent then NPV, IRR, and MIRR yield the same results. However, if projects are mutually exclusive and differ in size conflicts arise but NPV is the best method because it picks the project that maximizes value.

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Slide 9

NPV profiles

To construct a NPV profile for a project we determine the project’s NPV for a number of different discount rates and plot the values to create a graph with NPV plotted on the Y-axis and the cost of capital plotted on the X-axis. Recall that the IRR is the discount rate that equates NPV to zero. It turns out that the IRR is the rate at which the profile line crosses the horizontal axis. If there are two competing projects constructing NPV profiles show the conditions under which conflicting rankings may occur. The crossover rate is rate at which the NPVs for competing projects are equal. NPV profiles intersect at the crossover rate because of differences in cash flows and project size.

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Slide 10

Profitability index

The profitability index, PI, is another method used to evaluate projects. Mathematically, the PI is given by the following:

PI equals summation t equals one through N CF sub T divided by the quantity one plus R raised to the tth power that quantity divided by CF sub zero;

Where CF sub T is the expected future cash flow at time T and CF sub zero is the initial cost.

It shows the relative profitability of a project which is also the present value per dollar of initial cost. Using the PI method a project is acceptable if its PI is greater than one. The higher the PI the higher the project’s ranking. For normal, independent projects NPV, IRR, MIRR, and PI always lead to the same accept or reject decisions. Whenever a project’s NPV exceeds a zero, its IRR and MIRR are always greater than R and its PI exceeds one. However, if projects are mutually exclusive the methods may yield conflicting results when the projects differ in the timing or size of cash flows. Whenever there is a conflict between the PI and NPV methods, the NPV ranking should be used.

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Slide 11

Payback period

While the NPV end IRR are the most commonly used project evaluation methods historically the method used by firms was the payback period. It is defined as the number of years required by a project to recover the funds invested in a project from its operating cash flows. Mathematically the payback period is given by:

Payback equals the number of years prior to a full recovery plus unrecovered cost at the start of the year divided by cash flow during full recovery year.

The firm compares the calculated payback period with its required payback period and accepts a project provided the calculated payback period is less than the required payback period. But the payback period has three problems. It ignores the time value of money. It ignores cash flows beyond the payback period. Last the method only tells us how long it takes to recover the initial investment and tells us nothing about the amount of wealth the project adds to the investor wealth. To address the time value of money issue analysts calculate the discounted payback period in which cash flows are discounted at the WACC. The discounted cash flows are used to determine the payback period. However, this method also ignores cash flows beyond the payback period. Additionally, the results of both the payback period and the discounted payback period can conflict with NPV if projects are mutually exclusive. As a result, we don’t know how to specify an acceptable payback period.

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Slide 12

Conclusions on capital budgeting methods

Of the available capital budgeting decisions NPV is the best method because it yields a direct measure of the value a project adds to shareholder wealth. IRR and MIRR measure a project’s profitability as a percentage rate of return while the PI measures profitability relative to the amount of investment. MIRR is a better decision method then IRR because it avoids the problem of multiple rates of return and uses the WACC as the reinvestment rate. In addition to the quantitative information provided by the various decision-making methods, qualitative information such as the possibility of a tax increase or a major liability lawsuit should also be considered in capital budgeting decisions.

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Slide 13

Decision criteria used in practice

Historical surveys of managers indicate that prior to the nineteen eighties the NPV method was not the primary method used to evaluate projects but since nineteen ninety-nine this method is widely used and is second only to the IRR method. In the opinion of the authors if a survey were taken today the NPV method would most likely be the predominant evaluation method. However, managers still use the payback method because it is easy to calculate.

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Slide 14

Other issues in capital budgeting

Suppose we have two mutually exclusive projects. Project one has a life of three years while project two has a life of six years. To evaluate the projects using the NPV method we must make an adjustment using either the replacement chain also called the common life approach or the equivalent annual annuities or EAA method. If we use the replacement chain or, life approach we assume that project one of is replaced in years four through six and assume its annual cash inflows and its cost of capital do not change. This allows us to compare the projects. If we use the EAA method we convert the annual cash flows for both projects into a constant cash flow stream whose NPV equals a NPV of the initial stream.

Sometimes it is advantageous to terminate a project prior to the end of its physical life and sell the asset is sold for its expected salvage value. The manager determines the project economic life which is the life that maximizes the NPV and hence shareholder wealth. This method should always be used if the expected salvage value is relatively high.

A firm’s optimal capital structure is that set of independent projects with positive NPVs and mutually exclusive project with the highest NPV. These are the projects that maximize value the firm. But there are two complications that can arise: the cost of capital can increase as a size of the capital budget increases and the firm may set an upper limit on the size of their capital budget which is referred to as capital rationing.

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Slide 15

Check Your Understanding

Slide 16

Summary

We have now reached the end of this lesson. Let’s review what we’ve covered.

First, we provided an overview of capital budgeting. We learned the firm has several methods it can use to evaluate investment projects.

Next, we learned that the NPV method is considered the best project evaluation method because it is directly related to the objective of maximizing the firm’s intrinsic value.

Also, we identified and described the NPV, IRR, MIRR and PI methods. If projects are independent the NPV, IRR, MIRR and PI methods yield the same result. If, however, projects are mutually exclusive conflicting results may occur and the NPV method should be used for project evaluation.

Next, we learned that the payback period is used by firms because it is easy to calculate. However, it ignores the time value of money and cash flows beyond the payback period and only tells us how long it takes to recover the initial investment and nothing about the amount of wealth the project adds to the investor wealth.

Also, we discussed that in order to address the time value of money issue; analysts calculate the discounted payback period in which cash flows are discounted at the WACC. The discounted cash flows are used to determine the payback period. However, this method also ignores cash flows beyond the payback period.

Next, we discovered that the results of both the payback period and the discounted payback period can conflict with NPV if projects are mutually exclusive. As a result, we don’t know how to specify an acceptable payback period.

Then, we learned that it is important to consider qualitative information when making capital budgeting decisions.

Also, we looked at how to modify the NPV formula if we have two mutually exclusive projects with unequal lives. This is done using either the replacement chain or equivalent annual annuities.

Finally, our last two topics dealt with terminating a project prior to the end of its useful life and the optimal capital structure of the firm.

This concludes this lesson.