PROJECT CASH FLOWS, PROJECT TIMING, COMPARING PROJECTS, AND MODIFIED INTERNAL RATE OF RETURN (MIRR)

<< NET PRESENT VALUE (NPV) AND INTERNAL RATE OF RETURN (IRR):RANKING TWO DIFFERENT INVESTMENTS

SOME SPECIAL AREAS OF CAPITAL BUDGETING:SOME SPECIAL AREAS OF CAPITAL BUDGETING, SOME SPECIAL AREAS OF CAPITAL BUDGETING >>

Financial Management MGT201

Lesson 10

PROJECT CASH FLOWS, PROJECT TIMING, COMPARING PROJECTS, AND MODIFIED

INTERNAL RATE OF RETURN (MIRR)

Learning Objectives

After completing this lecture, you would be able to understand

· Cash flows relevant to NPV and IRR

· Project timing on the cash flows relationship

· Steps involved in preparing pro forma cash flow statement

· Project options

· Problems with IRR

· Modified Internal Rate of Return

· Problems of comparison among projects of unequal life

Today, we are going to talk about project cash flows, along with the concepts of net present value

(NPV) and internal rate of return (IRR), as they relate to the project cash flows. NPV and IRR are

important and widely used techniques of evaluating investment in real assets. Before going into details

of these techniques, one must have a clear understanding of what these real assets are.

Real assets projects may also include entire businesses. Investors have the option of investing in

running businesses, which are also a collection of assets. The way a project can be evaluated using the

IRR and NPV techniques, the cash flows being generated from a business can also be evaluated in the

same manner.

The actual NPV and IRR for real assets are not very easy to calculate despite having an easy

formula, because the inputs used in the formula are only estimates. Cash flows, the basic input is based

on forecasts, hence majority of errors that may take place in calculating the actual NPV or IRR of any

project may be because of forecasting errors. The next important challenge is to assess or forecast the

anticipated life of the business, which could only be based on an educated guess. Although, you might

have studied in financial accounting about the perpetual concern, however, in reality businesses have

finite life. Another important input is the discount rate. Picking the right discount rate is not an easy task

either. However, we will talk more about discount rates when we would discuss the concept of risk. All

these factors combined together make the calculation of NPV very difficult.

Let us begin with a relatively simple formula for calculating net incremental after tax cash flows.

Net incremental after tax cash flows = net operating income + depreciation +

Tax savings from depreciation + net working capital + other cash flows

· Net operating income is obtained from the income statement

· Depreciation is added back since it is a non-cash expense

· Net working capital requirements for the project as estimated are also added

· Other cash flows which are associated with NPV

Other Cash flows relevant to the NPV of the project

Broadly speaking, these other cash flows can be categorized into three types

1. Opportunity costs relevant to the cash flows of the project

Suppose you are to invest in a new project, a small production unit with 4 weaving looms. You

would also need to have a piece of land where the machinery would be installed. Suppose

further, that you already have that piece of land. While calculating the NPV for the project, you

would have to include the value of the land that you are using. Although you are not buying that

land, but that land has a certain market value. You could have sold that land at the market price

and by not doing so you are incurring an opportunity cost.

2. Cash flows associated with externalities

Externalities in financial terms may be defined as incidental cash flows that arise because of the

effect of new project on the existing or running business. For instance, if a company adds a new

product to its produce line, the launching of the new product can adversely affect the sales

revenue of the existing product line. This phenomenon of competition among the brands of the

same company is also known as cannibalization. When an entrepreneur is embarking on a new

project, he might either hurt or increase the sales of the existing products and that is an

externality. While calculating the net incremental after tax cash flows, the incremental effect of

these externalities, whether negative or positive should be included in the calculation.

Financial Management MGT201

3. Sunk costs:

Sunk costs need to be excluded while calculating the incremental cash flows. Sunk

costs are the costs that have already incurred in the past. Whether you decide to invest your

money in the new project or not, the sunken costs cannot be recovered. For instance, if a

company has purchased an import/export license and a few years after the company decides to

export a certain commodity, the cost incurred to purchase the license would not be included in

the cash flows. Whether the company decides to undertake the new export project or not, the

license fee cannot be recovered.

Timing of the projects:

The next important issue that we need to look at is the different times in which project or

business cash flows have incurred. Broadly speaking, there are three phases.

1. Initiation of the project, the time of investment

2. Life of the project

3. Termination of the project

Time of investment:

Time of business refers to the initiation time when the initial cash outflow occurs. In addition to

the investment in the fixed assets, you may also have net working capital requirements or mobilization

requirements to get the project started. You can add these two types of initial cash outflows since they

are occurring at the same point in time. You might also have to subtract any tax paid on the sale of old

assets to get a net figure for the initial cash outlay. As we discussed earlier, we need to invest in new

assets if the old assets become less productive. These old assets, despite losing their productivity have

some market value at which they can be disposed off. If the market value of the project is higher than its

book value, the company earns as gain on the sale of the asset, which may be taxable1.

Life of the project:

This second phase encompasses a major duration since it is concerned with the cash flows that

occur during the life of the project. The relevant cash flows for the period would be the operating cash

flows, in the form of cash receipts from sales revenue and other income, as well as cash expenses or

payments in the form of operating, marketing and administrative costs. It is important to keep in mind

that all these revenues and costs would be seen on a cash basis. We would also need to take into account

if there are any tax savings that are coming about because of showing increased depreciation. The

change in depreciation takes place as the new assets are included in the business and these new assets

are usually depreciated at an accelerated rate in comparison to the old replaced assets, which were being

depreciated at a low rate in the final year of their useful life. The amount of depreciation could also

increase if the new asset has a high price, the amount of depreciation charged to the asset would also be

high. Since depreciation is a non-cash expense, it has to be added back to the net profit to get the cash

flows. If the new asset has replaced an old one, the difference between the depreciation of the two

would be added to the cash flows.

Termination of the project:

Termination of the project refers to the period when the project life ends. At this time, we need

to take into account the salvage value of the project assets, the price at which the assets can be sold out.

Selling an asset results in a cash inflow--represented by salvage value. In addition, you would also

recover the working capital that you have invested in the business at the beginning. This would be

another cash flow because of liquidating accounts receivable and other accrued assets.

Steps involved in preparing estimated cash flow statement:

Cash flow statement is a consolidated statement of changes in financial position. Following are the

steps involved in preparing a cash flow statement.

· Net Operating Income (from Performa P/L)

· Add back Depreciation (non-cash expense)

· Add Additional Net Working Capital Required

· Subtract Additional Investments in Fixed Assets

· Add Any Tax Savings from Change in Depreciation

· Add Any Cash from Sale of Assets at Salvage Value

In certain countries, like Pakistan, capital gains are not taxed at all

Financial Management MGT201

Add Any Tax Savings from Gain on Sale of Assets

The following example would help you in understanding the composition of a cash flow statement

based on the pro forma profit & loss account.

PRO FORMA (FORECASTED) CASH FLOW

A SAMPLE YEAR IN PROJECT'S LIFE

Amount in Rupees

Net Operating Income (from Pro forma P/L):

1,000

Cost Savings (2000) + Revenues (1000) Expenses

(2000)

Add back Depreciation (non-cash expense):

100

Add Additional Net Working Capital Required

200

Subtract Additional Investments in Fixed Assets

(500)

Add Any Tax Savings from Change in Depreciation

Add Any Cash from Sale of Assets at Salvage Value

100

Add Any Tax Savings from Gain on Sale of Assets

NET CASH FLOWS

1000

Explanation:

The main items we need for preparing is the net operating income, which is an estimated

income as it has been obtained from the pro forma income statement. The net operating income is

calculated by adding revenues to cost savings minus expenses, which in our example is Rs.1000. The

next item used in preparing a cash flow statement is the depreciation. Depreciation is added back to the

net operating income, as it is a non-cash expense. Assume the depreciation to be at Rs.100, which would

be added to the net operating income. Another thing that we need to add to the net operating profit is the

additional working capital requirements, which in our example is assumed Rs 200.

We would also need to subtract any additional investment in fixed assets. Investments in fixed

assets result in cash outflows, which need to be subtracted to get net cash flows. We would also add any

tax savings that come about because of changes in depreciation. When you show more depreciation,

your taxable income reduces and as a result, you have to pay lesser taxes. Depreciation is a non-cash

expense but tax is paid in cash form. By paying less tax, the business is in fact saving tax by applying a

high depreciation rate. You would also add any cash flow resulting from the sales of assets. Assets that

are sold at salvage value represent cash inflows. Any tax advantage on the gain would also be added.

Based on these additions and subtractions, we arrive at the net cash flow figure as shown in the example.

Management overestimates the cash flows. They portray a very optimistic picture of the cash flows and

the NPV, which is also known as an upward bias in NPV calculations. This is one of the ways of

window-dressing.

Project Options:

Some of the companies in certain situations accept projects with negative NPV, or NPV less

than zero. Although, the mathematical details would be discussed in the later lectures, we need to

understand why companies do that.

Companies invest in projects with negative NPV because there is a hidden value in each project. This

hidden value is an opportunity, which is known as an option. These opportunities and options carry

some value. For instance, there are a number multinational companies investing in China these days,

even though, the net present value of there projects might be significantly lower than zero. It is because

they are sacrificing short and medium term cash flows for a long-term market share. They see China as

a potential market owing to its huge market size, and for long-term benefits, they are willing to invest in

projects with negative net present value.

The same concept is true for technology industry. We can take the example of Amazon.com, a

web based company where the CEO and the managers are willing to invest even if the net present value

is negative. The management believes that the growth of the market is such that the negative net present

value would be compensated in future by heavy downpour of positive cash flows later in the life of the

project. You must keep in mind that these options are hidden and might not be very visible to you.

When we talk about the option to abandon a project, the abandonment too has a value. For instance, if

you find that one of the projects has started losing money, you would have the option to end the project

Financial Management MGT201

and thereby cutting the losses. This is the abandonment value of the project. In contrast, for larger

project the abandonment option might be very difficult to exercise. When we make decision of investing

cash in a project, we bear the opportunity cost of not investing the cash in another project and thereby

losing option. Locking up your money & time in a bad project today can reduce your Option Value to

invest in better opportunities in future

Problems with IRR:

Let us now discuss some problems with the calculations of IRR. The problems with calculation

of IRR come about when the project's useful life is for more than two years. Another problem arises

when there are non-normal cash flows or one or more net cash outflow at some point in future (in

addition to the initial investment outflow). This creates multiple real roots (or more than one IRR's) that

bring the NPV of the project equal to zero.

Let us take a simple example for explanation of the concept. For instance, you have made an initial

investment (outflow) of Rs.100, the Net Cash Receipts (inflow) at the end of Year 1 is of Rs.500, and

net loss (outflow) at end of Year 2 is of Rs.500. The cash flow pattern can be explained in the diagram

below.

CF 1 = +Rs.500

Sign Change #1

Yr 0

Yr 1

Yr 2

Sign Change #2

Io = - Rs.100

Note: More than 1 Sign Change in

CF 2 = -Rs.500

Direction of Cash Flow Arrows suggests

Multiple IRR's

In the above diagram, we have a cash

outflow of Rs.100 represented by a

downward arrow in the year 0. The upward arrow represents cash inflow of Rs.500 in the year 1, and the

last downward arrow in the second year represents another cash outflow of Rs.500. The IRR of the

project can be calculated as under

IRR Equation:

NPV = 0 = -100 + 500/ (1+IRR) - 500/(1+IRR)2

Solve by Iteration (or Trial & Error):

IRR = 38% and 260% approx!

Solving the equation, we come up with two values of IRR. Which of the two values is correct? The best

way to deal with this situation is to leave both the found of rates and use another important tool for the

calculation of the IRR known as Modified Internal Rate of Return.

Modified Internal Rate of Return:

The logic used in this technique is to separate the cash inflows and outflows for each year and

use a market discount rate "k" (or the cost of capital). Plotting the cash inflows and outflows on a

diagram, we would keep them separate instead of finding the net cash flow. The next step is to discount

all the future cash outflows and discount them to the present. The third step is to compound the

company's cash inflows to the future end period, which represents the end of the life of the project. The

idea of compounding the cash inflows is on the assumption that they are reinvested at the cost of capital.

Financial Management MGT201

After doing the compounding and discounting of cash flow, we use a rate at which the future value of

cash inflows is equal to the present value of cash outflows. The rate at which the two equate is known as

the Modified Internal Rate of Return. The formula for the MIRR is given as under.

Find the Modified IRR (MIRR) using:

(1+MIRR) n = Future Value of All Cash Inflows....

Present Value of All Cash Outflows

CF in * (1+k) n-t

(1+MIRR) =

CF out / (1+k) t

Now the question arises as to why are we using two different interest or discount rates in the

equation. One of the interest rate is the MIRR and the other is the discount rate used in the NPV

calculation (opportunity cost of capital).

Life of the project:

In our previous example, where we compared a saving certificate to a bank deposit, the lives of

the two investments were not of the same duration. The net present value of the two projects is not

comparable due to the difference in life spans. There are two approaches used to make two projects with

different life spans comparable.

Common Life Approach:

In order to make the two investment opportunities we equate the life of the two projects. We

would repeat the cash flow pattern of each project over a horizon that matches the least common

multiple of the lives of the two projects. For instance, if there are two projects, and the life of first

project is one year and that of the second is two years, the least common multiple would be two and the

cash flow pattern of the project would be repeated for the next year, in order to make the two projects

comparable. Similarly, if first project has a life of two years and second project has a life of three years,

the least common multiple would be six. In that case, the cash flows of the first project would be

repeated thrice and that of the second project would be repeated twice. Having equated the lives of the

project the net present value of both the projects can be calculated and compared.

Equivalent Annual Annuity Approach:

The other approach is to calculate the NPVs of the projects and multiply the result with the

annuity factor. This method converts the projects of different lives into annuity of the same duration in

time.

Inflation consideration

· Use Inflation Discount Factor: Multiply each future cash flow term in the NPV equation by

the Inflation Discount Factor: 1 / (1+g) t. Where g = % inflation per year and t = number of

years.

Table of Contents: