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Financial Management ­ MGT201
VU
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.
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Financial Management ­ MGT201
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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
1
In certain countries, like Pakistan, capital gains are not taxed at all
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·
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
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Add Any Cash from Sale of Assets at Salvage Value
100
Add Any Tax Savings from Gain on Sale of Assets
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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
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Financial Management ­ MGT201
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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.
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Financial Management ­ MGT201
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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
n
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.
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Table of Contents:
  1. INTRODUCTION TO FINANCIAL MANAGEMENT:Corporate Financing & Capital Structure,
  2. OBJECTIVES OF FINANCIAL MANAGEMENT, FINANCIAL ASSETS AND FINANCIAL MARKETS:Real Assets, Bond
  3. ANALYSIS OF FINANCIAL STATEMENTS:Basic Financial Statements, Profit & Loss account or Income Statement
  4. TIME VALUE OF MONEY:Discounting & Net Present Value (NPV), Interest Theory
  5. FINANCIAL FORECASTING AND FINANCIAL PLANNING:Planning Documents, Drawback of Percent of Sales Method
  6. PRESENT VALUE AND DISCOUNTING:Interest Rates for Discounting Calculations
  7. DISCOUNTING CASH FLOW ANALYSIS, ANNUITIES AND PERPETUITIES:Multiple Compounding
  8. CAPITAL BUDGETING AND CAPITAL BUDGETING TECHNIQUES:Techniques of capital budgeting, Pay back period
  9. NET PRESENT VALUE (NPV) AND INTERNAL RATE OF RETURN (IRR):RANKING TWO DIFFERENT INVESTMENTS
  10. PROJECT CASH FLOWS, PROJECT TIMING, COMPARING PROJECTS, AND MODIFIED INTERNAL RATE OF RETURN (MIRR)
  11. SOME SPECIAL AREAS OF CAPITAL BUDGETING:SOME SPECIAL AREAS OF CAPITAL BUDGETING, SOME SPECIAL AREAS OF CAPITAL BUDGETING
  12. CAPITAL RATIONING AND INTERPRETATION OF IRR AND NPV WITH LIMITED CAPITAL.:Types of Problems in Capital Rationing
  13. BONDS AND CLASSIFICATION OF BONDS:Textile Weaving Factory Case Study, Characteristics of bonds, Convertible Bonds
  14. BONDS’ VALUATION:Long Bond - Risk Theory, Bond Portfolio Theory, Interest Rate Tradeoff
  15. BONDS VALUATION AND YIELD ON BONDS:Present Value formula for the bond
  16. INTRODUCTION TO STOCKS AND STOCK VALUATION:Share Concept, Finite Investment
  17. COMMON STOCK PRICING AND DIVIDEND GROWTH MODELS:Preferred Stock, Perpetual Investment
  18. COMMON STOCKS – RATE OF RETURN AND EPS PRICING MODEL:Earnings per Share (EPS) Pricing Model
  19. INTRODUCTION TO RISK, RISK AND RETURN FOR A SINGLE STOCK INVESTMENT:Diversifiable Risk, Diversification
  20. RISK FOR A SINGLE STOCK INVESTMENT, PROBABILITY GRAPHS AND COEFFICIENT OF VARIATION
  21. 2- STOCK PORTFOLIO THEORY, RISK AND EXPECTED RETURN:Diversification, Definition of Terms
  22. PORTFOLIO RISK ANALYSIS AND EFFICIENT PORTFOLIO MAPS
  23. EFFICIENT PORTFOLIOS, MARKET RISK AND CAPITAL MARKET LINE (CML):Market Risk & Portfolio Theory
  24. STOCK BETA, PORTFOLIO BETA AND INTRODUCTION TO SECURITY MARKET LINE:MARKET, Calculating Portfolio Beta
  25. STOCK BETAS &RISK, SML& RETURN AND STOCK PRICES IN EFFICIENT MARKS:Interpretation of Result
  26. SML GRAPH AND CAPITAL ASSET PRICING MODEL:NPV Calculations & Capital Budgeting
  27. RISK AND PORTFOLIO THEORY, CAPM, CRITICISM OF CAPM AND APPLICATION OF RISK THEORY:Think Out of the Box
  28. INTRODUCTION TO DEBT, EFFICIENT MARKETS AND COST OF CAPITAL:Real Assets Markets, Debt vs. Equity
  29. WEIGHTED AVERAGE COST OF CAPITAL (WACC):Summary of Formulas
  30. BUSINESS RISK FACED BY FIRM, OPERATING LEVERAGE, BREAK EVEN POINT& RETURN ON EQUITY
  31. OPERATING LEVERAGE, FINANCIAL LEVERAGE, ROE, BREAK EVEN POINT AND BUSINESS RISK
  32. FINANCIAL LEVERAGE AND CAPITAL STRUCTURE:Capital Structure Theory
  33. MODIFICATIONS IN MILLAR MODIGLIANI CAPITAL STRUCTURE THEORY:Modified MM - With Bankruptcy Cost
  34. APPLICATION OF MILLER MODIGLIANI AND OTHER CAPITAL STRUCTURE THEORIES:Problem of the theory
  35. NET INCOME AND TAX SHIELD APPROACHES TO WACC:Traditionalists -Real Markets Example
  36. MANAGEMENT OF CAPITAL STRUCTURE:Practical Capital Structure Management
  37. DIVIDEND PAYOUT:Other Factors Affecting Dividend Policy, Residual Dividend Model
  38. APPLICATION OF RESIDUAL DIVIDEND MODEL:Dividend Payout Procedure, Dividend Schemes for Optimizing Share Price
  39. WORKING CAPITAL MANAGEMENT:Impact of working capital on Firm Value, Monthly Cash Budget
  40. CASH MANAGEMENT AND WORKING CAPITAL FINANCING:Inventory Management, Accounts Receivables Management:
  41. SHORT TERM FINANCING, LONG TERM FINANCING AND LEASE FINANCING:
  42. LEASE FINANCING AND TYPES OF LEASE FINANCING:Sale & Lease-Back, Lease Analyses & Calculations
  43. MERGERS AND ACQUISITIONS:Leveraged Buy-Outs (LBO’s), Mergers - Good or Bad?
  44. INTERNATIONAL FINANCE (MULTINATIONAL FINANCE):Major Issues Faced by Multinationals
  45. FINAL REVIEW OF ENTIRE COURSE ON FINANCIAL MANAGEMENT:Financial Statements and Ratios