5.4 Mixed Streams
LG 4 5.4 Mixed Streams
Two basic types of cash flow streams are possible, the annuity and the mixed mixed stream
stream. Whereas an annuity is a pattern of equal periodic cash flows, a mixed
A stream of unequal periodic
stream is a stream of unequal periodic cash flows that reflect no particular pat-
cash flows that reflect no
tern. Financial managers frequently need to evaluate opportunities that are
particular pattern.
expected to provide mixed streams of cash flows. Here we consider both the
CHAPTER 5
Time Value of Money
FUTURE VALUE OF A MIXED STREAM Determining the future value of a mixed stream of cash flows is straightforward.
We determine the future value of each cash flow at the specified future date and then add all the individual future values to find the total future value.
Example 5.12 3 Shrell Industries, a cabinet manufacturer, expects to receive the following mixed stream of cash flows over the next 5 years from one of its small customers.
End of year
Cash flow
If Shrell expects to earn 8% on its investments, how much will it accumulate by the end of year 5 if it immediately invests these cash flows when they are received? This situation is depicted on the following time line:
Time line for future value of a $15,645.62 mixed stream (end-of-year
17,635.97 cash flows, compounded at
15,046.56 8% to the end of year 5)
$83,608.15 Future Value
End of Year
Calculator Use You can use your calculator to find the future value of each individual cash flow, as demonstrated earlier (on page 167), and then sum the future values to get the future value of the stream. Unfortunately, unless you can program your calculator, most calculators lack a function that would allow you to input all of the cash flows, specify the interest rate, and directly calculate the future value of the entire cash flow stream. Had you used your calculator to find the individual cash flow future values and then summed them, the future value of Shrell Industries’ cash flow stream at the end of year 5 would have been $83,608.15.
Spreadsheet Use
A relatively simple way to use Excel to calculate the future value of a mixed stream is to use the Excel future value (FV) function discussed on page 167 combined with the net present value (NPV) function (which will be discussed on page 181). The trick is to use the NPV function to first find the present value of the mixed stream and then find the future of this present value
PART 2
Financial Tools
A B FUTURE VALUE OF A MIXED 1 STREAM 2 Interest rate, pct/year
8% Year-End Cash
3 Year
Flow 4 1 $11,500 5 2 $14,000 6 3 $12,900 7 4 $16,000 8 5 $18,000
9 Future value
Entry in Cell B9 is =–FV(B2,A8,0,NPV(B2,B4:B8)). The minus sign appears before FV to convert
the future value to a positive amount.
PRESENT VALUE OF A MIXED STREAM Finding the present value of a mixed stream of cash flows is similar to finding the
future value of a mixed stream. We determine the present value of each future amount and then add all the individual present values together to find the total present value.
Parts
» The Prentice Hall Series in Finance
» 1 Merger Fundamentals 716 Major Causes of Business Failure 738
» The Financial Market Environment INTEGRATIVE CASE 1 Merit Enterprise Corp.
» LG 2 1.1 Finance and Business
» REVIEW QUESTIONS 1–7 What is the goal of the firm and, therefore, of all managers and
» LG 5 1.3 Managerial Finance Function
» PART 1 Introduction to Managerial Finance FINANCIAL MARKETS
» 2.3 Regulation of Financial Institutions and Markets
» 3.1 The Stockholders’ Report
» 3.8 A Complete Ratio Analysis
» LG 2 4.1 Analyzing the Firm’s Cash Flow
» 8 3 Coulson Industries has gathered the following data needed for the preparation of
» 4.5 Preparing the Pro Forma Income Statement
» 4.6 Preparing the Pro Forma Balance Sheet
» Evaluate the simplified approaches to pro forma financial statement
» 5.1 The Role of Time Value in Finance
» Explain yield to maturity (YTM), its calculation, and the procedure used
» LG 3 7.2 Common and Preferred Stock
» 7.4 Decision Making and Common Stock Value
» Explain the relationships among financial decisions, return, risk, and
» LG 4 8.3 Risk of a Portfolio
» 12 3 Consider two assets—Lo and Hi—with the characteristics described in the table below:
» LG 6 8.4 Risk and Return: The Capital Asset Pricing Model (CAPM)
» 15 3 In the preceding example for Benjamin Corporation, the risk-free rate, R F , was
» Explain the capital asset pricing model (CAPM), its relationship to the
» Calculate the weighted average cost of capital (WACC), and discuss
» 10.3 Net Present Value (NPV)
» 10.4 Internal Rate of Return (IRR)
» Discuss NPV and IRR in terms of conflicting rankings and the theoret-
» LG 2 11.1 Relevant Cash Flows
» LG 4 11.2 Finding the Initial Investment
» 11.3 Finding the Operating Cash Inflows
» 11.4 Finding the Terminal Cash Flow
» Determine the terminal cash flow associated with a proposed capital
» 12.3 International Risk Considerations
» LG 6 12.5 Capital Budgeting Refinements
» Explain the role of real options and the objective and procedures for
» LG 4 13.2 The Firm’s Capital Structure
» 19 3 We can plot coordinates on the EBIT–EPS graph by assuming specific EBIT
» 14.1 The Basics of Payout Policy ELEMENTS OF PAYOUT POLICY
» 14.2 The Mechanics of Payout Policy
» 14.4 Factors Affecting Dividend Policy
» Explain stock splits and the firm’s motivation for undertaking them.
» LG 5 15.4 Accounts Receivable Management
» LG 2 16.1 Spontaneous Liabilities
» LG 4 16.2 Unsecured Sources of Short-Term Loans
» LG 6 16.3 Secured Sources of Short-Term Loans
» Describe the various ways in which inventory can be used as short-term-
» 17.4 Stock Purchase Warrants
» LG 4 18.3 Analyzing and Negotiating Mergers
» Explain bankruptcy legislation and the procedures involved in reorgan-
» 19.1 The Multinational Company and Its Environment
» 3 3 Assume that the current exchange rate between the United States and the new
» 19.4 Long-Term Investment and Financing Decisions
» 19.6 Mergers and Joint Ventures
» Review recent trends in international mergers and joint ventures.
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