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Essential Concepts
Time Value of Money
Evaluating Cash Flows
Risk and Return

PreMBA Analytical Methods
Evaluating Cash Flows: Introduction

The "Time Value of Money" section lays the groundwork for examining cash flows at different points in time using present value, future value, and compound interest. "Evaluating Cash Flows" focuses on ways of measuring cash flows for special cases, such as annuities and perpetuities. Those formulas are necessary to generate and analyze several types of financial instruments, such as bond payments, dividend-paying stocks and fully amortizing loans.


In this section, you should learn TVM techniques that you can use to evaluate multiple cash flows across time. Using a single formula, you will be able to compute the present value of a 30-year loan with monthly payments, at a given interest rate. Most loans have fixed payment amounts that occur at equally spaced intervals of time. Cash flow streams with these two characteristics are called annuities.


Annuity streams that are assumed to last forever are called perpetuities. When visualizing perpetuities, imagine a time line that goes to infinity. A simplistic way of valuing a company is to view a dividend stream as a perpetuity. Alternatively, one can imagine that the cash flows associated with a perpetuity will grow uniformly through time. As you might guess, there is a single TVM method that can deal with this sort of cash flow stream.

Net Present Value

There are, of course, cash flow streams that are not equal in size. Generally, you must discount unequal cash flows individually to obtain the present value of the combined flows. Many business projects have unequal cash flows, including negative as well as positive cash flows thoughout the life of the project.

Regardless of the type of future cash flows generated by a project, you can use time value of money techniques to compute the present value of the future cash flows. The net present value is the present value of the future cash flows less the initial cash invested. The NPV is used as a decision tool that provides the current dollar amount that an investment is expected to provide.

Internal Rate of Return

Another decision tool provides an interest rate measure of an investment. The internal rate of return, IRR, is the interest rate that makes the present value of the future net cash flows equal to the initial investment. Stated differently, the IRR is the interest rate that makes the NPV equal to zero. While the NPV provides a dollar measure of the value of an investment, the IRR provides a rate of return measure. You will learn that IRR is a potentially flawed decision tool because it is easily misapplied.

It should be obvious to you at this point that TVM techniques are used to value cash flows that occur through time. You can compute the value today of a cash flow to occur 60 years from now. Conversely, you can compute what the value of a cash flow you receive today would be 60 years from now. Even better, you can value or price investments that have any number of cash flows occuring at any time. You will see that TVM has many applications for individuals and business. You can price a new mortgage for your home, a dividend-paying stock, or a project for your company. The price of each accounts for the risk inherent in each project or investment.

Using the principles of TVM, you should be able to

  • compute the future value of a stream of fixed cash flows occurring at even intervals across time (i.e., future value of an annuity)
  • compute the present value of a stream of fixed cash flows occurring at even intervals across time (i.e., present value of an annuity)
  • compute the present value of an infinite stream of fixed or growing cash flows occurring at even intervals across time (i.e., present value of a perpetuity)
  • compute the present value of a series of future cash inflows and outflows minus the amount invested (i.e., net present value)
  • compute the internal rate of return of a set of cash flows occurring across time

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