# ch06 - Chapter 6 Discounted Cash Flows and Valuation...

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Chapter 6 Discounted Cash Flows and Valuation Learning Objectives 1. Explain why cash flows occurring at different times must be adjusted to reflect their value as of a common date before they can be compared, and compute the present value and future value for multiple cash flows. 2. Describe how to calculate the present value and the future value of an ordinary annuity and how an ordinary annuity differs from an annuity due. 3. Explain what a perpetuity is and where we see them in business, and be able to calculate the value of a perpetuity. 4. Discuss growing annuities and perpetuities, as well as their application in business, and calculate their values. 5. Discuss why the effective annual interest rate (EAR) is the appropriate way to annualize interest rates, and calculate EAR. I. Chapter Outline 6.1 Multiple Cash Flows A. Future Value of Multiple Cash Flows In contrast to Chapter 5, we now consider situations in which there are multiple cash flows. Solving future value problems with multiple cash flows involves a simple process.

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First, draw a timeline to make sure that each cash flow is placed in the correct time period. Second, calculate the future value of each cash flow for its time period. Third, add up the future values. B. Present Value of Multiple Cash Flows Many situations in business call for computing the present value of a series of expected future cash flows. This could be to determine the market value of a security or business or to decide whether a capital investment should be made. The process is similar to determining the future value of multiple cash flows. First, prepare a timeline to identify the magnitude and timing of the cash flows. Next, calculate the present value of each cash flow using Equation 5.4 from the previous chapter. Finally, add up all the present values. The sum of the present values of a stream of future cash flows is their current market price, or value. 6.2 Level Cash Flows: Annuities and Perpetuities There are many situations in which both businesses and individuals would be faced with either receiving or paying a constant amount for a length of period. When a firm faces a stream of constant payments on a bank loan for a period of time, we call that stream of cash flows an annuity . Individual investors may make constant payments on their home or car loans, or invest a fixed amount year after year to save for their retirement.
Any financial contract that calls for equally spaced and level cash flows over a finite number of periods is called an annuity. If the cash flow payments continue forever, the contract is called a perpetuity . Constant cash flows that occur for a finite number of periods at the end of each period are called ordinary annuities .

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