# 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 discounted to a common date before they can be compared, and be able to compute the present value and future value for multiple cash flows. When making decisions involving cash flows over time, we should first identify the magnitude and timing of the cash flows and then discount each individual cash flow to its present value. The process of discounting the cash flows adjusts them for the time value of money, because today’s dollars are not equal in value to dollars in the future. Once all of the cash flows are in present value terms, the cash flows can be compared to make decisions. Section 6.1 discusses the computation of present values and future values of multiple cash flows. 2. Describe how to calculate the present value of an ordinary annuity and how an ordinary annuity differs from an annuity due. An ordinary annuity is a series of equally spaced level cash flows over time. The cash flows for an ordinary annuity are assumed to take place at the ends of the periods. To find the value of an ordinary annuity, we start by calculating the annuity factor, which is equal to (1 – present value factor)/ i . Then, we multiply this factor by the constant future payment. An annuity due is an annuity in which the cash flows occur at the beginnings of the periods. A lease is an example of an annuity due. In this case, we are effectively prepaying for the service. To calculate the value of an annuity due, we multiply the ordinary annuity value times (1 + i ). Section 6.2 discusses the computation of level cash flows (annuities and perpetuities). 1

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3. Explain what a perpetuity is and how it is used in business, and be able to calculate the value of a perpetuity. A perpetuity is like an annuity except that the cash flows are perpetual—they never end. British Treasury Department bonds, called consols, were the first widely used securities of this kind. The most common example of perpetuity today is preferred stock. The issuer of preferred stock promises to pay fixed rate dividends forever. The preferred stockholders must be paid before common stockholders. To calculate the present value of a perpetuity, we simply divide the promised constant dividend payment (CF) by the interest rate ( i ). Learn by Doing Application 6.8 in Section 6.2 illustrates an application and calculation of a perpetuity problem found in business. 4. Discuss growing annuities and perpetuities, as well as their application in business, and be able to calculate their value. Financial managers often need to value cash-flow streams that increase at a constant rate over time. These cash flow streams are called growing annuities or growing perpetuities. An example of a growing annuity would be a 10-year lease contract with an annual adjustment for the expected rate of inflation over the life of the contract. If the cash flows continue to grow at a constant rate indefinitely, this cash flow stream is called a growing perpetuity. Application and
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