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CHAPTER 6

Discounted Cash Flow Valuation

187

CONCEPT QUESTIONS 6.4a What is a pure discount loan? An interest-only loan? 6.4b What does it mean to amortize a loan? 6.4c What is a balloon payment? How do you determine its value?

SUMMARY AND CONCLUSIONS
This chapter rounds out your understanding of fundamental concepts related to the time value of money and discounted cash flow valuation. Several important topics were covered, including: 1. There are two ways of calculating present and future values when there are multiple cash flows. Both approaches are straightforward extensions of our earlier analysis of single cash flows. 2. A series of constant cash flows that arrive or are paid at the end of each period is called an ordinary annuity, and we described some useful shortcuts for determining the present and future values of annuities. 3. Interest rates can be quoted in a variety of ways. For financial decisions, it is important that any rates being compared be first converted to effective rates. The relationship between a quoted rate, such as an annual percentage rate (APR), and an effective annual rate (EAR) is given by: EAR [1 (Quoted rate/m)]m 1

6.5

where m is the number of times during the year the money is compounded or, equivalently, the number of payments during the year. 4. Many loans are annuities. The process of providing for a loan to be paid off gradually is called amortizing the loan, and we discussed how amortization schedules are prepared and interpreted. The principles developed in this chapter will figure prominently in the chapters to come. The reason for this is that most investments, whether they involve real assets or financial assets, can be analyzed using the discounted cash flow (DCF) approach. As a result, the DCF approach is broadly applicable and widely used in practice. For example, the next two chapters show how to value bonds and stocks using an extension of the techniques presented in this chapter. Before going on, therefore, you might want to do some of the problems that follow.

C h a p t e r R e v i e w a n d S e l f - Te s t P r o b l e m s 6.1 Present Values with Multiple Cash Flows A first-round draft choice quarterback has been signed to a three-year, $25 million contract. The details provide for an immediate cash bonus of $2 million. The player is to receive $5 million in salary at the end of the first year, $8 million the next, and $10 million at the end of the last year. Assuming a 15 percent discount rate, is this package worth $25 million? How much is it worth? Future Value with Multiple Cash Flows You plan to make a series of deposits in an individual retirement account. You will deposit $1,000 today, $2,000 in two years, and $2,000 in five years. If you withdraw $1,500 in three years and

6.2

188

PART THREE

Valuation of Future Cash Flows

6.3

6.4

6.5

6.6

$1,000 in seven years, assuming no withdrawal penalties, how much will you have after eight years if the interest rate is 7 percent? What is the present value of these cash flows? Annuity Present Value You are looking into an investment that will pay you $12,000 per year for the next 10 years. If you require a 15 percent return, what is the most you would pay for this investment? APR versus EAR The going rate on student loans is quoted as 8 percent APR. The terms of the loans call for monthly payments. What is the effective annual rate (EAR) on such a student loan? It’s the Principal That Matters Suppose you borrow $10,000. You are going to repay the loan by making equal annual payments for five years. The interest rate on the loan is 14 percent per year. Prepare an amortization schedule for the loan. How much interest will you pay over the life of the loan? Just a Little Bit Each Month You’ve recently finished your MBA at the Darnit School. Naturally, you must purchase a new BMW immediately. The car costs about $21,000. The bank quotes an interest rate of 15 percent APR for a...
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