Chapter_04_app

Chapter_04_app - Chapter 4 Discounted Cash Flow Valuation 4A-1 Appendix 4A Net Present Value First Principles of Finance In this appendix we show

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Chapter 4 Discounted Cash Flow Valuation 4A-1 Net Present Value: First Principles of Finance In this appendix, we show the theoretical underpinnings of the net present value rule. We ± rst show how individuals make intertemporal consumption choices, and then we explain the net present value (NPV) rule. The appendix should appeal to students who like a theo- retical model. Those of you who can accept the NPV analysis contained in Chapter 4 can skip to Chapter 5. 4A.1 Making Consumption Choices over Time Figure 4A.1 illustrates the situation faced by a representative individual in the ± nancial market. This person is assumed to have an income of $50,000 this year and an income of $60,000 next year. The market allows him not only to consume $50,000 worth of goods this year and $60,000 next year, but also to borrow and lend at the equilibrium interest rate. The line AB in Figure 4A.1 shows all of the consumption possibilities open to the person through borrowing or lending, and the shaded area contains all of the feasible choices. Let’s look at this ± gure more closely to see exactly why points in the shaded area are available. We will use the letter r to denote the interest rate—the equilibrium rate—in this market. The rate is risk-free because we assume that no default can take place. Look at point A on the vertical axis of Figure 4A.1. Point A is a height of: A 5 $60,000 1 [$50,000 3 (1 1 r )] For example, if the rate of interest is 10 percent, then point A would be: A 5 $60,000 1 [$50,000 3 (1 1 0.1)] 5 $60,000 1 $55,000 5 $115,000 Point A is the maximum amount of wealth that this person can spend in the second year. He gets to point A by lending the full income that is available this year, $50,000, and consuming none of it. In the second year, then, he will have the second year’s income of $60,000 plus the proceeds from the loan that he made in the ± rst year, $55,000, for a total of $115,000. Appendix 4A Figure 4A.1 Intertemporal Consumption Opportunities www.mhhe.com/rwj Consumption next year Slope = – (1 + r ) C Y D B $115,000 $71,000 $60,000 $49,000 $40,000 $60,000 $50,000 Consumption this year Borrowing Lending A $104,545
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4A-2 Part II Valuation and Capital Budgeting Now let’s take a look at point B. Point B is a distance of: B ± $50,000 ² [$60,000 ± (1 ² r )] along the horizontal axis. If the interest rate is 10 percent, point B will be: B ± $50,000 ² [$60,000 ± (1 ² 0.1)] ± $50,000 ² $54,545 ± $104,545 (We have rounded off to the nearest dollar.) Why do we divide next year’s income of $60,000 by (1 ² r ), or 1.1 in the preceding computation? Point B represents the maximum amount available for this person to consume this year. To achieve that maximum he would borrow as much as possible and repay the loan from the income, $60,000, that he was going to receive next year. Because $60,000 will be available to repay the loan next year, we are asking how much he could borrow this year at an interest rate of r and still be able to repay the loan. The answer is: $60,000 ± (1 ² r ) because if he borrows this amount, he must repay it next year with interest. Thus, next year he must repay: [$60,000 ± (1 ² r )] ³ (1 ² r ) ± $60,000 no matter what the interest rate, r , is. In our example we found that he could borrow
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This note was uploaded on 06/22/2009 for the course ECON 134a taught by Professor Lim during the Spring '08 term at UCSB.

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Chapter_04_app - Chapter 4 Discounted Cash Flow Valuation 4A-1 Appendix 4A Net Present Value First Principles of Finance In this appendix we show

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