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# Ross7e ch04appendix

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• The point at which the intertemporal opportunity set pivots depends upon where your endowment is when interest rates change. If the person had \$95,000 in current consumption and no future consumption, the pivot would have been at the x -axis intercept. Such a pivot
• ### Transcript

• 1. CHAPTER 4A Net Present Value: First Principles of Finance
• 2. Outline
• Making Consumption Choices Over Time
• Making Investment Choices Over Time
• Illustrating the Investment Decision
• 3. Making Consumption Choices over Time
• An individual can alter his consumption across time periods through borrowing and lending.
• We can illustrate this by graphing consumption today versus consumption in the future.
• This graph will show intertemporal consumption opportunities.
• 4. Intertemporal Consumption Opportunity Set A person with \$95,000 who faces a 10% interest rate has the following opportunity set. One choice available is to consume \$40,000 now; invest the remaining \$55,000; consume \$60,500 next year. \$0 \$20,000 \$40,000 \$60,000 \$80,000 \$100,000 \$120,000 Consumption today \$0 \$20,000 \$40,000 \$60,000 \$80,000 \$100,000 \$120,000 Consumption at t+1
• 5. Intertemporal Consumption Opportunity Set Another choice available is to consume \$60,000 now; invest the remaining \$35,000; consume \$38,500 next year . \$0 \$20,000 \$40,000 \$60,000 \$80,000 \$100,000 \$120,000 \$0 \$20,000 \$40,000 \$60,000 \$80,000 \$100,000 \$120,000 Consumption today Consumption at t+1
• 6. Taking Advantage of Our Opportunities A person’s preferences will tend to decide where on the opportunity set they will choose to be. \$0 \$20,000 \$40,000 \$60,000 \$80,000 \$100,000 \$120,000 \$0 \$20,000 \$40,000 \$60,000 \$80,000 \$100,000 \$120,000 Consumption today Consumption at t+1 Ms. Patience Ms. Impatience
• 7. Changing Our Opportunities A rise in interest rates will make saving more attractive … … and borrowing less attractive. \$0 \$20,000 \$40,000 \$60,000 \$80,000 \$100,000 \$120,000 \$0 \$20,000 \$40,000 \$60,000 \$80,000 \$100,000 \$120,000 Consumption today Consumption at t+1 Consider an investor who has chosen to consume \$40,000 now and to consume \$60,000 next year.
• 8. Illustrating the Investment Decision
• Consider an investor who has an initial endowment of income of \$40,000 this year and \$55,000 next year.
• Suppose that he faces a 10-percent interest rate and is offered the following investment.
Cash inflows Time Cash outflows 0 1 -\$25,000 \$30,000
• 9. Illustrating the Investment Decision Our investor begins with the following opportunity set: endowment of \$40,000 today, \$55,000 next year and a 10% interest rate. One choice available is to consume \$15,000 now; invest the remaining \$25,000 in the financial markets at 10%; consume \$82,500 next year. \$0 Consumption today \$0 \$99,000 Consumption at t+1 \$90,000 \$55,000 \$82,500 \$40,000 \$15,000
• 10. Illustrating the Investment Decision A better alternative would be to invest in the project instead of the financial markets. He could consume \$15,000 now; invest the remaining \$25,000 in the project at 20%; consume \$85,000 next year. \$0 Consumption today \$0 \$99,000 Consumption at t+1 \$90,000 With borrowing or lending in the financial markets, he can achieve any pattern of cash flows he wants—any of which is better than his original opportunities. \$55,000 \$82,500 \$40,000 \$85,000 \$15,000
• 11. Illustrating the Investment Decision Note that we are better off in that we can command more consumption today or next year. \$0 Consumption today \$0 \$99,000 Consumption at t+1 \$101,500 \$101,500 = \$15,000 ×(1.10) + \$85,000 \$90,000 \$92,273 \$55,000 \$82,500 \$40,000 \$85,000 \$15,000 \$92,273 = \$15,000 +