13.07.2015 Views

Money and Markets: Essays in Honor of Leland B. Yeager

Money and Markets: Essays in Honor of Leland B. Yeager

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Reflections on reswitch<strong>in</strong>g <strong>and</strong> roundaboutness 193presentvalue$0.40$0.30$0.20$0.10$0<strong>in</strong>terestrate2 4 6 8 10 12 14–$0.10–$0.20Figure 13.2 Present value (0%–14%).presentvalue$100$80$70$60$50$40$30$20$10<strong>in</strong>terest$0rate0 200 400 600 800 1000Figure 13.3 Present value (0%–1000%).period might be clean-up costs or costs <strong>of</strong> comply<strong>in</strong>g with a service contract. Thebreak-even rates <strong>of</strong> return are still 2 percent <strong>and</strong> 8 percent. But with <strong>in</strong>comes <strong>and</strong>outlays reversed, the middl<strong>in</strong>g <strong>in</strong>terest rate <strong>of</strong> 5 percent puts the project <strong>in</strong> the blackby $0.08, <strong>and</strong> for all rates less than 2 percent or greater than 8 percent, the projectis <strong>in</strong> the red. The graph <strong>of</strong> the outlays <strong>and</strong> revenues <strong>of</strong> this mirror-image project,along with the graphs <strong>of</strong> the dependence <strong>of</strong> present value on the rate <strong>of</strong> <strong>in</strong>terest, arethe same as Figures 13.1–13.3 – but with the positive <strong>and</strong> negative segments <strong>of</strong> thevertical axis reversed.

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