CHAPTER 15 • Investment, Time, and Capital Markets 565 PDV of 2.0 cash flow 1.9 (thousands of dollars) 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.05 0.10 0.15 0.20 Interest rate F IGURE 15.1 PRESENT VALUE OF THE CASH FLOW FROM A BOND Because most of the bond’s payments occur in the future, the present discounted value declines as the interest rate increases For example, if the interest rate is percent, the PDV of a 10-year bond paying $100 per year on a principal of $1000 is $1386 At an interest rate of 15 percent, the PDV is $749 the bond is worth, we simply compute the present value of the payment stream: PDV = $100 $100 $1000 $100 + + g + + 10 (1 + R) (1 + R) (1 + R) (1 + R)10 (15.1) Again, the present value depends on the interest rate Figure 15.1 shows the value of the bond—the present value of its payment stream—for interest rates up to 20 percent Note that the higher the interest rate, the lower the value of the bond At an interest rate of percent, the bond is worth about $1386, but at an interest rate of 15 percent, its value is only $749 Perpetuities A perpetuity is a bond that pays out a fixed amount of money each year, forever How much is a perpetuity that pays $100 per year worth? The present value of the payment stream is given by the infinite summation: PDV = $100 $100 $100 $100 + + + + g (1 + R) (1 + R) (1 + R) (1 + R)4 • perpetuity Bond paying out a fixed amount of money each year, forever