No Free Lunch: Economics for a Fallen World: Third Edition, Revised

Chapter Sixteen: Valuing the Future - Concepts in Capital & Finance 398 since that amount invested at 8% interest would be worth the same amount as the series of cash flows subsequently invested at the same 8% interest rate. For another illustration, consider the data in Figure 16.2 for a series of five cash flows of $100 with an interest rate of 10%. Our first observation is that the present value of the five cash flows is less than the sum of the five cash flows in all cases. This is because each cash flow is discounted; we prefer consumption today to the same promised consumption tomorrow. When the interest rate is 10%, as in the first case, $100 paid one year from now is worth only $90.91 today. A second observation is that as cash flows are received further into the future, their present value falls. Looking again at Figure 16.2 and the 10% interest rate, $100 one year from now is worth $90.91, but a promise of $100 five years from now is only worth $62.09. This results from the opportunity cost—the money could have been productively used in each of the year’s 2-5 to earn interest. A third observation is that as the interest rate increases, the present value of future cash flows is reduced. Since money received today could be invested at a higher interest rate, a promise for the same amount of money in the future is worth significantly less. For example, the same $100 received in year 5 that is worth $62.09 in present value terms when the interest rate is 10%, is worth only $26.93 when the interest rate rises to 30%. Or you can look at the other way; if interest rates fall, out-year (future) cash flows increase significantly more in value. This leads to a very important observation: as interest rates fall, any investment will increase in value because the present value of its future cash flows is higher, and an increase in interest rates, ceteris paribus, will decrease the value of any investment. Figure 16.2, Present discounted value of five payments of $100 at various interest rates. Discounting each of the cash flows back to the present and summing shows the value at significantly less tham the sum of the cash flows. Also note that as cash flows extend further in the future or as interest rates rise the present value falls. PV for N=5, CF=$100 CF/ (1+i ) CF/(1+i ) 2 CF/(1+i ) 3 CF/(1+i ) 4 CF/(1+i ) 5 Present Value 1 = 20% $83.33 $69.44 $57.87 $48.22 $40.18 $299.02 $243.55 1=10% $90.91 $82.64 $75.13 $68.30 $62.09 $379.07 1=30% $76.92 $59.17 $45.52 $35.01 $26.93 As interest rates fall, any investment will increase in value because the present value of its future cash flows is higher.