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

Chapter Sixteen: Valuing the Future - Concepts in Capital & Finance 396 the $105 could grow to $110.25. How? We simply multiply the amount by 1, plus the rate of interest for each year (since multiplying by one returns the principle, and the rate of interest pays the interest on the principle). Or… Future Value = Present Value ( 1+ i ) FV = PV x ( 1+ i ) $105 = $100 ( 1+ .05 ) For two years, it would be… FV = PV x ( 1+ i )( 1+ i ) $110.25 = $100 ( 1+ .05 )( 1+ .05 ) For any t years, the formula would be… [Equation 1] FV = PV x ( 1+ i ) t It is a simple matter of algebra to calculate the opposite: how much would X dollars paid in the future be worth today? We simply divide both sides of equation 1 by (1 + i) t . [Equation 2] PV = FV/ ( 1+ i ) t So let’s give that a try. If you are promised $100,000 in fifteen years, how much is that worth today? It depends on the interest rate; let’s say 10%. So with t=15, i=.10, and FV = $100,000, using equation 2 we can calculate the present value as equaling $23,939—that’s significantly less than $100,000! If I asked you if you preferred $50,000 to $100,000, you would almost certainly say ‘no way!’ But if I asked you if you’d prefer $50,000 today to $100,000 fifteen years from now, I think from the calculation above, you’d gladly take the $50,000 today—if the going interest rate for 15 years is 10%. With the aid of a financial calculator you could solve for the interest rate in equation 2 (with PV=$50,000, FV=$100,000, and t=15) to find an interest rate of 4.73%. In effect, an offer of $100,000 fifteen years from now instead of $50,000 today is an offer to pay you an interest rate of 4.73%, even while the going interest rate is 10%. Present value calculations help us make comparisons on the value of different amounts of money across time. The process of calculating the present value (as in equation 2) is often called discounting . A future amount is discounted because a dollar paid in the future is not as valuable as a Discounting: The process of converting future cash flow(s) into present value