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

Chapter Sixteen: Valuing the Future - Concepts in Capital & Finance 397 dollar today. Click here for a tutorial of how to use a financial calculator for these type calculations (thanks to Professor Bill Ragle). Equation 1 does the opposite by calculating future dollars from a present amount, and this is called compounding . RULE OF 72 As seen in the text example, one can calculate the interest rate, present value, future value or the number of years (given the remaining 3 variables) with the aid of a financial calculator. However, the rule of 72 offers a simple way to calculate the number of years to double your money, if you know the interest rate. Simply divide 72 by the interest rate and you get a good approximation for how long it will take for your money to double. So if the interest rate is 6%, then it will take ≈12 years to double your money. Yet if the interest rate is 8%, it only takes ≈9 years to double your money. The next logical step is how to value multiple payments across time. For example, how much should you pay to receive $1,000 per year for the next 20 years, if the interest rate on 20-year deposits at a bank is 8%? Basically you have to discount each of the payments (or cash flows [CF]) back to the present value, with the formula looking like this: [Equation 3] PV = (1+i) CF 1 (1+i) 2 CF 2 + (1+i) 3 CF 3 + ... + (1+i) t CF t + With t=20, i=8%, and CF=$1000, the present value equals $9,818.15; much less than the $20,000 sum of the cash flows. More generally, equation 3 can be expressed as: [Equation 4] Equation 4 is a very useful equation for valuing any asset (whether a stock, a bond, or a truck used in business). An asset’s fundamental value is said to be the present discounted value of its future cash flows. In other words, a capital asset is worth the amount of money it will yield in the future, discounted back into present value. To visualize this process, consider a possible investment that will yield differing cash flows over four years. What is the most an investor would be willing to pay today for those cash flows? As illustrated in Figure 16.1 , each cash flow must be discounted back to present value, and then all the cash flows can be summed to find an overall present value. An investor would not be willing to pay more than $888.81 today for those cash flows, PV =∑ n j = 1 (1+i) j CF j Compounding: the process of converting current dollars into future value. Fundamental value: the present discounted value of an asset’s future cash flows Figure 16.1, Present discounted value of four differing payments at an interest rate of 8%. Each cash flow must be discounted back to the present and summed to find what the present value is. An investor should be willing to pay more than $888.81 for an investment in any project that yields this series of cash flows. 185.19 171.46 238.15 294.01 888.81 = PV 200 200 300 400 0 1 2 3 4 8%