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

Chapter Sixteen: Valuing the Future - Concepts in Capital & Finance 412 CALCULATION OF A FUTURE VALUE In some cases a firm or individual may need to have a specific amount available in the future. Let’s say you are the advancement officer for a large university, and you have been charged with raising funds to establish endowed chairs for economics faculty— what a noble endeavor! To pay the exorbitant salaries of economists, you are told that you must raise $3,000,000 and need to have it at the end of four years. How much do you need to raise per year (assume equal amounts) if the interest rate is expected to be 10%? As seen in Figure 16.8 , you will need to raise $906,344 per year to have a total of $3M at the end of three years. The easiest way to do this is with a financial calculator, setting N=3, PV=0, FV=3,000,000 and I=10%, and then compute PMT to arrive at the result. CALCULATION OF REQUIRED RATE OF RETURN Many Americans have not saved enough for their retirement, but better late than never. You have a profligate Uncle Jeff who spent too much money on Hot Rods and tools, and put too little in the bank for retirement. But now your Uncle Jeff has come to you for advice; he knows you have taken introductory finance in your economics classes, and he wants to know what he should do if he wants to have $200,000 in savings at the end of ten years. He tells you he’s committed to saving $10,000 per year. What do you tell him? First, you will want to calculate the required rate of return that would be necessary to compound $10,000 per year into $200,000 after ten years. Using a financial calculator as in Figure 16.9 , you arrive at a required interest rate of almost 15%—a very difficult rate of return to achieve annually for 10 years. You will want to inform your Uncle Jeff that to achieve that high a rate of return, he will have to accept significantly higher risk than is prudent, since risk and returns go together. You explain that what you mean by risk is that the returns he might receive in any given year will be highly variable and he could certainly lose money. After failing to save for years, you inform him that while markets are not necessarily as efficient as EMH suggests, it is very difficult to beat the market. You then tell him he should put his $10,000 per year into a stock index fund and be content with less than $200,000 after ten years, or you tell him that he needs to save more than $10,000 per year. Figure 16.8, Annual payments required to save $3,000,000 at the end of three years. Using a financial calculator, it can be found that three payments of $906,344 will result in a total of $3M at the end of three years. 906,344 906,344 906,344 0 1 2 3 10% FV = $3,000,000 INPUTS 3 10% 0 3M N I/YR PV PMT FV OUTPUT -906,344 996,978 1,096,677 Figure 16.9, Calculating Required Return with a Financial Calculator. Using a financial calculator (such as Texas Instrument’s BAII Plus, it can be found that is Uncle Jeff can find an investment paying 14.69% per year, his projected savings of $10,000 (entered as a negative in the calculator for cash out) per year will accumulate to $250,000 after ten years. INPUTS 10 0 -10,000 200,000 N I/YR PV PMT FV OUTPUT 14.69%