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An amount received or paid at some time in the future is not worth as much as the same amount today. There are a variety of factors which support this observation; risk, inflation, opportunity cost, etc. You probably know that if you leave money sitting idly in your checking account, you are actually losing income you could be earning if you had it in an interest-bearing account. If you let money earn interest, it will grow over time. This isthe time value of money. The time value of money is integral to the concept of leasing. Accelerating payments (Advance rentals, deposits) and deferring expenses (taxes, loan payments) significantly affect the pricing of the lease. The time value of money theory contains three concepts -- compound interest, present value and discount rates. Compound Interest If you were to invest $l00 for one year in an investment that paid l0% annually you would receive $ll0 at the end of the year. Put another way, the future value of your $l00 investment would be $ll0. This is a return of $l0 on your original principal invested. Here's the formula for this calculation: FV = P + (P x i) = $l00 + ($l00 x .l0) = $l00 + $l0 = $ll0 where: FV = future value P = principal = $l00 i = interest rate = .l0 Now let's extend this investment for a three-year period and assume that the interest earned each year will be added to the principal and earn interest as well. In other words, the interest will be compounded. What will the value of your investment be at the end of three years? Here's the compound interest formula again: FV = P + (P x i) where: FV = future value P = principal i = interest rate To determine the investment value after three years, apply the formula to the 2nd and 3rd years, using the future value (FV) from the previous calculation as the new principal value (P). If you work through the formula, you should come up with $l33. Notice that if you had used simple interest (l0% per year of $l00), you would get $l30. The extra $3 results from calculating the 2nd and 3rd year interest on the interest previously earned. In our examples, the compounding period was a year. But it could be a quarter, month, day, or any period of time. You always have to divide the annual interest rate by the number of periods in a year to give you the correct periodic interest. As an example of a different compounding period, suppose you had a 3-year loan at a l2% annual interest rate, compounded quarterly. Because you are compounding four times during the year, you divide the interest rate by 4 to give a 3% periodic interest. You would also multiply the years by 4 to get the number of periods (l2). Computer models than use a 3% rate instead of 12 and 12 periods instead of 3. Present Value You know the old saying - "A bird in the hand is worth two in the bush". Well, a dollar received today is worth more than a dollar received tomorrow or a year from now. Why? Because that dollar can be invested in order to earn interest. If a payment received today is not worth the same as one received next year because of the lost investment opportunity, then what is it worth? What is its present value? Let's look at an example. If you were to receive a payment of $ll0 next year and your investment opportunity is l0%, the present value of that payment is $l00. If someone interested in purchasing your investment offered you $l05 for it today, it would be a good deal because it would increase your present value by $5. Basically, present value is the mathematical opposite of compounding. Lease pricing also uses the present value of annuities. An annuity factor represents the value of $l received or paid in each period over a specified number of periods. This factor is used to present value a stream of payments, like lease rentals. The concept of present value is very useful in comparing investment alternatives that have different cashflows, interest rates and spread over different periods of time. Discount Rates The interest rate used for determining present value is most often referred to as the discount rate because it is used to discount a future payment back to the present. How is that rate determined? Businesses use a variety of methods to arrive at a discount rate for future receipts and payments. Since this rate is often used to evaluate current investment alternatives such as leasing, each business chooses a method relating to its own circumstances. Here are four common methods for determining the discount rate:
Companies also have the option to analyze their investments on a pre-tax or post-tax basis. As you can see, there are various approaches to determining the proper discount rate. |
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