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TIME VALUE OF MONEY PROBLEMS
Much of what we do in finance requires calculating payments, future values, present values, yields and internal rates of return. While we often use Excel or another spreadsheet program to calculate these items, proficiency with a financial calculator sometimes is faster, and the calculator is more easily used when explaining a concept to a client or figuring out things on the fly in a business meeting. On a personal note, typical time value of money problems are as simple as calculating payments on a mortgage or as complex as figuring out the money one needs to save, adjusted for inflation, to meet a survivorship need. No matter what the task, consistently following the following method will help you avoid errors.
Whenever you are presented with a statement problem that involves the Time Value of Money, you need to identify what you know and what you need to find. The easiest way to do this is to write
FV =
PMT =
PV =
I =
N =
Begin/End?:
Number of Compounding Intervals per N:
(I usually write CP/N to keep it simple.)
Make it a habit to write this down before you even start reading the problem, then fill it in as you read through the problem. Sometimes a variable will not be mentioned in the problem, such as no mention of a payment. In that case, put down ? for the payment. When you are finished, you should have all the information that you need to calculate the items that have question marks. In simple lump sum calculations, the payment will often be implied to be 0. Always enter the 0 on your calculator. That way, you won't get caught with some other number from a previous calculation inadvertently stored in your payment variable, and then throw off your current calculation.
The meaning of the Minus Sign
In Time Value of Money problems, + and - indicate the direction the money is flowing, not subtraction or addition. So, for example, when you borrow money to buy a car, the money you receive (PV) is positive and the payment is negative. If you do not change the sign, you will get an error message on your calculator. (Usually Error 5)
Compounding per N is necessary to know, since it affects outcomes substantially. While some calculators have a way to input Payments per period, most often, we have to multiply the N by the number of periods, and if the interest rate is given, divide by the number of periods in the year to get the correct answer. If the I is not known, you will have to multiply the answer by the number of compounding periods to get the correct annual rate. Once you have correctly filled in the variables, indicating cash flows and adjusting for the compounding periods, solving the problem is almost trivial.
www.teachmefinance.com has excellent instruction on time value of money, bond calculations, uneven cash flows, etc.
Whenever we do statement problems, it is important to read the problem carefully. It is surprising how often students lose points on homework or tests because they didn't take time to read the problem carefully. Most often they don't take the last step necessary to get the requested answer, even though it is clear that they could have gotten the right answer. If a problem asks for an annual interest rate, and the compounding is quarterly, you would be surprised how often students stop when they have found the quarterly interest rate.
There are a few key phrases that will let you know which variable is which:
If the problem says: You have (or Joe has) x amount of money, this is a present value.
If the problem says
Compounded annually--the period (N) is the number of years
Compounded quarterly -- the number of periods is the number of years multiplied by 4. If you are given an annual interest rate, you will need to divide it by 4 before doing your calculation, If you are finding the interest rate, you will get the interest per quarter, and will have to multiply it by 4 to get the annual rate. Similarly, for compounded daily, multiply the number of years by 365 and divide the interest rate by 365 if given.
If the problem says " paid per month, paid per quarter", or something similar, chances are that the number preceding is the Payment.
When we get to Chapter 5, remember that the present value of an irregular cash flow is just the sum of the present values of the future payments. If you get hopelessly frazzled, just break the problem down into several present value of a future sum problems, then sum the results.
I have worked all the homework problems for Chapter 4 for you so that you can see the steps, not just the answers. Once I have activated the link below, no homework for Chapter 4 will be accepted. Link to Chapter 4 homework
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