The Time Value of Money

Financial managers use time value of money techniques when assessing the value of the expected cash flow streams associated with decision alternatives. Alternatives can be assessed either compounding to find future value or discounting to find present value. Because they are at zero when making decisions, financial managers rely primarily on present value techniques. Future versus Present Value Financial values and decisions can be assessed by using either future or present value techniques. Although they will result in the same decisions, they view the decisions differently.

Future value techniques typically measure cash flows at the end of a project’s life; present value techniques measure cash flows at the start of a project’s life (time zero). Future value is cash you will receive at a given future date, and present value is just like cash in hand today. Because money has a time value, all of the cash flows associated with an investment must be measured at the same point in time. The future value technique uses compounding to find the future value of each cash flow at the end of the investment’s life and then sums those values to find the investment’s future value.

Alternatively, the present value technique uses discounting to find the present value of each cash flow at time zero and then sums these values to find the investment’s value today. Future Value of a Single Amount Compound interest is the amount of interest earned on a given deposit has become part of the principal at the end of a specified period. The term principal refers to the amount of money on which the interest is paid. Annual compounding is the most common type. The future value of a present amount is found by applying compound interest over a specified period of time. An annuity is a stream of equal annual cash flows.

These cash flows can be inflows of returns earned on investments or funds invested to earn future returns. Two basic types: ordinary annuity and annuity due. For an ordinary annuity, the cash flow occurs at the end of each period. For an annuity due, the cash flow occurs at the beginning of each period. Because the annuity due’s cash flow occurs at the beginning of the period rather than the end, the future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity. Example 4: What is the future value of a 4-year ordinary annuity, if the annual interest is 5%, and the annual payment is $1,000?

Example 5: What is the future value of a 4-year annuity due, if the annual interest is 5%, and the annual payment is $1,000? Present Value of a Single Amount Present value is the current dollar value of a future amount. Present value depends largely on the investment opportunities of the recipient and the point in time at which the amount is to be received. The process is referred to as discounting cash flows. It is concerned with the question: “If I can earn k% on my money, what is the most I would be willing to pay now for an opportunity to receive dollars periods from today?

“Two basic types of cash flow streams are possible: The mixed stream and the annuity. A mixed stream of cash flows reflects no particular pattern; an annuity is a pattern of equal annual cash flows. Present Value of a Mixed Stream To find the present value of a mixed stream of cash flows, determine the present value of each future amount, and then add together all the individual present values. Example 7: A company has been offered an opportunity to receive the following mixed stream of cash flows over the next 5 years.

If the firm must earn at least 9% on its investments, what is the most it should pay for this opportunity? The method for finding the present value of an annuity is similar to that used for a mixed stream, but can be simplified. The present value of an annuity can be found by multiplying the annual cash flows by the sum of appropriate present value interest factors. Example 8: A company wants to determine the most it should pay to purchase a particular annuity. The firm requires a minimum return of 8% on all investments, and the annuity consists of cash flows of $700 per year for 5 years.

Calculate the present value of the annuity. Present Value of a Perpetuity A perpetuity is an annuity with an infinite life – in other words, an annuity that never stops providing its holder with a cash flow at the end of each year. Example 9: Mr. Clark wishes to determine the present value of a $1. 000 perpetuity discounted at 10%. Find the present value of the perpetuity. Means, if he had $10. 000 and earned 10% interest on it each year, $1. 000 a year could be withdrawn indefinitely without touching the initial$10. 000, which would never be drawn upon.