Print this chapterPrint this chapter

BUS202 Study Guide

Unit 3: Time Value of Money


3a. Explain the time value of money

  • Why does the value of money change over time?
  • What is the difference between discounting and compounding?

While the value of money is relatively stable in the American economy, time does affect its value. Time is a measure of risk in finance. Economic conditions, inflation, interest rates, the money supply, and investor expectations all change over time and, therefore, affect the value of money. The saying is true: "A dollar today is worth more than a dollar tomorrow". This is true because no one can accurately predict what will happen between today and tomorrow or between now and the next minute. There is a risk when investing or holding money in any form for any period. The more money or assets held in forms less liquid than cash, the greater the risks.

Financial calculations take into account the relationship between time and monetary value. These calculations compute what is called the time value of money. When computing the value of money over multiple time periods, finance uses formulas to reflect that the value of a lump sum in the future (future value) or the value of a future lump sum in the present (present value) differs based on the interest rate, whether the investment earns simple or compound interest, the number of periods interest is earned for, and the total life of the investment.

The process of calculating the future value of an investment by applying interest or returns to both the original principal and previously accumulated interest over multiple periods is called compounding. Calculating values back to the present is called discounting. To find the present value, you will give a discount (a reduction applied to a future value to account for the time value of money and determine what that future amount is worth in today's dollars) on the present value. To find the future value of a lump sum, you compound it into the future.

Review

To review, see:


3b. Compute present and future values

  • What is the difference between present value and future value?
  • How do we calculate the future value of a lump sum?
  • How do we calculate the present value of a future lump sum?

Finance has two ways of computing the value of a lump sum of money over a period of time to account for changes in the time value of money. An investor needs to answer two basic questions in money valuation: 1. How much is a lump sum worth at n periods into the future? and 2. How much is a future lump sum worth today?

These questions represent the future value and present value, respectively. To answer the first question, you need to compound; to answer the second question, you need to discount. To compound a lump sum, you multiply it by the compound factor. To discount a lump sum, you multiply it by the discount factor.

The valuation of every type of financial instrument or transaction is a variation on the present value or future value computation. Present value is the current worth of a future sum of money or stream of cash flows, discounted at a specific interest rate. Future Value is the amount of money an investment made today will grow to at a specified interest rate over time.

To accurately calculate the present or future value, you need some standard inputs, such as the interest rate (which becomes the discount rate or compound rate), the number of times in one year the investment compounds, the total number of years in the life of the investment, and the lump sum amount. The lump sum amount is multiplied by all of the other elements of the equation, which combine to form either a compound factor or a discount factor. The compound factor and the discount factor are inverses of each other. Future and present values can be computed for lump sums or multiple flows. The future value of multiple flows and the present value of multiple flows require the same basic components.

The present value and future value equations are:

Present Value: FV(1+r)t
Future Value: PV(1+r)t
Review

To review, see:


3c. Compute rates of return and their use in financial decision-making

  • How do we compute the profit earned on an investment?
  • Why is profit earned quoted as a percentage rate?
  • How do rates of return influence investment decisions?

The ultimate goal of investing is to profit from the investment. In finance, the profit is called return. The rate of return (or yield), expressed as a percent, is the ratio of the profit to the amount invested. Sometimes, firms or investors desire a certain rate of return before entering into a transaction. After calculating the potential value, the investor can decide not to enter the transaction if the rate of return is unacceptable. A predetermined rate of return can also be used as the discount rate when valuing a transaction. A desired rate of return can be arbitrarily chosen based on market conditions or historical returns an investor has received. Thus, rates of return influence investment decisions by measuring and comparing investment attractiveness to determine profitability. It helps determine if return justifies risk, guides acceptance/rejection based on required returns, and supports allocation to maximize overall portfolio return.

Review

To review, see:


3d. Calculate simple and compound interest

  • What is the difference between simple interest and compound interest?
  • How do we compute simple interest?
  • How do we compute compound interest?

Interest is the amount paid for or earned on a transaction, depending on which side of the transaction you sit on. An interest rate is a price paid for money, stated as a percentage of the principal or some other specified amount. There are many interest rates in the economy, and they differ based on the relevant product and market.

There are two main ways to calculate interest: simple or compound interest. With simple interest, you only earn interest on the principal amount. Simple interest is calculated by multiplying the stated interest rate by the principal amount. The product of that operation is the amount of interest for the given period. Repeat these steps for each period interest is earned. For the final step, sum all the interest amounts for each period to get the total interest earned on the transaction using simple interest.

We can calculate simple interest using the formula 𝐼 = 𝑃 x r x t

Compound interest differs from simple interest because it allows one to earn interest on their interest. This means that in the equation, over multiple periods, the interest calculation includes the principal and interest from all prior periods. This results in a final amount when using compound interest that is greater than the simple interest, which would use the same inputs for the equation. We can calculate compound interest using the formula A=P(1+r/n)nt

Review

To review, see:


3e. Calculate present values, future values, and payments using non-annual compounding

  • How does the frequency of compounding change the future value?
  • What is non-annual compounding, and how does it differ from annual compounding?
  • How do you calculate time value of money problems using non-annual compounding?

Financial investments are typically held over a period of time or usually earn interest over a period of time. When calculating future or present value, the investment can last for one period or multiple periods. Each period represents a period of compounding.

When computing future value, the greater the number of periods, the greater the final amount will be. The time horizon matters, as well. The longer the time the investment compounds, the greater the final future value after multiple compounding periods. The opposite is true when calculating the present value for multiple periods. The more frequently the investment is discounted and the longer the investment's life, the smaller the present value.

Non-annual compounding refers to the process of calculating interest more than once per year, such as monthly, quarterly, semiannually, or even daily. It contrasts with annual compounding, where interest is added to the principal only once a year. When multiple periods are used, the value of n in the equations below is greater than one. Compounding for one period usually uses the word annual, whereas compounding for multiple periods uses words other than annual, such as daily, continuously, biannually, semiannually, or quarterly. The value of n is always written in comparison to annual terms. For example, an investment that compounds every two years (biannually) would have an n of 0.5, whereas something compounding every six months (semiannually) would have an n of 2.

Try these examples:

  1. You invest $1,000, earning 5% interest compounded semiannually. How much will you have in total at the end of three years?
  2. You invest $1,000, earning 5% interest compounded biannually. How much will you have in total at the end of three years?
Review

To review, see:


Unit 3 Vocabulary

This vocabulary list includes terms you will need to know to successfully complete the final exam.

  • annual
  • compound factor
  • compounding
  • compound interest
  • discount
  • discount factor
  • discount rate
  • future value
  • interest rate
  • present value
  • rate of return
  • simple interest
  • time value of money