Economics
Present Value
Present value is a financial concept that calculates the current worth of a future sum of money, taking into account the time value of money. It is used to determine the value of an investment or a stream of cash flows in today's terms, considering factors such as interest rates and inflation. This calculation helps in making informed financial decisions.
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12 Key excerpts on "Present Value"
- Ivan E Brick(Author)
- 2017(Publication Date)
- WSPC(Publisher)
CHAPTER 2TIME VALUE OF MONEY
The Time Value of Money
The value of money a year from now is less than the value of that money today. Why is that? The reason is that you can invest money today and hopefully receive a larger amount in the future. Since money has a time value associated with it, financial analysts must consider the Present Value (PV) of future cash flows when they are making financial decisions.Learning how to take Present Value of future cash flows is one of the most important lessons in finance. Why? As we will discuss later, the price of any asset is the Present Value of its cash flows. Moreover, Present Value provides the framework that allows managers to rank competing capital projects and to help determine the cheapest source of financing.Finding the Present Value of Future Cash Flows
Imagine that our bank is willing to offer us 10% interest on a $100 deposit. At the end of the year the future value (FV) of our investment should be our initial investment of $100 plus the promised interest of 10% on our investment or $110. Another way of saying this is that the promised future value of $110 one year from now has a Present Value of $100 today. In fact, an investor should be indifferent from receiving $100 today or $110 one year from now because the investor is able to invest $100 today at an interest rate of 10% and receive $110 at the end of the year.Let us analyze our problem more closely so that we can generalize the relationship between Present Value and future value. We made the observation that if we invested $100 at 10% it will be worth $110 at the end of year 1. That is, we will receive our original investment of $100 and interest of 10% of that $100. Mathematically this is written as:$100(1.1) = $110. By dividing both sides of that equation by 1.1 we find the Present Value of the $110 or PV = $110/(1.1) = $100. The more general mathematical formula for PV is given by:where CFT is the cash flow at time T and R is the interest rate. In the example above, R is the annual interest of 10%. In our example, T
eBook - PDF- Robert Parrino, David S. Kidwell, Thomas Bates(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
The application of the future value formula in business decisions is presented in Section 5.4. 3. Explain the concept of Present Value and how it relates to future value, and be able to use the Present Value formula to make business decisions. The Present Value is the value today of a future cash flow. Computing the Present Value involves discounting future cash flows back to the present at an appropriate discount rate. The process of discounting cash flows adjusts the cash flows for the time value of money. Computationally, the Present Value factor is the reciprocal of the future value factor, or + i 1/(1 ). The computation and application of the Present Value formula in business decisions are presented in Section 5.3. 4. Discuss why the concept of compounding is not restricted to money, and be able to use the future value formula to calculate growth rates. Any number of changes that are observed over time in the physical and social sciences follow a compound growth rate pattern. The future value formula can be used in calculating these growth rates. S U M M A R Y O F L E A R N I N G O B J E C T I V E S 1. Explain what the time value of money is and why it is so important in the field of finance. The idea that money has a time value is one of the most fundamental concepts in the field of finance. The concept is based on the idea that most people prefer to have goods today rather than wait to have similar goods in the future. Since money buys goods, they would rather have money today than in the future. Thus, money today is worth more than money received in the future. Another way of viewing the time value of money is that your money is worth more today than at some point in the future because, if you had the money now, you could invest it and earn interest. Thus, the time value of money is the opportunity cost of forgoing consumption today. Applications of the time value of money focus on the trade-off between current money and money received at some future date.
eBook - ePubThe Capital Budgeting Decision
Economic Analysis of Investment Projects
- Harold Bierman, Jr., Seymour Smidt(Authors)
- 2012(Publication Date)
- Routledge(Publisher)
Chapter 2The Time Value of Money
The frenetic buying of Internet stocks is going to make the tulip buyers of the 17th century look like value players.Rick Berry, director of equity research at J. P. Turner &Company in Atlanta. The New York Times, January 9, 1999Compound interest is one of the wonders of this world. It is the basis of the Present Value calculations. The Safra Bank issued bonds that mature in 1,000 years. The Present Value of $1,000,000,000 of principal payments of this bond at a 0.08 annual interest rate is much less than $0.01. Compound interest is very powerful. A future sum may have a very small Present Value. A very small present amount might grow to a large sum in the future.To better understand the time value of money, we shall first assume that both the discount rate and the dollar amounts are known with certainty. These assumptions enable us to establish basic mathematical relationships and to compute exact relationships between future sums and their Present Values.Time Discounting
One of the basic concepts of business economics and managerial decision-making is that the Present Value of an amount of money is a function of the time of receipt or disbursement of the cash. A dollar received today is more valuable than a dollar to be received in some future time period. The only requirement for this concept to be valid is that there be a positive rate of interest at which funds can be invested or borrowed.The time value of money affects a wide range of business decisions, and how to incorporate time value considerations systematically into a decision is essential to an understanding of finance. The objective of this chapter is to develop skills in finding the present equivalent of a future amount or future amounts and the future equivalent of a present amount.Symbols Used
X Cash flow. If X is greater than zero there is a cash inflow. If X is less than zero, there is a cash outflow. t Time index. It can refer to a point in time or an interval (for example, t 
eBook - PDF- Donald E. Kieso, Jerry J. Weygandt, Terry D. Warfield(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
In accounting (and finance), the phrase time value of money indicates that a dollar received today is worth more than a dollar promised at some time in the future. Why? Because of the opportunity to invest today’s dollar and receive interest on the investment. Yet, when decid- ing among investment or borrowing alternatives, it is essential to compare today’s dollar and tomorrow’s dollar on the same footing—to compare “apples to apples.” Investors do that by using the concept of Present Value, which has many applications in accounting. The Importance of Time Value Concepts Financial reporting uses different measurements in different situations—historical cost for equipment, net realizable value for inventories, fair value for investments. As we discussed in Chapters 1 and 3, the FASB increasingly is requiring the use of fair values in the measurement of assets and liabilities. However, for many assets and liabilities, market-based fair value information is not available. In these cases, fair value can be estimated based on the expected future cash flows related to the asset or liability. Such fair value estimates are generally considered Level 3 (most subjective) in the fair value hierarchy. They are based on unobservable inputs, such as a company’s own data or assumptions related to the expected future cash flows associated with the asset or liability. As discussed in the fair value guidance, Present Value techniques are used to convert expected cash flows into Present Values, which represent an estimate of fair value. [1] (See the FASB Codi- fication References near the end of the chapter.) Some of the applications of Present Value-based measurements in accounting topics, which we discuss in this text, include the following. 1 1 GAAP addresses Present Value as a measurements basis for a broad array of transactions, such as accounts and loans receivable [2], leases [3], postretirement benefits [4], asset impairments [5], and stock-based com- pensation [6].
eBook - ePub- Robert Irons(Author)
- 2019(Publication Date)
- Routledge(Publisher)
Compounding, or calculating future values, results in the cash flows growing larger over time as they continue to earn compound interest. Thus, the multiplier used to calculate the future value of a single cash flow will be greater than one. How much greater than one it is will depend upon the interest rate used and the number of periods in the future required. This will be shown in greater detail in the section “Future Value and Compounding.”Discounting, or calculating Present Values, results in cash flows growing smaller the further back in time the value is calculated. For this reason, the multiplier used to calculate the Present Value of a single cash flow will be less than one. How much less than one it is depends upon the interest rate used and the number of periods back in time required. This will be made clear in the section “Present Value and Discounting.”Figure 2.1 The Future Value of $1,000 Invested to Earn 5% APR Over One YearNote that discounting involves the removal of value over time. The value removed represents the return that would be earned by the money if it were available to be invested today. In later chapters, you will see that:- The Present Value of a bond is calculated by removing the required yield on the bond over the life of the bond;
- The Present Value of a stock is calculated by removing the required return on the stock;
- The Present Value of a production project is calculated by removing the cost of money to all investors (bond holders and shareholders); and
- The Present Value of the firm is calculated by removing the cost of money to all investors (bond holders and shareholders).
Thus, when valuing an asset, the purpose of discounting is to account for the return the firm owes to its investors for being able to use their money. In this chapter, we will be valuing future cash flows, and in this case the discount rate represents the opportunity cost of the investment—the yield on the next best investment available.A tool that is helpful in time value calculations, particularly for complex time value problems, is the time line. The time line is used to list cash flows based on when they occur, whether those cash flows are being compounded to calculate a future value or discounted to calculate a Present Value. The time line in Figure 2.1
eBook - PDF- Robert Parrino, David S. Kidwell, Thomas Bates, Stuart L. Gillan(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The idea that money has a time value is one of the most fundamen- tal concepts in the field of finance. The concept is based on the idea that most people prefer to consume goods today rather than wait to have similar goods in the future. Since money buys goods, they would rather have money today than in the future. Thus, a dollar today is worth more than a dollar received in the future. Another way of view- ing the time value of money is that your money is worth more today than at some point in the future because, if you had the money now, you could invest it and earn interest. Thus, the time value of money is the opportunity cost of forgoing consumption today. Applications of the time value of money focus on the trade-off between current dollars and dollars received at some future date. This is an important element in financial decisions because most investment decisions require the comparison of cash invested today Concluding Comments This chapter has introduced the concept of time value of money and the basic principles of Present Value and future value. The table at the end of the chapter summarizes the key equa- tions developed in the chapter. The equations for future value (Equation 5.1) and Present Value (Equation 5.4) are two of the most fundamental relations in finance and will be applied throughout the rest of this textbook. Before You Go On 1. What is the difference between the interest rate (i) and the growth rate (g) in the future value equation? APPLICATION 5.6 Calculating Projected Earnings Problem Disney’s net income in 2019 was $11.05 billion. Wall Street analysts expect Disney’s earn- ings to increase by 1.55 percent per year over the next three years. Using your financial calculator, determine what Disney’s earnings should be in three years. Approach This problem involves the growth rate (g) of Disney’s earnings. We already know the value of g, which is 1.55 percent, and we need to find the future value.
eBook - PDF- Robert Zipf(Author)
- 2003(Publication Date)
- Academic Press(Publisher)
C H A P T E R 4 Present Values Chapter 3 showed how someone who started with a certain amount of money would answer the question, “How much will I have in a given time at a given interest rate?” This chapter covers the opposite case. Suppose you need a certain amount of money at a definite future time, and you have an interest rate you can earn. How much must you set aside now to make sure you have the required future amount at the required future time? This is called a Present Value. In this chapter, we look at the Present Value equations and at Present Value interest tables and we examine how the Present Values change as interest rate and time change. We then use the Present Value concept to analyze a proposed project, so we can determine whether or not we should proceed with the project. We use this Present Value analysis of a project to develop the concept of internal rate of return. This is a common problem in many activities, including many busi-ness applications. We will use the concept of Present Value throughout this book. It is the most important of the concepts we present in the chapters on compound inter-51 est functions, even more widely used than the compound interest concept. You should understand this chapter on Present Values thoroughly, including the Present Value equations, before you go on to the next part of the book. This chapter also builds on the previous chapter. Mathematical develop-ments presented in the previous chapter, such as compounding within a period and continuous compounding, will not be repeated here. WHAT IS Present Value? Suppose you need a given amount of money at some given time in the future. You might want to know, “How much do I need to put aside now, at a given interest rate, to have the money I need at the time I need it?” Here are some examples. You wish to provide a college education fund for your 2-year-old child. You figure you will need $100,000 in 16 years, and you can earn 6% interest, com-pounded yearly.
eBook - ePub- Brümmer LM, Hall JH, Du Toit E(Authors)
- 2017(Publication Date)
- Van Schaik Publishers(Publisher)
criterion is whether the discounted future sum has a higher value than the initial cost or principal of the investment as it stands at present. If the discounted income is less than the initial cost, a loss will result and the investment is best avoided. If the discounted income is greater than the cost of the investment, the investment should be a profitable one.The decision to invest is made easier when the fundamentals of the Present Value formula are extended to create another formula, namely the net Present Value (NPV) formula. In this section, we shall extend the Present Value formula so that it may be applied in the NPV method of investment analysis. In this book, any reference to investments would include those such as the purchase of fixed assets, or an additional project such as another business, and investing in shares.The Present Value formula
In the previous section, we derived the future value formula as:If we now wish to determine the Present Value (PV), then by algebraic transposition we would get:FV = PV(1 + k )nPV=FV( 1 + k )n= FV ×1( 1 + k )nThe expressionis used to calculate the discount factor or Present Value factor (PVF). This factor, multiplied by the future value of a certain sum of money, will then give the Present Value of that future sum.1( 1 + k )nLet us suppose that we have a future sum of R100 due in three years’ time, and that we want to determine what that sum is worth at present. Let us suppose further that the opportunity cost of capital is 10%, which is the rate we must use as our discount rate. Substituting these values into the PV formula, we get:= R100 ×1( 1 + 0.10 )3Now, the PVF is calculated in the same way as the compounding factor except that, in terms of the formula, the compounding or future value factor must be 156 divided into 1 each time a Present Value factor is calculated. Therefore, the discounting factor for three years at 10% is calculated as follows.We found previously that the compounding factor of (1 + 0.10)3
eBook - PDF- Robert Parrino, David S. Kidwell, Thomas Bates(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
When you work through Learning by Doing Application 5.4, you will see the new notation. Calculator Tip: Calculating the Present Value of Multiple Cash Flows To calculate the Present Value of future cash flows with a financial calculator, we use exactly the same process we used in finding the future value, except that we solve for the Present Value instead of the future value. We can compute the Present Values of the individual cash flows, save them in the calculator’s memory, and then add them up to obtain the total pres- ent value. 152 CHAPTER 5 I The Time Value of Money, Discounted Cash Flows, and Valuation 1. Explain how to calculate the future value of a stream of cash flows. 2. Explain how to calculate the Present Value of a stream of cash flows. 3. Why is it important to adjust all cash flows to a common date? BEFORE YOU GO ON > LEARNING BY DOING A P P L I C A T I O N 5 . 4 PROBLEM: For a student—or anyone else—buying a used car can be a harrowing experi- ence. Once you find the car you want, the next difficult decision is choosing how to pay for it—cash or a loan. Suppose the cash price you have negotiated for the car is $5,600, but that amount will stretch your budget for the year. The dealer says, “No problem. The car is yours for $4,000 down and payments of $1,000 per year for the next two years. Or you can put $2,000 down and pay $2,000 per year for two years. The choice is yours.” Which offer is the best deal? The interest rate you can earn on your money is 8 percent. APPROACH: In this problem, there are three alternative streams of cash flows. We need to convert all of the cash flows (CF n ) into today’s dollars (Present Value) and select the alternative with the lowest Present Value (price).
eBook - PDF- Scott Besley, Eugene Brigham, Scott Besley(Authors)
- 2021(Publication Date)
- Cengage Learning EMEA(Publisher)
Because we discuss the application of this function in much greater detail in Chapter 9, we will wait until then to describe in more detail the process of solving for NPV using a financial calculator. After computing the Present Value of an uneven cash flow stream, we can use either Equation 4.1 or a finan- cial calculator to determine its future value. For the cur- rent situation, FVCF 3 5 $869.02(1.05) 3 5 $1,006. This is the same result we found earlier using Equation 4.4. 6 4-3f Comparison of FV with PV— Understanding the Numbers It is important you get the correct solutions when solv- ing TVM problems; more important, however, is that you interpret the solutions correctly when making busi- ness decisions. The secret to understanding FV and PV values is to realize that an FV amount contains interest, whereas a PV amount does not. For example, earlier we showed that a $700 investment will grow to $931.70 in three years if the opportunity cost rate is 10 percent; that is, the $700 investment will accumulate $231.70 of inter- est over the three-year period. Let’s examine what this means when making business decisions by considering the following question: If the opportunity cost rate is 10 percent, which amount is it better (preferred) to receive, a $700 pay- ment today or a guaranteed (certain) payment of $931.70 in three years? To answer this question, remember the reason we per- form TVM computations is to restate dollars from one time period to another time period; that is, to “move values through time.” Also remember that we move dollars through time by adjusting the amount of inter- est those dollars have the opportunity to earn, because today’s dollars do not contain the same amount of inter- est as future dollars. Different dollar amounts can be compared only when they have comparable amounts of interest; that is, they are stated in values from the same time period.
eBook - PDF- Timothy Mayes(Author)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. CHAPTER 8 The Time Value of Money 230 Future Value Imagine that you have $1,000 available to invest. If you earn interest at the rate of 10% per year, then you will have $1,100 at the end of one year. The mathematics behind this example is quite simple: 1,000 1 1,000(0.10) 5 1,100 In other words, after one year you will have your original $1,000 (the principal amount) plus the 10% interest earned on the principal. Because you won’t have the $1,100 until one year in the future, we refer to this amount as the future value. The amount that you have today, $1,000, is referred to as the Present Value. If, at the end of the year, you choose to make the same investment again, then at the end of the second year you will have: 1,000 1 1,000(0.10) 1 100(0.10) 1 1,000(0.10) 5 1,210 The $1,210 at the end of the second year can be broken down into its components: the original principal, the first year’s interest, the interest earned in the second year on the first year’s interest, and the second year’s interest on the original principal. Note that we could restate the second year calculation to be: 1,100 1 1,100(0.10) 5 1,210 Or, by factoring out the 1,100 we get: 1,100(1 1 0.10) 5 1,210 Notice that in the second year the interest is earned on both the original principal and the interest earned during the first year. The idea of earning interest on previously earned interest is known as compounding. This is why the total interest earned in the second year is $110 versus only $100 the first year. Returning to our original one-year example, we can generalize the formula for any one-year investment as follows: FV 1 5 PV 1 PV(i) where FV 1 is the future value at the end of year 1, PV is the Present Value, and i is the one-year interest rate (compounding rate).
- Robert Parrino, Hue Hwa Au Yong, Nigel Morkel-Kingsbury, Jennifer James, Paul Mazzola, James Murray, Lee Smales, Xiaoting Wei(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
To make economic decisions involving cash fows, even for a small business such as your pizza restaurant, you cannot compare cash values from different time periods unless they are adjusted for the time value of money. The Present Value Pdf_Folio:176 176 PART 2 Valuation of future cash fows and risk formula takes into account the time value of money and converts the future cash fows into current or present dollars. The cost of the machine is already in current dollars. The correct analysis is as follows: the machine costs $25 000 and the Present Value of the cost savings is $21 506. Thus, the cost of the machine exceeds the benefts; the correct decision is not to buy the new dough-preparation machine. Finding the number of payments Another important financial calculation is determining the number of payments for an annuity. The number of payments tells us the time required on an annuity contract to repay a debt. For example, suppose you decide to purchase a campervan for $35 000 and you agree to pay $700 per month. The bank charges an annual rate of 7.42 per cent compounding monthly. How long will you need to pay off the loan? As we did when we found the payment amount, we can insert these values into equation 6.1: PVA n = CF × 1 − 1∕(1 + i) n i $35 000 = $700 × 1 − 1∕(1.006 183) n 0.006 183 50 = 1 − 1∕(1.006 183) n 0.006 183 0.309 15 = 1 − 1∕(1.006 183) n 1∕(1.006 183) n = 1 − 0.309 15 1.006 183 n = 1∕0.690 85 n × ln 1.006 183 = ln 1.447 5 n × 0.006 164 = 0.37 n = 60 payments n = 5 years To determine the number of payments for the annuity, we need to solve the equation for the unknown value n. First, we need to calculate the monthly interest rate (7.42% ÷ 12 = 0.6183%). You will need to use natural logarithms (ln on your calculator) to solve this equation. Solving this problem as shown above, we find that it will take 60 months for you to pay off this loan, which equals 5 years.
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