Economics
Present Value Calculation
Present value calculation is a method used to determine the current worth of a future sum of money, taking into account the time value of money. It involves discounting future cash flows back to the present using a discount rate. This allows for comparing the value of money received or paid at different points in time.
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11 Key excerpts on "Present Value Calculation"
eBook - PDF- Kumar, K Nirmal Ravi(Authors)
- 2021(Publication Date)
- Daya Publishing House(Publisher)
In effect, Rs.181.40 received right now is equivalent to Rs. 200 received after two years, if the rate of interest is 5 percent. That is, Rs.181.40 and Rs. 200 are just two ways of looking at the same thing. This process of finding the present value of a future cash flow is called discounting. This concept of present value is of central importance in economic analysis. We know that, benefits and costs from projects may not accrue immediately, but rather over a period of time. Since a dollar received today is worth more than a dollar received in the future, future streams of costs and benefits must be reduced to a present-day value. The difference between present and future dollar values is dependent upon the interest or discount rate. For example, the higher the interest rate, the more a dollar will return in the future, if loaned with interest. This logic can also be reversed so that, if future costs and benefits are known, and the interest rate is given, their present value can be calculated by the process of discounting. The concept of discounting is exemplified through Table 10.1.1 . It is clear that, with increase in discount factor, the PWC in a project will decline. Since, no discounting is followed, the undiscounted cost structure lie parallel to the X-axis i.e ., remains same for the entire life of the project ( Figure 10.3 ). From the above discussion, it is clear that, ‘i’ refers to interest (discount) rate, (1+i) refers to compounding factor and 1/(1+i) refers to discounting factor.
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).
- 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- 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- 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 - PDF- Robert Parrino, David S. Kidwell, Thomas Bates, Stuart L. Gillan(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
5-28 CHAPTER 5 The Time Value of Money interest earned on interest. For future value calculations, the higher the interest rate, the faster the investment will grow. The application of the future value formula in business decisions is presented in Section 5.2. 3 Explain the concept of present value and how it relates to future value, and use the present value formula to make business decisions. The present value is the value today of a future cash flow. Comput- ing the present value involves discounting future cash flows back to the present at an appropriate discount rate. The process of discount- ing 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 1/(1 + i). The calculation and application of the present value formula in business decisions is presented in Section 5.3. 4 Discuss why the concept of compounding is not restricted to money, and use the future value formula to calculate growth rates. Any number of changes that are observed over time in the physi- cal and social sciences follow a compound growth rate pattern. The future value formula can be used in calculating these growth rates, as illustrated in Section 5.4. Summary of Key Equations Equation Description Formula 5.1 Future value of an n-period investment FV n = PV × (1 + i) n 5.2 Future value with more frequent than annual compounding FV n = PV × (1 + i/m) m×n 5.3 Future value with continuous compounding FV ∞ = PV × e i×n 5.4 Present value of an n-period investment PV = FV n _______ (1 + i) n 5.5 Rule of 72 TDM = 72 ___ i 5.6 Future value with general growth rate FV n = PV × (1 + g) n Self-Study Problems 5.1 Amit Patel is planning to invest $10,000 in a bank certificate of deposit (CD) for five years. The CD will pay interest of 9 percent. What is the future value of Amit’s investment? 5.2 Megan Gaumer expects to need $50,000 for a down payment on a house in six years.
eBook - PDF- Peter Moles, Robert Parrino, David S. Kidwell(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
For example, the process of discounting (compounding) the cash flows adjusts them for the time value of money because today’s money is not equal in value to money in the future. Once all of the cash flows are in present (future) value terms, they can be compared to make decisions. We discuss the computation of present values and future values of multiple cash flows. 2. Describe how to calculate the present value of an ordinary annuity and how an ordinary annuity differs from an annuity due. An ordinary annuity is a series of equally spaced, level cash flows over time. The cash flows for an ordinary annuity are assumed to take place at the end of each period. To find the present value of an ordinary annuity, we multiply the present value of an annuity factor, which is equal to (1 – Present value factor)/i, by the amount of the constant cash flow. An annuity due is an annuity in which the cash flows occur at the beginning of each period. A lease is an example of an annuity due. In this case, we are effectively prepaying for the service. To calculate the value of an annuity due, we calculate the present value (or future value) as though the cash flows were an ordinary annuity. We then multiply the ordinary annuity value times (1 þ i). We discuss the calculation of the present value of an ordinary annuity and annuity due. 3. Explain what a perpetuity is and how it is used in business and be able to calculate the value of a perpetuity. A perpetuity is like an annuity except that the cash flows are perpetual – they never end. British Government bonds, called consols, were the first widely available securities of this kind. The most common example of a perpetuity today are preference shares. The issuer of preference shares promises to pay fixed-rate dividends forever. To calculate the present value of a perpetuity, we simply divide the promised constant payment (CF) by the interest rate (i).
eBook - PDFThe Economics Of Livestock Systems In Developing Countries
Farm And Project Level Analysis
- James R Simpson(Author)
- 2019(Publication Date)
- CRC Press(Publisher)
., '---..----' '---r----' '---,-----' L-.--,r-----1 I I L...---,,----' '-------'1-----.JL.------''------' { ;u~3 '-------' '-------' '-------' '-------' •cALCULATE FO~ EACH ITEM OF COST 0~ INCOME WHE~E THE PAYMENT IS EITHEII IN VARYINC AMOUNTS 011 ,.AID AT llflfi!CUUR IHTEifVAU. FIGURE 9.1 FORMULAS USED IN TIME VALUE OF MONEY PROBLEMS SOURCE: ADAPTED FROM WALRATH (1977). ....... ...... , 1.0 180 Table 9.1. Formulas and examples for problems with one-time cost or income Example investment problem Formula 1) Future amount of a present value (compounding) a A -P(l +i)n Definition of symbols A -amount of future value P -present value or principal i -interest rate per conversion period n -number of conversion periods Example A parcel of land is sold for $10,000 and invested for 10 years at 12 percent compounded annually. What is the value at the end of 10 years? A -P(l + i)n A-$10,000 (1.12)10 A-$10,000 (3.106) A -$31,060 2) Present value of a future amount (discounting) a Example P -A(l +i)-n You sell a parcel of land with the agreement made that the money will be invested at 12 percent compounded annually for 10 years. The value at the end of 10 years is to be $10,000. What is the present value? P .. A(l + i) -n P = $10,000 (1.12)-n p-$10,000 (0.322) p = $3,220 asee Appendix 9.1 for (1 + i)n and Appendix 9.2 for the (1 + i)-n factors. 181 A very common application of this problem is opportunity-cost comparison problems. Opportunity cost is defined as the value of other opportunities given up in order to produce or consume another good. For example, if cattle prices drop it may be more profitable (or less costly) for a producer to simply sell part or all of his or her herd and invest the money in some other alternative investment, perhaps outside the livestock industry. The formula provides a quick way to calculate the alternative total return. The present value of a future amount (discounting) is reverse of the preceding problem.
- James J. Farley(Author)
- 2009(Publication Date)
- CRC Press(Publisher)
As stated in the heading of this section, discounted cash flow is the single most important concept in managerial finance, and I hope that you see its application to some of the prob-lems that you now face in your business. As you progress through this book, you will realize how important it is. FINANCE 63 Table 4.6 Present Value of Annuity of $1 per Period for n Periods PERIOD (n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 Formula: PVIFA k k k k k k n t n n k t , ( ) ( ) ( ) = − + = − + + = ∑ = 1 1 1 1 1 1 1 1 1 n 64 THE EXECUTIVE MBA FOR ENGINEERS AND SCIENTISTS Bond Valuation We have already mentioned that the payment on a bond is comprised of a series of regular, usually annual, payments of interest, plus repay-ment of the original investment at the end of the term. If for example, you purchased a $1,000, 10-year, 15% annual interest bond and con-tinued to hold it, you would have given the issuer $1,000 at the begin-ning. At the end of the first year and subsequent years, you would have received $150 from the issuer, until the end of the tenth year, at which time you would receive $150 for interest plus your $1,000 investment back. The return represents two difference sources of funds. The $150 (in this case) you received at the end of each year for ten years.
- 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.
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 234 value (in E5) is always the same as the present value input in B2. This is because the present value and future value are inverse functions of each other. Annuities Thus far, we have examined the present and future values of single cash flows (also referred to as lump sums). These are powerful concepts that will allow us to deal with more complex cash flows. Annuities are a series of nominally equal cash flows, equally spaced in time. Examples of annuities abound. Your car payment is an annu- ity, so is your mortgage (or rent) payment. If you don’t already, you may someday own annuities as part of a retirement program. The cash flow pictured in Figure 8-1 is another example. FIGURE 8-1 A Timeline for an Annuity Cash Flow 0 1 2 3 4 5 100 100 100 100 100 How do we find the value of a stream of cash flows such as that pictured in Figure 8-1? The answer involves the principle of value additivity. This principle says that “the value of a stream of cash flows is equal to the sum of the values of the compo- nents.” As long as the cash flows occur at the same time, they can be added together. Therefore, if we can move each of the cash flows to the same time period (any time period), we can add them to find the value as of that time period. Cash flows can be moved around in time by compounding or discounting. Present Value of an Annuity One way to find the present value of an annuity is to find the present value of each of the cash flows separately and then add them together. Equation (8-4) summarizes this method: PV A 5 a N t 5 1 Pmt t (1 1 i) t (8-4) where PV A is the present value of the annuity, t is the time period, N is the total num- ber of payments, Pmt t is the payment in period t, and i is the discount rate. Copyright 2021 Cengage Learning. All Rights Reserved.
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