PLEASE FIND THE ATTACHMENT FOR THE LESSON PROVIDED FOR SOME EXAMPLES OF TVM PROBLEM SCENARIO

1.This week, the lesson provided some examples of TVM problem scenarios. For your first post, provide a story problem that can be solved using one or more of the TVM calculations.

2.Your second post will be a description of how the problem posed by another student can be solved.

3.For your next post, describe some of the assumptions behind the TVM calculations. How do these assumptions limit our application of these calculations?

Why Is the Value of Money Related to Time? The time value of money (TVM) is a huge concept in managerial finance. The existence of TVM drives a good deal of the financial decision-making undertaken by business and individuals. TVM may be the most important concept in finance. In the opinion of many, it is no less important than any other concept. TVM is based on the idea that a given amount of money in the present time is worth more than that same amount of money in a future time. Typically, we say that a dollar today is worth more than a dollar a year from now. But TVM concepts don't depend on the money being a dollar and the time period being a year. Three basic concepts underlie the time value of money. Inflation: Inflation is a condition in which prices generally rise. So, if a loaf of bread costs $2.00 today, a similar loaf of bread will probably cost more than $2.00 a year from now. That means that each of the two dollars today are worth more than they will be a year from now because it will take more than two of them to buy the same loaf of bread. The effects of inflation on TVM assumes that the economy is in an inflationary period. This is very often the case. Deflationary periods are pretty rare in our economy. Risk: Let's say that your favorite professor asked to borrow $1,000 for one year, and you were kind enough to lend it to them. At the end of the year, you e-mailed the professor to ask for your money, and the e-mail bounced. You tried to call the professor, but the phone number they had given you was disconnected. Then you contacted the school and found out that the professor had been gone for about a year, and they didn't know where he went. So, you lost your $1,000. One way that you could have avoided this problem was by not lending money at all. But if you do lend money, and you don't want to lose it, you might want to lend money to a lot of different people and charge them interest. Some of them won't pay, but the ones who do pay will pay enough to make up for the ones who don't pay. You don't know which ones are not going to pay, or you would not lend them the money in the first place. So, what you might do is to lend the money to all of your borrowers as long as in return for the $1,000 today they promise to give you $1,100 one year from now. So, one dollar would be worth 1/1,000th of today's but only 1/1,100th of the amount required to establish equality one year from now. Preference for immediate gratification: Apparently humans prefer to have good experiences sooner rather than later and bad experiences later than sooner. If you were going to receive $1,000,000 in lottery winnings, would you prefer to receive it today or five years from now? Unless there is something unusual, like you were planning to divorce your spouse, you probably would want to receive the winnings today. There are a few exceptions to this rule. For example, if you were getting married (and you considered that to be a good thing), you might prefer to get married a year from now rather than right now so that you could enjoy the anticipation and planning. For something that you would prefer to get sooner rather than later and that could be translated into monetary terms, you might be willing to receive it later as long as you were properly compensated for the delay. An example of that is the time, effort, and money you are putting into the pursuit of your master's degree. You are probably doing that because you believe that the payoff in the future will be much greater than the cost now. Five Components of the Time Value of Money The TVM relationship can be encapsulated into a set of five terms with concepts and formulas that tie them together. The five terms are present in every TVM relationship. If we know the values for four of the five terms, we can always solve for the fifth term. If we do not know the values for four of the terms, we can never solve for the fifth term. It doesn't make any difference which term we are solving for. We can find any of them as long as we know the other four. Here are the five terms with brief descriptions. These descriptions will be enough to get you started. We will then work through a few scenarios to help you nail down the concepts. The abbreviations for the terms are taken from primarily the HP-12C calculator (we'll explain why in a little bit.), Excel, and a few finance textbooks. Different books or applications use slightly different abbreviations for the terminology. That is just something we need to adapt to. Present Value (PV) is the amount of money now. We are generally looking from now into some future time period. If we are looking into the past, we consider that past time to be the present and now to be the future. For example, if we have $100,000 now having started 10 years ago with a certain amount earning 10% per year, what was the amount that we started out with? The amount that we started out with 10 years ago is the present value, and the amount that we have now is the future value. Confusing enough? Future Value (FV) is the amount of money in the future. Let's say that right now we have $10,000 (PV), we can earn 10% per year on it, and we can leave it on deposit for 10 years. How much money will we have in 10 years? That amount of money is the future value. Rate (I, i, r, R) is the annual percentage rate at which our investment will grow. One easy way to think about this is that it is the interest rate that we would be paid on a bank deposit, but interest rates on bank deposits are pretty much stated. Sometimes we need to find an imputed interest rate or an actual interest rate earned. These are essentially the same idea with some technical differences. Term (N, NPERS, TIME, YEARS) is the amount of time in the scenario. The term can be in any time unit: days, weeks, months, half years, or years. The unit doesn't really matter as long as we know what the unit is and make our decisions accordingly. Payment (PMT) is the periodic payment that is either an addition to or a withdrawal from a current amount. For example, the monthly payment on a car loan is an example of payment. The annual payment you might receive if you won the Publishers Clearing House sweepstakes instead of the $20,000,000 lump sum you thought you would receive is another example. Demonstration Below is a demonstration that will help you understand some of the ideas behind TVM. Transcript TVM Demonstrator.xlsx Example Scenarios TVM concepts are applicable to many types of problems. Some of those problems don't even have to be financial. Some example scenarios are provided below. See if you can determine how TVM would be used to solve the scenarios. You may wish to ask about any of these that you're not sure of in this week's discussion. Mary buys a bottle of wine for $300. She expects that it will appreciate in value at a rate of 15% per year. What will the bottle of wine be worth in five years? Jos is presented with a business opportunity. The opportunity would result in cash flows of $5,000 per year for each of the next 10 years. Jos is currently earning 12% per year on his other investments. What is the most Jos could pay for this opportunity and have it make sense? David is bothered by the number of chipmunks living in his yard. There seem to be about 50 of them, and the population seems to be increasing by about 20% per year. If nothing changes, how many chipmunks will be in his yard in 10 years? Rhonda wants to borrow some money to buy a car. She needs $25,000 and wants a five-year loan. The finance manager is offering a rate of 3% per year. What would her monthly payments be at this rate? What if she could negotiate the rate down to 2% per year? What if the finance manager asked her for 4% per year but, in return, would reduce the price of the car by $1,000? Making up and solving your own scenarios or working with classmates to do this would be beneficial as well. Self Quiz Here some flashcards that you can use to review TVM concepts. TVM Concepts Print Shuffle Other things being equal, a higher interest rate on a car loan will result in ____________ payments. Higher. Card 1 of 7 View each term then click "Flip Card" to see the definition. Previous Card Flip Card Next Card Finding TVM Values There are roughly five ways of doing TVM calculations. Brute Force, Trial and Error, Repetitive Calculations: This method involves performing calculations that will eventually lead someone to the right answer. For example, given a car loan of $20,000 with a five-year term and a 3% interest rate, what would be the payment? Someone could guess at the amount, do all 60 calculations, and see if he or she guessed at payment results in a balance of zero dollars at the end of the 60 months. If the balance is more than zero, he or she would then try it again with a higher payment. If the balance was less than zero, he or she would then try again with a lower payment. Eventually, this would lead to the right answer, but there are better ways of doing it. These methods are not appropriate for use in a course at our level. Formulas: There are formulas for finding any of the five components of the TVM model as long as the four others are known. Using these formulas takes a little more time than some other methods, but it has the advantage of not requiring a specialized calculator. In the olden days, students had to memorize the formulas. There isn't much point in memorizing the formulas now, but there are two formulas that you should know. The future value of a fixed sum is found using FV = PV(1 + i)n. The present value of a fixed sum is found using PV = FV/(1 + i)n . You don't need to know any more TVM formulas. One benefit of knowing all of the formulas is that in the event of a zombie apocalypse, you could become the finance expert who could be in charge of banking during the rebuilding of the world. Tables: Tables that give, for instance, the future value of $1 at a combination of ranges of interest rates and terms exist. If someone was trying to find the future value of $800 in five years at 6% interest, he or she would use the table to find the future value of $1 in five years at 6% interest and multiply it by 800. There are tables for all relevant calculations. If you would like to see examples of these tables, Google "present value table". Spreadsheets: Spreadsheet programs, such as Microsoft Excel, include functions for all of the calculations you will need to do for this course and real life. People typically have a computer capable of doing these calculations handy. The only significant drawbacks are that someone using the spreadsheet would need to know how to use the functions and would have to set up the spreadsheet. Calculators: Specialized financial calculators are available with built-in functions for TVM calculations. One example is the Hewlett-Packard HP-12C. Another example is the Texas Instruments BAII Plus. Many people are of the opinion that the HP-12C is more user-friendly, but with a retail price of about $68, it is more expensive than the Texas Instruments BAII Plus at about $27. Apps that run on cell phones as well as emulators that run on PCs are available at much lower cost and have the advantage of being on one's phone. Scientific calculators typically do not have the built-in functions necessary for TVM calculations and are not suitable for this purpose. TVM Examples Transcript Transcript Helpful Hints Besides an understanding of the fundamental concepts, there are some nitty-gritty items that could get in the way of TVM calculations. Here are some things you will want to make sure you take into account when doing TVM calculations. Time Units: Units of time must be consistent. If the payment is monthly, the term and interest rate must also be stated using monthly figures. For example, when we talk about car loans, we usually talk about an annual rate, and we often talk about a loan for a certain number of years. However, the payment on a car loan is typically made monthly, so instead of saying we have a rate of 5%, we would need to use a rate of .4167 percent. Additionally, instead of talking about a five-year term, we would need to use a 60-month term. Direction of Signs: Usually, when we're talking about TVM values, we don't consider whether the numbers are positive or negative. For example, if we put $1,000 in the bank today at a 5% interest rate, we believe it will be worth $1,050 a year from now. But for calculators and spreadsheets, we would probably say that the PV is -1000 and the FV is 1050. Basically, receiving money and giving money have to have opposite signs. This is easy enough for some basic calculations, but it can get more complicated. One way, albeit a childish way, of keeping this straight is to think about putting money into your pocket as being positive and taking money out of your pocket as being negative. So, if I take $100 out of my pocket and deposit it in the bank, that amount is really -100. If I withdraw $100 from the bank, that amount is +100. If I take out a $20,000 car loan, the PV is positive because the lender gave me $20,000 (this is a separate transaction from buying the car), and the payments are negative because the monthly payments are coming out of my pocket. If you go the other way with the signs, that will be fine. You will still get the right answer. However, sometimes the problems are a little bit more complicated. Let's say that I take out a loan of $20,000 for five years at 8% interest and will be making monthly payments, but the loan is structured so that it will have a balloon payment of $4,000 at the end of the fifth year rather than paying off to zero. In this case, the $20,000 is positive, the monthly payments are negative, and the future value is negative, as well. Decimal Places: Different ways of calculating TVM values expect different forms of input for interest rates. An interest rate of 5% is entered as 5 in an HP-12C but as .05 in Excel and in most formulas. Just be sure to know which way the input should be for the method you are using. Otherwise, you may get some really weird results. Conclusion TVM is a vital concept to finance. This lesson and the reading in the textbook will help you get started. The Problem Set, the Discussion, and the Quiz will help you continue to learn about TVM. TVM is something that you will use throughout your management career