Submitted By reduxn

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Words 433

Pages 2

1) Valuation formulae

Let V be the present value of an asset or security that pays cash flows in the future, where the last cash flow is to be received at time T (note that, if cash flows are to be received forever, then T = ∞). Let CFt be the cash flow to be received at time t, and let rt be the appropriate discount rate for the period from now to time t. Then, [pic]

Special cases: i) Time periods between cash flow payments are of equal length ii) The discount rate is the same for all periods (rt = r) [pic] iii) The discount rate is the same for all periods (rt = r), cash flows for times from next period until the maturity of the asset are constant (CFt = C), with an additional final payment being made at maturity (when T = M) [pic] iv) There is only one cash flow to be received, at the maturity of the asset (T = M) [pic] v) The discount rate is the same for all periods (rt = r) and cash flows for times from the next period until the maturity of the asset are constant (CFt = C) [pic] vi) The discount rate is the same for all periods (rt = r) and cash flows are constant forever (CFt = C) [pic]

2) TVM keys on a financial calculator

How do these valuation formulae translate to the TVM keys on a financial calculator?

[pic]

3) Types of cash flow streams

Most general case:

(i) Equal time periods:

(ii) Equal time periods and discount rate:

(iii) Bond valuation:

(iv) Single cash flow:

(v) Annuity:

(vi) Perpetuity:

4) Interest rate conversion formula

Suppose a credit card company charges its customers a nominal rate of 1% per month on their credit balances. This is also referred to as the stated rate or quoted rate. The annual…...

...TIME VALUE of MONEY Exercises Author: Luigi V. TAVA Copyright SDA Bocconi revised 2004.10 EMQ 901 1 1) For a loan of 9.2 estimate the future refund value (principal, interest, total) with simple interest: a) yearly rate 5%, for 6 years and 4 months b) yearly rate 8%, for 7 years, 2 months and 15 days 2) With a starting investment of 3.65 how long does it take to have a final total value of 4.779 with a 5.2% yearly rate, simple interest ? 3) 10 years ago you deposited 15.6 in a bank account paying 5% (yearly compounding). Six years ago you withdraw 8.465 from the same account and reinvested the same amount at 7.25% (yearly) How much is available now (total)? 4) 3 years ago your parents opened a “saving account” in your favour with a bank paying a 10.75% yearly interest rate. How much do you own today for each € deposited? 5) You borrow, as an overdraft on your current account, 50 with an Italian bank charging you a nominal yearly rate of 18%. How much is your debt with the same bank two years later (Italian banks use Nominal Rates convertible quarterly)? 6) You are entitled to receive 100, 3 years from now. What is the present value of your credit discounted at 16% yearly rate? 7) Your bank charges a 16% yearly nominal rate (quarterly compounding) for a loan in your current account; how much will you pay after 3 years for a 400 loan? 8) How much do you have to invest to have 50 after 4 years with a 12% yearly return? 9) An initial bank deposit of 10 is equal to 50......

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...Gregory Cayo Time value of money & inventing Davenport University/ Finc 510 Time Value of money plays a major role in our lives. Whether you are an investor or a worker, somehow you still have to deal with it. As an investor, when starting an investment with a present value, the future value would eventually make profit in the next year or so. In other words, compounding is the name given to a starting investment that generates interest. Additionally, many jobs have 401(k), which allow workers to save and invest their money after their retirement. Some companies are already stockholders. Therefore, workers can be asked to work beyond their retirement deadline when there is a crash in the market. As a result, workers might no longer benefit from their 401 (k) saving. However, they would rather be part of the government retirement plan, which offer a lot lower than the 401(k) retirement plan (Ehrhard & Brigham, 2011). Financial problems are being solved easier when using spreadsheets on excel. The use of spreadsheets provides a visual concept of time value of money including all the transactions that are made by a company. By using spreadsheets, all the calculations are being made using a specific formula respectively. It is also helpful to use a time line when solving finance problems. Whether the problem involves excel or not, a time line is usually required to set up all the formula needed. A Time line tends to simplify the amount of work in a much simpler......

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...Introduction The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year. Additionally, the concept of time value of money is important to financial decision-making because it emphasizes earning a return on invested capital, recognizes that earning a return makes $1 worth more today than $1 received in the future and it can be applied to future cash flows in order to compare different streams of income. A dollar to be paid or received in different time periods will have different values. For instance, a dollar today is worth more than a dollar in two years from now. This is because we can invest the dollar today, which will earn us a rate of return (interest) and create an increased value in two years. This process is called compounding and it involves taking a dollar today (present value), and investing it so that it grows into a larger amount in the future (future value). Additionally, managers must also understand factors which affect time value of money such as annuities which could include interest rates, opportunity costs, future and present values of money, and compounding. According to Brealey, Myers & Marcus, 2004, “each time value of money has five variables: interest rate or return, time or number of periods, future value, present value, and amount of payments either made or received” (pg. 812). The two key components of time value of money are present value (PV) and future value......

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...Time Value of Money: Simple Interest versus Compound Interest Outline I. Applications of Time Value of Money 1.1 Example One 1.2 Example Two 2. Interest 2.1 What is Interest? 2.2 Three Variables of Interest 1. Principal 2. Interest Rate 3. Time 2.3 Why is Interest Charged? 3. Simple Interest 3.1 What is Simple Interest? 3.2 Simple Interest Formula 4. Compound Interest 4.1 What is Compound Interest? 4.2 Compound Interest Formula 5. Compound Interest Tables 1. Future Value of $1 2. Present Value of $1 3. Present Value of an Ordinary Annuity of $1 4. Present Value of an Annuity due 5. Present Value of a Deferred Annuity 6. Conclusion 7. References Abstract The time value of money (TVM) is based on the principle that "a dollar today is worth more than a dollar in the future, (Mott, 2010, pp.31). Waiting for future dollars involves a cost -the cost is foregoing the opportunity to earn a rate of return on money while you are waiting" (pp.31). TVM was developed by Leonard Fibonnacci in 1202 and is one of the basic concepts of finance. One hundred dollars today has a different buying power than it will have in the future. For example, $100 invested in a savings account at your local bank yielding 6% annually will grow to $106 in one year. The difference between the $100 invested now-the present value of the investment-and its $106 future value represents the time value of money,......

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...The Time Value of Money 1 LASA 1 The Time Value of Money Carla E. Holbrook Argosy University 20 September 2013 The Time Value of Money 2 Abstract This analysis is an exercise that examines the problem of a woman who has been working for 25 years and is now approaching retirement. During this exercise I will be required to calculate the following things and give an analysis of what the answer means. a. Calculate compound interest to evaluate the value of her savings account after 20 years of deposits. b. Calculate the bonus payout over 20 years vs a one time payment with interest and distinguish which bonus option would be better for the client. c. Calculate the present value of the bonus and analyze the difference in bonus for the client. d. Analyze the tuition cost for the cline and determine what the future cost will be and determine how these funds can be accumulated over time. The Time Value of Money 3 The Time Value of Money Mary has been working for a university for almost 25 years and is now approaching retirement. She wants to address several financial issues before her retirement and has asked you to help her resolve the situations below. Issue A: For the last 19 years, Mary has been depositing $500 in her savings account , which has earned 5%......

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...The Time Value of Money Mary has been working for a university for almost 25 years and is now approaching retirement. She wants to address several financial issues before her retirement and has asked you to help her resolve the situations below. Her assignment to you is to provide a 4-5 page report, addressing each of the following issues separately. You are to show all your calculations and provide a detailed explanation for each issue. Issue A: For the last 19 years, Mary has been depositing $500 in her savings account , which has earned 5% per year, compounded annually and is expected to continue paying that amount. Mary will make one more $500 deposit one year from today. If Mary closes the account right after she makes the last deposit, how much will this account be worth at that time? Issue B: Mary has been working at the university for 25 years, with an excellent record of service. As a result, the board wants to reward her with a bonus to her retirement package. They are offering her $75,000 a year for 20 years, starting one year from her retirement date and each year for 19 years after that date. Mary would prefer a one-time payment the day after she retires. What would this amount be if the appropriate interest rate is 7%? Issue C: Mary’s replacement is unexpectedly hired away by another school, and Mary is asked to stay in her position for another three years. The board assumes the bonus should stay the same, but Mary knows the present value of her...

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...Time Value of Money: Name: Professor’s Name: Institution: Course Title: Date: Introduction Time Value of Money is the concept that a certain amount of money has a different value today than it would in the future. It is explained as the idea that money at hand at the present time is worth much more than the equal amount would in future (Crosson, 2008). If you lend your friend money today, most likely he will refund the same amount you lend him in future. That money will have added no value to itself. Lending it to your friend is not an investment. The sooner you get the money back, the better because you can invest it elsewhere. Therefore, if one was not to use a given amount of money today, with intentions of using it in the future, he should put that money in a saving account. That way, the money will accrue interest and it will not be of the same amount as initially saved. The amount of interest accrued on saved money depends on three things: the initial amount saved, the bank interest rate and the span of time the money will be saved. Inflation is another factor to be considered when calculating the interest to be accrued. If the inflation is high, the interest reduces since the ‘value’ of money reduces (Carr, 2006). This paper will discuss this concept of time value of money with the help of a question problem. Assuming I am 30 years old plans and I plan to accumulate $1 million by my retirement date, which is 30 years from......

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...12/9/2012 Chapter 9 The Time Value of Money 1 Chapter 9- Learning Objectives Identify various types of cash flow patterns (streams) that are observed in business. Compute (a) the future values and (b) the present values of different cash flow streams, and explain the results. Compute (a) the return (interest rate) on an investment (loan) and (b) how long it takes to reach a financial goal. Explain the difference between the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR), and explain when each is more appropriate to use. Describe an amortized loan, and compute (a) amortized loan payments and (b) the balance (amount owed) on an amortized loan at a specific point during its life. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 2 1 12/9/2012 Time Value of Money The principles and computations used to revalue cash payoffs at different times so they are stated in dollars of the same time period The most important concept in finance used in nearly every financial decision Business decisions Personal finance decisions Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 3 Cash Flow Patterns Lump-sum amount – a......

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...TIME VALUE OF MONEY Future Values and Compound Interest Interest is the price paid for the use of borrowed money You have $100 invested in a bank account. Suppose banks are currently paying an interest rate of 6 percent per year on deposits. So after a year, your account will earn interest of $6: Interest = interest rate × initial investment = .06 × $100 = $6 You start the year with $100 and you earn interest of $6, so the value of your investment will grow to $106 by the end of the year: Value of investment after 1 year = $100 + $6 = $106 Notice that the $100 invested grows by the factor (1 + .06) = 1.06. In general, for any interest rate r, the value of the investment at the end of 1 year is (1 + r) times the initial investment: Value after 1 year = initial investment × (1 + r) = $100 × (1.06) = $106 What if you leave this money in the bank for a second year? Your balance, now $106, will continue to earn interest of 6 percent. So Interest in Year 2 = .06 × $106 = $6.36 You start the second year with $106 on which you earn interest of $6.36. So by the end of the year the value of your account will grow to $106 + $6.36 = $112.36. In the first year your investment of $100 increases by a factor of 1.06 to $106; in the second year the $106 again increases by a factor of 1.06 to $112.36. Thus the initial $100 investment grows twice by a factor 1.06: Value of account after 2 years = $100 × 1.06 × 1.06 = $100 × (1.06)2 = $112.36 If you keep your money invested for......

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..."Time Value of Money and Annuity" Please respond to the following: • From the e-Activity, create a personal scenario that exemplifies the time value of money that includes the opportunity cost involved. According to Investopedia, the time value of money is the concept that money available today is worth more than the same amount of money in the future based on its earning potential up until the time the future amount is received. It is the potential of money to grow in value over time. The basic understanding is that a bird in hand is worth two in the bush. Money is worth more to the user when it is available immediately because money can be invested or earn interest. It applies to many contracts where delayed payment requires compensation for the time value of money. Suppose you were to receive $100 today or the same amount in one year. If you were to invest the $100 at an annual interest rate of 8%, it would increase by a factor of 1.08 to $108 in a year. If you were to divide the $100 by the same factor, the $100 received in a year would be worth $92.59 today. The time value of money, also referred to as the present discounted value, is clearly illustrated. The sooner you have money, the more worthy it is because you can put it to use. • Describe one (1) real-life example that shows the manner in which a person can use an annuity for retirement planning. An annuity is an insurance product that pays out income. You make an investment in the annuity, and it then......

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...Time Value of Money Terminology Terminology (AKA jargon) can be a major impediment to understanding the concepts of finance. Fortunately, the vocabulary of time value of money concepts is pretty straightforward. Here are the basic definitions that you will need to understand to get started (calculator key abbreviations are in parentheses where appropriate): Banker's Year A banker's year is 12 months, each of which contains 30 days. Therefore, there are 360 (not 365) days in a banker's year. This is a convention that goes back to the days when "calculator" and "computer" were job descriptions instead of electronic devices. Using 360 days for a year made calculations easier to do. This convention is still used today in some calculations such as the Bank Discount Rate that is used for discount (money market) securities. Compound Interest This refers to the situation where, in future periods, interest is earned not only on the original principal amount, but also on the previously earned interest. This is a very powerful concept that means money can grow at an exponential rate. Compounding Frequency This refers to how often interest is credited to the account. Once interest is credited it becomes, in effect, principal. Note that the compounding frequency and the frequency of cash flows are not always the same. In that case, the interest rate is typically adjusted to an effective rate that is of the same periodicity as the cash flows. For example, if we have quarterly cash......

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...1. The four basic variables of the time value of money (TVM) equation are: FV = future value PV = present value r = interest rate, yield, discount rate or growth rate n = the time period between the present value and the future value These variables can be arranged in several ways to solve many questions about money. The most basic form of the equation is FV = PV x (1+r)^n Example: if I have $1,000.00 in my bank account today earning 5% interest for a period of 10 years, what is the future value? FV = 1000 x (1+.05)^10 = $1,628.89 When the interest (growth) rate increases, future value increases as well. Example: if I have $1,000.00 in my bank account today earning 10% interest for a period of 10 years, what is the future value? FV = 1000 x (1+.10)^10 = $2,593.74 Discount rate is the opposite of growth rate. When the discount rate increases, present value decreases. 2. A series of payments can be described as making payments at regular intervals in varying amounts. In other words, if I make payments to a creditor on the 5th day of every month for 1 year, with each amount being different depending on my purchases that month, I am making a series of payments. An annuity, on the other hand, is a series of equal payments at regular intervals. If I make all my payments for $100.00 to a creditor on the 5th day of every month, this is considered an annuity. These are typically found in contractual obligations or other similar legally binding agreements...

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...Time value of money is the concept that shows the value of money which decreases day by day. There are so many factors which contribute to the time value of money such as inflation and increasing interest rates. The time value of money is sued to solve the problems which are related to the loans, mortgage, leases, saving and annuities. In the investment, time value of money is used to compare the alternatives of investment (Weil, 1990). The time value of money is based on the concept that money that anyone has today is worth more than the expectation which one will receive in the future. The money which is hold in the present is worth more because it can be invested and can earn the interest. For example, one can invest the dollar for one year at a 6% annual interest rate and accrue &1.06 at the end of the year. Then it can be said that the future value of the dollar is $1.06 given an interest rate and the present value of the $1.06 it is expected to receive in one year is only $1 (Drake, & Fabozzi, 2009). Interest rates and series of payments are included in the transactions. If the time value money is not used in past then there may be risk in the transaction. This helps in reaching at the comparable value of the money. that anyone has today is worth more than the expectation which one will receive in the future. The money which is hold in the present is worth more because it can be invested and can earn the interest. For example, one can invest the dollar......

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...Time Value of Money I recently opened a Roth IRA account in 2014. Being in my 30’s already, I got started a tad bit late but nonetheless I’m planning for my retirement now. My main focus is to maximize contribution each year and allow for it’s steady growth so that I can afford to sustain my lifestyle after I retire. I plan to save at least a million dollar for my retirement. Although there are not any tax deduction provisions for Roth IRA, the earnings are tax-free. So, in the long run it will be beneficial, as I don’t have any plans to withdraw the money until I retire. I opened the Roth IRA account with $3500 at the end of 2014 at the age of 30. I intend to contribute $3500 at end of every year till the age of 65 years, which will be my retirement age. The annual expected return from investment is 7%. Since, I will be making a series of equal payments at fixed intervals for a specified number of time and doing it at the end of every year, the future value will be- PMT= $ 3500 I=7% N=35years FVA=? FVA=PMT [(1+I)^N-1÷I] FVA= 3500[(1+0.07)^35-1÷0.07] = $483829.10 So, if I stick to my current plan, I will only be able to save $483,829 at the age 65. Lets assume if I fulfill the maximum contribution of $5500 each year with same expected annual return of 7%, then my savings will be- PMT= $ 5500 I=7% N=35years FVA=? FVA=PMT [(1+I)^N-1÷I] FVA= 5500[(1+0.07)^35-1÷0.07] = $760302.83 It looks like although I make maximum contribution each year, I......

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...Time Value of Money Managerial Finance II/FIN476 October 21, 2007 Time Value of Money The Time Value of Money (TVM) serves as a foundation for all other notions in finance. It influences business finance, consumer finance and government finance. Time Value of Money (TVM) results from the concept of interest. Time Value of Money (TVM) is an important concept within the financial management. It compares investment alternatives and then to solve problems, which involving loans, mortgages, leases, savings, and annuities. “In determining the future value, we measure the value of an amount that is allowed to grow at a given interest rate over a period of time” (Block & Hirt 2005). “Why would any rational person defer payment into the future when he or she could have the same amount of money now? For most of us, taking the money in the present is just plain instinctual. So at the most basic level, the time value of money demonstrates that, all things being equal, it is better to have money now rather than later” (Croome 2003). The concept of Time Value of Money (TVM) is that the dollar that company has today is worth more than the promise or expectation that the company will receive a dollar in the future. Money, which a company holds today, is worth more because the company can then invest it and earn interest. Therefore, a company should receive some compensation for foregoing spending. For instance, a company can invest their dollar for one year......

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