...Time Value of Money Extra Problem Set 1 1. You are planning to retire in twenty years. You'll live ten years after retirement. You want to be able to draw out of your savings at the rate of $10,000 per year. How much would you have to pay in equal annual deposits until retirement to meet your objectives? Assume interest remains at 9%. [$1254] 2. You can deposit $4000 per year into an account that pays 12% interest. If you deposit such amounts for 15 years and start drawing money out of the account in equal annual installments, how much could you draw out each year for 20 years? [$19964.12] 3. What is the value of a $100 perpetuity if interest is 7%? [$1428.57] 4. You deposit $13,000 at the beginning of every year for 10 years. If interest is being paid at 8%, how much will you have in 10 years? [$203391.33] 5. You are getting payments of $8000 at the beginning of every year and they are to last another five years. At 6%, what is the value of this annuity? [35720.84] 6. How much would you have to deposit today to have $10,000 in five years at 6% interest compounded semiannually? [$7440.94] 7. Construct an amortization schedule for a 3-year loan of $20,000 if interest is 9%. 8. If you get payments of $15,000 per year for the next ten years and interest is 4%, how much would that stream of income be worth in present value terms? [$121663.50] 9. Your company must deposit equal annual beginning of year payments into a...
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...Time Value of Money Exercises 1. What is the balance in an investment account at the end of 10 years if $5,000 is invested today and the account earns 8% interest compounded annually? What would the value be after 50 years? After 100 years? 2. What is the present value of the following future amounts: Future Value Discount rate Number of periods $15,000 6% 5 $37,000 9% 10 $596,000 11% 4 $1,178,000 9.5% 12 3. Calculate the present value of the following cash inflows assuming an 11% discount rate. Year Cash flow 1 17,000 2 17,000 3 17,000 4 17,000 5 17,000 6 100,000 4. Consider the following two mutually exclusive projects Year Cash Flow Project 1 Cash Flow Project 2 0 -150,000 -150,000 1 $40,000 $100,000 2 $90,000 $80,000 3 $120,000 $60,000 a) Calculate the net present value (NPV) of each project assuming an 8% discount rate. b) Calculate the Internal Rate of Return (IRR) for each project. 5. Anne Jones checked her lottery ticket once again. The numbers matched; she had won the $10,000,000 grand prize. The lottery provided two options for payment of the grand prize. First, the winner could take $1,000,000 immediately, with the remainder payable in $1,000,000 instalments over nine years, starting one year from now. The alternative payment option was an immediate lump sum payment of $7,000,000. ...
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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 single...
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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 manner...
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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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...Abstract In this paper, Team C will discuss the concept of the time value of money and the importance of this concept in business. Also, we will provide a demonstration of the use of the formula used to calculate the present and future values of money to get the present value of $100 using different periods of time and interest rates. Time Value of Money In the world of business, it is essential to know what TVM represents and how it helps make better choices in how we spend our money. TVM is also known as Time Value of money which is a given amount of interest earned in a period of time (Wikipedia, 2011). Each member in group “C” will use 100 as our present value and we will choose an interest rate and period. Time value of money concept is used to determine present and future values of money. “The time value of money refers to the relationship between time, money, and the rate of interest.” (Letsche, 2011). The formula consist of four components FV = Future Value, PV = Present Value, i = the interestrate per period and n= the number of compounding periods (TeachMeFinance.com). In business, TVM is used to evaluate expected returns on investments and monitoring the company’s cash flow. “However, understanding the time value of money is also very important for you as an self-employed business person to make sure you are able to realize your spending, purchasing and retirement goals.” (Loughran, 2011). On a personal level, individuals can use TVM to calculate interest...
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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 at...
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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 won’t...
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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 (FV). Present...
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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 for...
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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 a...
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...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: ...
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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 now...
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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, (Spiceland...
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...1. "List and describe the purpose of each part of a time line with an initial cash inflow and a future cash outflow. Which cash flows should be negative and which positive" (Cornett, Adair, and Nofsinger, 2014, p. 91)? Time lines “shows the magnitude of cash flows at different points in time, such as monthly, quarterly, semiannually, or yearly” (Cornett, M. M., Adair, T. A., & Nofsinger J. (2014). Inflow cash is known as positive. Outflow cash (bills, deposits) are known as negative cash flow. 2. "How are the present value and future value related" (Cornett, Adair, & Nofsinger, 2014, p. 91)? Present value of cash today is used to figure the future value of funds invested. The $100 invested is the present value. At 5% interest in a year, the future value will be $105. Value in 1 year= Today’s value x (1 + interest rate) FV 1 = PV x (1+i) (Cornett, M. M., Adair, T. A., & Nofsinger J. (2014). 3. "How are present values affected by changes in interest rates" (Cornett, Adair, & Nofsinger, 2014, p. 91)? “Of course the higher the interest rate, the larger the future value will be” (Cornett, M. M., Adair, T. A., & Nofsinger J. (2014). 4. "How much would be in your savings account in eight years after depositing $150 today, if the bank pays 7 percent per year" (Cornett, Adair, & Nofsinger, 2014)? A = P(1 + r/n)nt A = Accrued Amount (principal + interest) P = Principal Amount I = Interest Amount R = Annual Nominal Interest Rate...
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