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Complete Problems 3, 4, and 5 on pp. 278 and 279 of Foundations of Financial Management

Due: Friday February 8, 2013

3. You will receive $5,000 three years from now. The discount rate is 8 percent.

a. What is the value of your investment two years from now? Multiply $5,000 x .926 (one year’s discount rate at 8 percent)

5,000 x .926 = $4,630

b. What is the value of your investment one year from now? Multiply your answer to part a by .926 (one year’s discount rate at 8 percent).

$4,630 x .926 = $4,287.38

c. What is the value of your investment today? Multiply your answer to part b by .926 (one year’s discount rate at 8 percent).

$4,287.38 x .926 = $3,970.11

d. Confirm that your answer to part c is correct by going to Appendix B (present value of $1) for n = 3 and I = 8 percent. Multiply this tabular value by $5,000 and compare your answer to part c. There may be a slight difference due to rounding.

$5,000 x .794 = $3,970

4. If you invest $9,000 today, how much will you have:

(I will be using Appendix A)

a. In 2 years at 9 percent?

$9,000 x 1.188 = $10,692

b. In 7 years at 12 percent?

$9,000 x 2.211 = $19,899

c. In 25 years at 14 percent?

$9,000 x 26.462 = $238,158

d. In 25 years at 14 percent (compounded semiannually)?

N = 25 x 2 = .50 i = 14% / 2 = 7%

$9,000 x 29.457 = $265,113

5. Your Uncle offers you a choice of $30,000 in 50 years or $95 today. If the money is discounted at 12 percent, which should you choose?

(I will be using Appendix B)

PV=FV×PVIf

Present value would be $30,000 x .003 = $90

I would choose $95 since in 50 years the present value of the annuity due will only be worth $90

References:

Block, B.B., Hirt, G.A., & Danielsen, B.R. (2009). Foundations of…...

...Part I: This part of the assignments tests your ability to calculate present value. A. Suppose your bank account will be worth $15,000.00 in one year. The interest rate (discount rate) that the bank pays is 7%. What is the present value of your bank account today? What would the present value of the account be if the discount rate is only 4%? The present value for a bank account that is worth $15, 000 in one year at an interest rate of 7% will be $14019.00. Using the Present Value Factors Table for a period of one year at a 7% rate value factor is .9346. $15, 000 x .9346= $14019.00 worth in value. The present value for a bank account that is worth $15, 000 in one year at an interest rate of 4% will be $14422.50. Using the Present Value Factors Table for a period of one year at a 4% rate value factor is .9615. $15, 000 x .9615= $14422.50 B. Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $6,500.00 in one year. Account B will be worth $12,600.00 in two years. Both accounts earn 6% interest. What is the present value of each of these accounts? Account A would be worth $6, 132.10. Account A in one year at a 6% interest rate value factor is .9434. $6500 x .9434= $6132.10 Account B would be worth $11, 214.00. Account B in two years at a 6% interest rate value is .8900. $12, 600 x .8900= $11. 214.00 C. Suppose you just inherited a gold mine. This gold mine is believed to have three years worth of gold......

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...appraisal. * Monitoring and review; Once the decision made and project is implemented, then it is necessary to ensure that the expected benefits are obtained and that authorised capital spending was not exceeded. Investment appraisal method; There are four methods which we can use to evaluate the investments. 1) The Payback period 2) The accounting rate of return 3) The net present value method 4) The internal rate of return method A. The Payback period; The payback period is the number of years it takes to recover its initial investment. This method assists with the project risk and liquidity. The projects with the less payback period consider less risky than the projects with greater payback period. Payback period = initial investment Annual cash flow B. The Accounting rate of return; The accounting rate of return is also known as the “Return on capital Employed”. It can also be used to evaluate the different projects to make the best choice. It is differ from other techniques due to accounting profit rather than cash flow used. Accounting rate of return= average annual profits Annual investment Its results are expressed in percentage %. RANK | PROJECT | | AVERAGE INVETMENT | AVERAGE CASH-FLOW | AROR/ROCE | | | | £ | £ | % | 3 | A | | 50,000 | 13333 | 26.7 | 6 |......

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...In finance, the net present value (NPV) or net present worth (NPW)[1] of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows of the same entity. In the case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). NPV is a central tool in discounted cash flow (DCF) analysis and is a standard method for using the time value of money to appraise long-term projects. Used for capital budgeting and widely used throughout economics, finance, and accounting, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met. NPV can be described as the “difference amount” between the sums of discounted: cash inflows and cash outflows. It compares the present value of money today to the present value of money in future, taking inflation and returns into account The NPV of a sequence of cash flows takes as input the cash flows and a discount rate or discount curve and outputs a price; the converse process in DCF analysis — taking a sequence of cash flows and a price as input and inferring as output a discount rate (the discount rate which would yield the given price as NPV) — is called the yield and is more widely used in bond trading....

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...Present value is where the value on a set date of a future payment is discounted to reflect the time value of money and other factors. This can also apply to a series of future payments. Present value calculations are commonly utilized in business and economics to provide a way to compare cash flows at different times. Present value can be described as the current worth of a future sum of money or stream of cash flows given a specified rate of return. (http://www.getobjects.com) Future cash flows are discounted at the discount rate. The higher the discounted rate, the lower the present value of the future cash flows. Determining what the appropriate discount rate is, is important to correctly place value future cash flows. The Present Value of an Ordinary Annuity is the value of a stream of promised or expected future payments that have been discounted to a single equivalent value today. It is extremely useful for comparing two separate cash flows that differ in some way. Present Value of an Ordinary Annuity can also be looked at as the amount you have to invest today at a specific interest rate so that when you withdraw an equal amount each period, the original principal and all accumulated interest will be completely used at the end of the annuity. Present Value of an Ordinary Annuity= Payment [(1 - (1 / (1 + Discount Rate per period)number of periods)) / Discount Rate Per Period] Future value measures the nominal future sum of money that a given sum of money is......

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...Brealey−Myers−Allen: Principles of Corporate Finance, Eighth Edition Back Matter Appendix A: Present Value Tables © The McGraw−Hill Companies, 2005 APPENDIX A PRESENT VALUE TABLES A P P E N D I X TA B L E 1 Discount factors: Present value of $1 to be received after t years 1/(1 r)t. Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1% .990 .980 .971 .961 .951 .942 .933 .923 .914 .905 .896 .887 .879 .870 .861 .853 .844 .836 .828 .820 2% .980 .961 .942 .924 .906 .888 .871 .853 .837 .820 .804 .788 .773 .758 .743 .728 .714 .700 .686 .673 3% .971 .943 .915 .888 .863 .837 .813 .789 .766 .744 .722 .701 .681 .661 .642 .623 .605 .587 .570 .554 4% .962 .925 .889 .855 .822 .790 .760 .731 .703 .676 .650 .625 .601 .577 .555 .534 .513 .494 .475 .456 5% .952 .907 .864 .823 .784 .746 .711 .677 .645 .614 .585 .557 .530 .505 .481 .458 .436 .416 .396 .377 6% .943 .890 .840 .792 .747 .705 .665 .627 .592 .558 .527 .497 .469 .442 .417 .394 .371 .350 .331 .312 7% .935 .873 .816 .763 .713 .666 .623 .582 .544 .508 .475 .444 .415 .388 .362 .339 .317 .296 .277 .258 8% .926 .857 .794 .735 .681 .630 .583 .540 .500 .463 .429 .397 .368 .340 .315 .292 .270 .250 .232 .215 9% .917 .842 .772 .708 .650 .596 .547 .502 .460 .422 .388 .356 .326 .299 .275 .252 .231 .212 .194 .178 10% .909 .826 .751 .683 .621 .564 .513 .467 .424 .386 .350 .319 .290 .263 .239 .218 .198 .180 .164 .149 11% .901 .812 .731 .659 .593 .535 .482 .434 .391 .352 .317 .286 .258 .232 .209 .188 .170......

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...301 Principles of Finance Present Value Part I: This part of the assignments tests your ability to calculate present value. A. Suppose your bank account will be worth $7,000.00 in one year. The interest rate (discount rate) that the bank pays is 8%. What is the present value of your bank account today? What would the present value of the account be if the discount rate is only 3%? PV=FV/(1+r)t, PV=7,000/1.08 = $6,481.48 at 8% PV=7,000/1.03, = $6,796.12 at 3% B. Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $4,000.00 in one year. Account B will be worth $9,600.00 in two years. Both accounts earn 5% interest. What is the present value of each of these accounts? Account A PV=FV/(1+r)t, PV=4,000/1.05 = $3,809.52 Account B PV=FV/(1+r)t, PV=9,600/1.1025 = $8,707.48 C. Suppose you just inherited an gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years: Year 1: $42,000,000 Year 2: $62,000,000 Year 3: $99,000,000 Compute the present value of this stream of income at a discount rate of 8%. Remember, you are calculating the present value for a whole stream of income, i.e. the total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this oil well at......

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...= FVn / (1+i)^n Present Value of annuity (PVA): the present value of the cash flows from an annuity, discounted at the appropriate discount rate Individual Cash Flow (CFn): Present value of annuity equation: CF/I x [1-1/(1+i)^n] Present Value of Ordinary Annuity: ***PMT x ((1-(1/1+i^n))/i) PVAn = CF x 1-1/(1+i)^n / i PVAn = present value of an n period annuity | CF = level and equally spaced cash flow | I = discount / interest rate | n = number of periods PVAn = CF x PV annuity factor PV annuity factor = 1-present value factor / i PVAn = CF x 1-present value factor/i For a 30 year mortgage: 30x 12 = 360 months; to calculate interest interest rate / 12 Present Value Factor: 1 / (1+i)^n PV Annuity Factor: 1 – Present Value factor / i PVAn = CF x PV Annuity Factor ## / PV Annuity Factor = CF Loan / amortization Interest Payment = I x P0 Principal Paid = Loan payment – interest payment Ending principal balance = Beginning principal balance – Principal Paid Steps repeat Finding interest rate: guess using equation: PVAn = CF x 1-1/(1+i)^n/n Future Value of Annuity FVn = PV x (1+i)^n Future Value of Annuity equations: FVAn = PVAn x (1+i)^n | ***Future Value Factor/ Future Value of Annuity Payment Equation: (FVAn) = CF x (1+i)^n – 1 / I ***OR PMT/((1+i^n-1)/i) Future Annuity Factor = CF x Future Value Factor – 1 | = CF x FV annuity Factor Perpetuities (PVP): CF/i x [1-1(1-i)^infinite | = CF/i x [1-0] | = CF/i Growing Annuities: PVAn = CF/i-g......

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...Difficulties of the NPV-method The Net Present Value (NPV) is a method to compare the value of an investment now and that amount in the future, taking into account the cost of capital and the cash flows generated by the investment. The formula to calculate the NPV is as follows: With t as the time of cashflow, i the discount rate and R the net cashflows. Although the formula to calculate the NPV is straightforward and takes into account the value of a cashflow (money) over time, there still is a lot of information that is up to discussion, to which numbers to use. The short comic below gives an idea: One of the umbers that is most easy to calculate is the investment, which is not more than a number. However, from that moment on all are just assumptions. An assumption of the future cash flows that will be generated and the discount rate of cost of capital. Let me use the example of the initial public offering of Twitter, for which the Financial Times has made a simplistic tool to calculate the market value of the company (http://www.ft.com/intl/cms/s/2/8ae5045c-4159-11e3-b064-00144feabdc0.html#axzz2lynPs27Z). Now, this short analysis does not have the goal to critique the tool, I merely use it to show what a different cost of capital can do with the ‘’market value of the company’’. A cost of capital of 10% will give an enterprise value of 23.1 billion dollar, while a cost of capital of 12% will give an enterprise value of 15.4 billion dollar. A discounted......

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... NPV 27.16 Effective Return ($20) $27 36% → Vs. → ($40) $27 -32% When calculating the effective return using the book value method I began with $3.5 (given) in 2004 and calculated each year forward. By 2014 the equity book value grew to $671.5. I took 60% of the present value of $671.5 and calculated the effective return using an initial investment of $40 million. Under these assumptions, I found that the effective return was 63%. This return immediately struck me as being high. Please refer to Exhibit 1 for these calculations. Similar results were found when calculating the effective return using the market value method. Using terminal earnings of $203 and a comparable P/E ratio of 15, I found Arcadian’s equity value to be $3039. I then took 60% of the present value of that amount and calculated the effective return using an initial investment of $40 million. Under these assumptions, the effective return was found to be 514%. This return was even more astronomical then that of the book value method. Due to the fact that the market value method is using a comparative P/E ratio when Arcadian currently has negative net incomes, I do not find the market value method to be a substantial indicator of the firm’s value. Recommendation The growth rate applied to the steady state phase must be revised in Arcadian’s forecast. Additionally, being how Arcadian and Sierra have polar opposite forecasts,......

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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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...budgeting, referred to as Net Present Value analysis(NPV). This concept evaluates a capital investment project measuring the difference between its cost and the present value of its expected cash flows (Parrino et al. 2014, p.339). More simply, the NPV tell us the amount by which the benefits from a capital expenditure exceed its costs (Parrino et al. 2014, p.339). Along with any valuation method for a capital project are associated advantages and disadvantages essential to determining its relevance when compared with other methods of analysis. The advantages of NPV include, but are not limited to: the inclusion and importance of the 'time value of money (Accounting-Management 2014),' consideration of cash flows before, during and after a business venture, consistency with financial management goals and the high priority of profitability and risk involved in capital investment (Accounting-Management 2014). The inclusion of the time value of money is the most notable advantage of NPV supported by the notion, 'a dollar today is worth more than a dollar in the future (Investopedia 2014).' Present currency holds more value due to three reasons, accruing interest on investments, future money is subject to inflation and finally there is always the risk of not receiving promised money (Investopedia 2014). An organisation is unlikely to want to invest in a project that does not create a positive return therefore knowledge of what the project is worth in the present holds great......

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...Present Value Exercise Part 1: Present Value Problems 1. FV = 2,500 x (1 + .14)^6 = 2,500 x (1.14)^6 = 2,500 x 2.19 = $5,475 2. PV = 10,000/(1 + .12)^5 = 10,000/(1.12)^5 = 10,000/1.76 = $5,681.82 3. PV = 52,500/(1 + .06)^4 = 52,500/(1.06)^4 = 52,500/1.26 = $41,667 4. PV = 13,000/(1 + 0.10)^3 = 13,000/(1.10)^3 = 13,000/1.331 = $9,767.09 Part 2: Contribution Margin Problems 1. 54,000/10 - 6 = 54,000/4 = 13,500 2. (10 – 6)/10 = 4/10 = 0.4 3. 54,000/0.4 = $135,000 4. 60,000 = 10x – 54,000 – 6x = 4x = x = 114,000/4 = x = 28,500 Part 3: Research Report • Personal savings is current disposable personal income less personal expenditures. Voluntary savings is money deposited in post offices, banks, LIC , Chit finds, shares, mutual funds and other such institution. The rates of interests vary depending on the institutions. It is fixed according to the time period of the deposited amount. And contractual savings is savings in the form of regular payments for long-term investment. • European Union is 28 member states who make decision at the European level to help raise citizens’ living standard, launched European currency and building Europe-wide free market for goods, services, people and capital. The current members: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Italy, Ireland, Latvia, Lithuania, Luxembourg, Malta, The Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden,......

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...$200 in year 1, $200 in year 2, $200 in year 3, $200 in year 4, and $10,200 in year 5. Once you’ve determined this, you have a couple of vital pieces of information: You know whether you’re looking at a lump sum, an annuity (a stream of payments), or both. In the first example, it’s a lump sum. In the second, it’s an annuity of $200, and a lump sum of $10,000 (because the $200 in year 5 belongs to the annuity of $200, not to the lump sum of the principal). This tells you what present value tables to use. You use the Present Value of $1 (Present Value of a Single Sum) table to value the lump sums. You use the Present Value of an Ordinary Annuity to value streams of payments. So in the second example, you’d use the PV of $1 table to get the present value of the $10,000 lump sum, and you’d use the PV of an Ordinary Annuity table to get the present value of the five $200 payments. Before you can use the tables, though, there is one more step. You need to find n, and i. * n is the number of interest compounding periods involved. * If you are looking at the PV of a lump sum, n = the number of years before the sum will be paid. In the first example, n = 5. * It is more complicated if you are looking at an annuity. If the annuity stream (interest, for purposes of Chapter 14) is paid annually, n = number of years during which the sum will be paid. In the second example, if we assume annual interest payments, n = 5. BUT if your interest is......

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...Tutorial: Present Values and Debt Pricing This material involves a review of topics covered during your FIN 214 course. You may also find more information on it in Chapter 6 of the AC 305/306 textbook (the first half of the book may be accessed through the “Read, Study, & Practice” module of WileyPlus). When you are considering any type of long-term investment – whether you are making the investment in a project, or making an investment in a long-term asset, or attempting to get long-term financing for your own projects or investments – it is not OK to consider the cash flows in terms of current dollars. The existence of inflation means that a dollar today will buy more than that same dollar next year. The year-to-year effect may be small when inflation is low, as it is now, but when your investment horizon is measured in decades instead of months, that inflation effect can get very large. If you are not sure what I mean by “large” – just ask your parents (or aunts, uncles, friends who are 15-20 years older than you) how much they paid for a gallon of gas when they were in college. For me, I graduated from college in 1996, and in that year, I usually paid about $1.30 for the gallon of gas that now costs me $3.50. I paid about $1.00 per pound for a whole chicken. Now that same chicken costs $1.35 per pound. That’s a 30% increase for the chicken, over the last 16 years…and for the gas? It’s a 169% increase over the same period. You can see from this......

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...Present Value and Capital Budgeting TUI University FIN301-Principles of Finance December 26, 2011 Abstract In this paper I will calculate the present value of income from a gold mine. Present Value and Capital Budgeting Part I A. Suppose your bank account will be worth $15,000.00 in one year. The interest rate (Discounted Rate) that the bank pays is 7%. is the present value of your bank account ? What would the present value of the account be if the discount rate is only 4%? NPV at 7% $15,000/1.07=$14,018.69 NPV at 4% $15,000/1.07=$14,423.08 B. Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $6,500.00 in one year. Account B will be worth $12,600.00 in two years. Both accounts earn 6% interest. What is the present value of each of these accounts? Account A NPV $6,500.00/1 year = $6,132.08 Account B NPV $12,600/2 year =$11,213.96 C. Suppose you just inherited an gold mine. This gold mine is believed to have three year worth of gold deposits. Here is how much income this gold mine is projected to bring you each year for the next three years. Year 1: $49,000,000 Year 2: $61,000,000 Year 3: $85,000,000 Compute the present value of this stream of income at a discount rate of 7%. Remember, you are calculating the present value for a whole stream of income i.e. the total value of receiving all three payments (how much you would pay right now to......

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