...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 deposit...
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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 .153...
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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 example...
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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 cash...
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...measures. Such evaluation will include asking questions whether the project fits with the long-term objectives of the organisation’s .Only those projects will be further evaluated which passed this initial screening. * Analysis and acceptance; At this stage, the organisation undertakes financial analysis using its preferred method of investment 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....
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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...
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...market value of $32,600. What is the difference between these two values called? A. net present value B. internal return C. payback value D. profitability index E. discounted payback The length of time a firm must wait to recoup the money it has invested in a project is called the: A. internal return period. B. payback period. C. profitability period. D. discounted cash period. E. valuation period. The internal rate of return is defined as the: A. maximum rate of return a firm expects to earn on a project. B. rate of return a project will generate if the project in financed solely with internal funds. C. discount rate that equates the net cash inflows of a project to zero. D. discount rate which causes the net present value of a project to equal zero. E. discount rate that causes the profitability index for a project to equal zero. Rossiter Restaurants is analyzing a project that requires $180,000 of fixed assets. When the project ends, those assets are expected to have an aftertax salvage value of $45,000. How is the $45,000 salvage value handled when computing the net present value of the project? A. reduction in the cash outflow at time zero B. cash inflow in the final year of the project C. cash inflow for the year following the final year of the project D. cash inflow prorated over the life of the project E. not included in the net present value The internal rate of return is: A. the discount rate that makes the net present value of a...
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...Present Value Applications 2. You are given a choice of being paid either $18,000 now or $20,000 two years from now. Which would you rather have, assuming you could earn 10% interest on any cash you have now? 18,000(121) = 21,780 It would be better to have 18,000 now than to have 20,000 in 2 years. 4. Would you be better off accepting $27,000 now or $10,000 at the end of each of the next three years, assuming that you can earn interest at 1) 6%? or 2) 4%? 6% 27,000(1.19102) = $32,157.54 4% 27,000(1.12486) = $30,371.22 6% 10,000(3.1836) = $31,836.00 4% 10,000(3.1216) = $31,216.00 If you can get 6% interest rate, then it is better to accept $27,000, but if you can only get 4% then it is better to accept $10,000. 6. An investor has $100,000 to invest for a period of 12 years and he desires an accumulation of $200,000 at the end of the period. Approximately what rate of compound interest must his money earn? $100,000 = $200,000(PVF i=?, n=12) 200,000 ÷ 100,000 = 2 2 = (n=12, i=6%) 6% interest rate 8. A company buys some new office equipment and agrees to pay it off in 24 monthly payments of $20,000 each, beginning at the end of the first month. The payments included 24% annual interest on the unpaid loan balance as of the beginning of each month. a. What is the cost of the office equipment? (Remember, monthly compounding!) Office equipment cost is, 24,000(30.42186) = $730,124.64 b. What is the interest expense for the first month? The second...
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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 receive...
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...Net Present Value and Decision Making: From the following information on a project, calculate its net present value (NPV) after its 4-year useful life and state whether it is an acceptable project. Assume a required rate of return of 10% pa: |End of year |0 |1 |2 |3 |4 |5 | |Capital outlay |–30,000 |–15,000 | | | | | |Cash inflows | | 15,000 |25,000 |20,000 |16,000 | | |(operating) | | | | | | | |Cash outflows | |-7,000 |-8,000 |-9,000 |-11,000 | | |(operating) | | | | | | | |Scrap | | | | | |6 000 | Solution: |End of year |0 |1 |2 |3 |4 |5 | |Capital outlay |-30,000 ...
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...FVn = PV*(1+i)^n | PV = 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...
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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 "worth"...
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...Net present Value, Mergers and acquisitions FIN501 - Strategic Corporate Finance Net present Value, Mergers and acquisitions To start I would like to explain the difference and meaning of the present value of the future cash flows from an investment and the amount of investment. Present value of the expected cash flows is computed by discounting them at the required rate of return. For example, an investment of $1,000 today at 10 percent will yield $1,100 at the end of the year; therefore, the present value of $1,100 at the desired rate of return (10 percent) is $1,000. The amount of investment ($1,000 in this example) is deducted from this figure to arrive at net present value which here is zero ($1,000-$1,000). A zero net present value means the project repays original investment plus the required rate of return. A positive net present value means a better return, and a negative net present value means a worse return, than the return from zero net present value. It is one of the two discounted cash flow techniques (the other is internal rate of return) used in comparative appraisal of investment proposals where the flow of income varies over time (BusinessDictionary.com, 2013). Part I: Given that Google's cost of capital (discount rate) is 11%, below is the projected net present value using the following data which was provided; Year Cash Flow, (0) -$2,425,000, (1) 450,000, (2) 639,000, (3) 700,000, (4) 550,000, (5) 1,850,000. To calculate present value (PV)...
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...You have been asked to support analysis of acquisition decisions involving net present value analysis. 1. You are analyzing the net present value of a project over a 16 year period. Based on the rates in the textbook, what is the actual discount rate you would use given that your analysis must consider the effects of inflation/deflation? In analyzing the pet present value of a project over a 16 year period, the inflation rate must be included in the computation of the discount rate to be used. This means that the nominal rate be adjusted for the inflation rate to arrive at the real interest rate which is then used as the discount rate. 2. What is the present value of $25,000 that you will receive at the end of two years? Given that there was no information provided for the discount rate, I assumed a discount rate of 10%, hence Present value of $25,000 to be received 2 years from now = $25,000/[(1+10%)^2] = $20,661.16 3. What is the present value of $2,000 a month over the next 3 years? 4. What is the net present value of a lease that requires you to pay $10,000 at the beginning of each year for the next five years and includes a provision for a rebate of $5,000 at eh end of Year 5? 5. What is the net present value of an item that has a purchase price of $20,000, requires $1,000 maintenance at the end of each year except year 4, and is expected to have a salvage valueof $1,000 at the end of the 5 year useful...
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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 importance...
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