...$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 paid some other way that annually – semi-annually, or...
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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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...Powerball Lotto Jackpot Lump Sum or Annuity. *Historical Lump Sum Lottery Winner’s post win catastrophes and financial mismanagement aside. A few of the main factors we need to consider are inflation, income tax and interest rate. Firstly, Using the Present Value Function we can calculate the compound interest of the lump sum ($334.1m) in relation to the total value of the annuity payout ($500m). Based on the PV Formula: PV = FV/(1+i)n 334.1 = 500/(1+i)29 500/334.1 = (1+i)29 29√1.49 = 1+i 1.0139 – 1 = i Interest Rate = 1.4% To meet the $500m Future Value of the annuity payout, Lucky Ducky would have to gain 1.4% compound interest on the lump sum settlement. If Lucky Ducky feels that he can beat a 1.4% interest rate with his own investments he will benefit from taking his chances with the lump sum. Eg. If Lucky Ducky feels he can get 3% interest rate on his lump sum that would equal a FV of over $787m. FV = PV x (1+i)n FV = 334.1 x (1+.03)29 FV = 334.1 x (1+.03)29 FV = 334.1 x 1.0329 FV = $787.32m Inflation, Income tax on the lump sum vs. the annuity as well as investing the annuity differently will have to be considered as well. But for the bases of advice based on financial responsibility I would suggest Lucky Ducky to take the lump sum. Of course this does not consider...
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...that refers to the study of human conduct and moral principles. The role of ethics and moral judgement is increasingly playing a more significant role in the corporate world. The concepts of personal values and moral judgement are inextricably connected. As a result, I believe that as professionals, whether we choose to act according to our morally intelligent conclusion, or ignore it, is highly related to individuals underlying personal values. When professionals are required into making moral decisions, they are forced to rely on their ethical reasoning. However Maggid’s web article argues that, Modern Actuary ethics goes further than the ‘minimal legal compliance’ (Maggid, 2010). Whilst an individual may know the ethical code, does that mean he or she will choose the morally right choice? Maggid seeks to answer this issue by extending our understanding of ethics into a combination of three key components. These three components are ethical reasoning, underlying personal values and reasonable self-interest. Subsequently, Maggid supports the notion that personal values are related to whether we choose to act morally. Underlying personal values refers to an individual’s core philosophy that drives ones belief and psychological reasoning. From a young age, it is our personal values that drive our rational thinking. It is a form of identity that allows an individual to distinguish from what is right and wrong. The issue is, that in the corporate world, we think of ethics as a kind...
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...Chapter 2: Time Value of Money Practice Problems FV of a lump sum i. A company’s 2005 sales were $100 million. If sales grow at 8% per year, how large will they be 10 years later, in 2015, in millions? PV of a lump sum ii. Suppose a U.S. government bond will pay $1,000 three years from now. If the going interest rate on 3‐year government bonds is 4%, how much is the bond worth today? Interest rate on a simple lump sum investment iii. The U.S. Treasury offers to sell you a bond for $613.81. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price? Number of periods iv. Addico Corp's 2005 earnings per share were $2, and its growth rate during the prior 5 years was 11.0% per year. If that growth rate were maintained, how long would it take for Addico’s EPS to double? PV of an ordinary annuity v. You have a chance to buy an annuity that pays $1,000 at the end of each year for 5 years. You could earn 6% on your money in other investments with equal risk. What is the most you should pay for the annuity? Payments on an annual annuity vi. Suppose you inherited $200,000 and invested it at 6% per year. How much could you withdraw at the end of each of the next 15 years? Payments on a monthly annuity vii. You are ...
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...Time Value of Money Compounding – The process of determining the value of a cash flow or series of cash flows at some point in the future when compound interest is applied. Discounting – The process of finding the present value of a cash flow or series of cash flows; the reverse of compounding. Time Line – A graphical representation used to show the timing of cash flows. If not otherwise stated, assume that the cash flow(s) occur at the end of the period indicated. Terminology PV0 = present value (normally at t = 0) FVn = future value at the end of n periods i = interest rate, discount rate, required rate of return, etc. n = number of periods interest is earned m = the number of compounding (discounting) periods per year FVIFi,n = future value interest factor for i and n (Table A-3) PVIFi,n = present value interest factor for i and n (Table A-1) FVIFAi,n = future value interest factor for an annuity of n payments at i interest (Table A-4) PVIFAi,n = present value interest factor for an annuity of n payments at i interest (Table A-2) FVA = future value of an annuity of n years PVA = present value of an annuity of n years PMT = the periodic level (equal) payment or deposit of an annuity e = Euler’s constant = 2.71828… (repeating decimal; approximately 2.7183) ln = natural logarithm ...
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...every available penny on frivolous crap." But what if someone won the lottery and then tried to handle it as rationally as possible? The key question we wanted to investigate is whether a winner should take all the cash up front or whether one should take the annuity, which consists of more money spaced out over several years. 1. If you were one of the winners, which option would you select ?Why? Most winners would select the cash option whereby 50% of the stated amount is paid out in a lump sum (less federal and state taxes). i.e. $90.75 million - 0.322(90.75m) = $61.53 million – the amount of money we will get after taxes. Let us outline several reasons why the lum sum option for us is more preferable against the annuity option: Many winners would probably prefer to invest the money at higher rates than the implied risk-free rate of interest that the annuity is based on. With the assistance of a solid financial adviser, you may turn your lump sum into a lifetime of income. On the other hand, by taking annuity payments, you don't have to rely on risky investments to ensure your income. You won't be required to make costly decisions about what to do with your money to make sure you...
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...This essay intends to compare a per unit subsidy to heating fuel to a lump-sum transfer, in the case of pensioners. Starting with an indifference curve analysis of the subsidy, moving on to the lump-sum transfer and finishing with a combined analysis the essay will provide general guidelines for the government to take in consideration when deciding which option to implement. In each of the analysis 100 units of income will be allocated, which will be translated to £100 for simplicity, therefor every unit of income will be equal to 1 Pound. Finally a recommendation on the advisable policy will be issued. With a price of £2.5 for a heating fuel unit the pensioners choose to buy the quantity of Q1= 17 units. This can be seen on Figure 1 at point X. The expenditure on all other goods is the remaining of A= £57.5. Figure 1 Applying a per unit subsidy of 50% will the budget line will pivot outwards from B1 to B2 as the new price of the heating fuel drops to £1.25. This will increase consumption, in our case the new optimum consumption point is Y where Q2= 38 units of heating fuel will be used. The consumer is better off hence moving on a superior indifference curve, I2. Both the income and the substitution effect are responsible for this change, to differentiate between them the budget line B1S, which is parallel to B2 but tangential to the initial indifference curve, is drawn. This shows the optimum point of Xs where Q1s= 31 units of heating fuel are used. Hence the substitution...
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...SIP SIP works on the principle of regular investments. It is like your recurring deposit where you put in a small amount every month. It allows you to invest in a MF by making smaller periodic investments (monthly or quarterly) in place of a heavy one-time investment i.e. SIP allows you to pay 10 periodic investments of Rs 500 each in place of a one-time investment of Rs 5,000 in an MF. Thus, you can invest in an MF without altering your other financial liabilities. It is imperative to understand the concept of rupee cost averaging and the power of compounding to better appreciate the working of SIPs. What is Systematic Investment Plan or SIP? SIP works on the principle of regular investments. It is like your recurring deposit where you put in a small amount every month. It allows you to invest in a MF by making smaller periodic investments (monthly or quarterly) in place of a heavy one-time investment i.e. SIP allows you to pay 10 periodic investments of Rs 500 each in place of a one-time investment of Rs 5,000 in an MF. Thus, you can invest in an MF without altering your other financial liabilities. It is imperative to understand the concept of rupee cost averaging and the power of compounding to better appreciate the working of SIPs. SIP has brought mutual funds within the reach of an average person as it enables even those with tight budgets to invest Rs 500 or Rs 1,000 on a regular basis in place of making a heavy, one-time investment. While making small investments...
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...SOLVING TIME VALUE OF MONEY PROBLEMS I. Single (Annual) Compounding Period Examples A. Future Value (FV) of a Single Current Lump Sum Received One Period Hence FV = PV(1+i) | PV: current (or present) value | | i: a given interest rate (or rate of return) | (If the tables are used, this is the related formula: FV = PV * FVIF Equation 2 in the Week 1 Lecture) Example: You place $100 today in a bank deposit account that pays 10% annual interest. In other words, interest on your $100 worth of principal is paid once a year and will be received one year from today. What will your deposit account be a year from today? Algebraically, the relationship is: FV = $100(1.1) = $110 Using Excel, try entering the following formula into a single spreadsheet cell (hit the "Enter" key on your keyboard after typing in the formula): =100*1.1 If you entered the formula correctly, the cell will display a value of 110. As an aside, while Excel contains numerous shortcuts for present- and future-value calculations, we will not consider these shortcuts for two reasons. First, they do not promote a thorough conceptual understanding of the algebraic processes that necessarily are involved; second, these shortcuts may not (under a variety of circumstances) accurately reflect the modeling required for the more complex cash flow processes that occur under real world conditions. B. Future Value (FV) of a Current Single Lump Sum Compounded Once Each Period for Multiple Periods FV...
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...3-1 Daily Sales Outstanding = 20 days; Average daily sale = $20,000; Accounts receivable/Sales = Daily sales outstanding AR/20000 = 20 AR = 20,000 x 20 = 400,000 3-2 Multiplier equity/Asset = 2.5; 1+x = 2.5 X = 2.5 -1.00 = 1.5 Debt Ratio = TL/TA 1.5/2.5 = 0.60 which is 60% D/A = 1-0.40 = 0.60 or 60% 3-3 Book value per share = Common equity/ Shares outstanding Book Value = 6,000,000,000/800,000,000 = 7.50 Market/book ratio = Market price per share/Book value per share =75/7.50 = 10 3-4 Price /cash flow per share = price cash flow ratio P/$3.00 = 8 x 3 = $ 24.00 P/E = $24.00/$1.50 =16.00 3-5 Profit margin x Total assets turn over x Equity multiplier = ROE =3% x 100,000,000/$50,000,000 x 2 = 12%. ROE = 12% 3-6 ROA = 10% Profit Margin = 2% Return on Equity = 15% Net income/Assets = Net income/Sales x Sales/Total assets 2%x S/TA =10% S/TA = 5. Net income/Equity = Net Income/Sales x Sales/Total Assets x Total Assets/Equity 2% x 5 x Total Assets/equity= 15% 10% x TA/E = 15% TA/E = 1.5. 3-7 Current asset/Current liability =Current Ratio 3,000,000/CL = 1.5 3,000,000 = 1.5CL CL = 2,000,000 CA – Inv /CL = 1.0 Therefore Current Assets – Inventory/Current Liability = Quick Ratio 3,000,000 - Inv / 2,000,000 = 1.0 3,000,000 – Inv = 2,000,000 Inventory = 1,000,000 For these questions I used a financial calculator http://www.arachnoid.com/lutusp/finance.html 4-1 = 10,000(1.10) to the power 5 ...
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...MIT Sloan School of Management Mini-Case © Anna Pavlova and Dimitri Vayanos February 23, 2004 Equitable Life Ever since the celebrated House of Lords’ ruling against the company in July 2000, life appeared awfully inequitable to policyholders of Equitable Life Assurance Company. Equitable Life, the staple of Britain’s pension industry, with over a million policyholders, including a plethora of the biggest British companies, the parliamentary pension fund, the Personal Investment Authority, had no choice left but to announce that it was up for sale. To be able to cover the liability worth about £1.5 billion, it froze the value of all current with-profit policies and imposed an exit penalty of 5% on withdrawals. Fifteen prospective purchasers looked at the books of the company, but all but one – Prudential – walked away from a deal. The final straw came in December 2000, when Prudential reached the decision not to buy Equitable Life. Following the decision, Equitable doubled the exit penalty for withdrawals to 10% and closed the fund for new investors. Numerous legal actions, investigations, and reports followed. Yet the debacle is still far from over, and new inquiries into this perhaps the most shocking collapse in the insurance industry keep pouring. Equitable Life’s growing problems and policyholders’ growing despair grab headlines in British press almost daily. On December 12, 2003, BBC News ran an article on Ann Berry, 65, a former physiotherapist from West Sussex...
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... 5,000 Required: Determine the amounts that Beldon should capitalize as the cost of the land and the new building. Capitalized cost of land: Purchase price $60,000 Demolition of old building $4,000 Sale of materials (2,000) 2,000 Title Investigation fees 2,000 Total cost of land $64,000 Capitalized cost of building: Construction costs $500,000 Architect's fees 12,000 Construction loan interest 5,000 Total cost of building $517,000 E 10–8: Lump-sum acquisition LO10–2 Pinewood Company purchased two buildings on four acres of land. The lump-sum purchase price was $900,000. According to independent appraisals, the fair values were $450,000 (building A) and $250,000 (building B) for the buildings and $300,000 for the land. Required: Determine the initial valuation of the buildings and the land. Fair Values Building A $...
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...Government and its influence on the allocation of resources and affect on the economy cannot be overlooked, which makes the subject of Public Finance such an important field in the study of economics. Government is made by the people for the people, and therefore government has the power to control resources based on what the people want. Sure, people don’t like to pay taxes. People would rather keep all of their money and spend it in the way that they’d like. However, people also know how important social security, Medicaid, and other governmental programs are to their future, and therefore are willing to pay taxes in exchange for the goods and services the government provides to its citizens. Essentially, it all comes down to an economic comparison between one option (no taxes and no governmental programs) versus another option (taxes and governmental programs), and how much people are willing to pay (money, opportunity costs, etc.) for one option versus another. Because taxation by the government is such an important subject to everyone, Public Finance is truly an important subject that affects everyone and is an important subject for everyone to learn about, since it affects their overall well-being. By know more about voting, government allocation of resources, redistribution programs, and other important topics in Public Finance, people can make better decisions about who to vote for and people can have a bigger say and better knowledge about how the government affects...
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...MEMORANDUM FOR CEO FROM: CFO SUBJECT: Time Value of Money 12 OCT 13 This memo accompanies the Excel Spreadsheet labeled Case FIN 50 and is intended to explain the significance of the various formulae and how our decisions with finances affect our bottom line numbers. Every Time Value of Money Problem has either four or five variables, we typically will know three to four of these variables and thus will only need to solve for the one remaining variable. Lump Sum Present Value Any time we take an amount of money and receive an annual rate of return on it, we should see a standard/preset growth on the initial amount. As you can see under “required calculation #1”, we have two columns addressing two amounts of money: $100,000 and $200,000. As you can see, the rate and the number of years the rate is compounded has a dramatic affect on the required initial investment. The higher the rate and the longer the investment compounds, the less the required initial investment. Lump Sum Future Value If we were to invest a specific amount of money today, in theory it should grow to a larger value at some point in the future. The value at the future point in time is called the future value. In order to calculate the future value, we have to know the rate at which the investment will grow. This rate is referred to as the interest rate. We then must know the length of time that the investment will be held or the number of periods. Much like in the Present Value explanation above, the longer we are...
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