...FNCE 100 Corporate Finance Discounting 1 First Basic Principle of Finance A dollar today is worth more than a dollar tomorrow » But how much more?.. 2 1 1 Topic Overview Compounding & Future Value Discounting & Present Value Multiple Cash Flows “Special” Streams of Cash Flows » Perpetuities » Annuities Interest Rates » APR versus EAR 3 Lottery Example You just won a lottery which gives you two options: (1) Receive $100 today (2) Receive $120 in one year $100 $120 0 Money Time 1 Which option should one take? 4 2 2 Lottery Example: Future Value If you take money now, you can put them in the bank at the current interest rate “r” of 5%, and have the following amount in one year: V0=$100 0 Money Time V1=$105 1 The amount in one year – future value (FV) – is calculated as FV = Principal + r × Principal = $100 + 0.05 × $100 = $105 Which option should we take now? 5 Lottery Example: Present Value Alternatively, we can compare the value at time 0: V0=$114.3 0 Money Time V1=$120 1 The amount in a given year – Present Value (PV) – is: $120 = PV+ r × PV = PV+ 0.05 × PV → PV = $114.3 Which option should we take? 6 3 3 Basic Terminology Timeline: a linear representation of the timing of potential cash flows. Two types of cash flows: 1. Inflows (i.e., money we get) are represented by positive numbers ...
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...25.2.12 Present Value of a Single Cash Flow Where: cash flow at time t. time periods. the effective rate over a single period. Not to be reproduced without the permission of the authors. 1-2 Calculation Example: Present Value of a Single Cash Flow Question: What is the present value of $100 received in 5 years when interest rates are 8% pa? Answer: Not to be reproduced without the permission of the authors. 1-3 Future Value of a Single Cash Flow Where: cash flow now. time periods into the future. the effective rate over a single period. Not to be reproduced without the permission of the authors. 1-4 Calculation Example: Future Value of a Single Cash Flow Question: You have $100 in the bank. Interest rates are 8% pa. How much will you have in the bank after 5 years? Answer: Not to be reproduced without the permission of the authors. 1-5 Calculation Example: Present and Future Values Question: If you pay this year's uni fees of $5,000 now, you will receive a 25% discount. Otherwise you incur interest on your $5,000 debt at the rate of inflation which is expected to be 2.5% pa. You can lend and borrow from the bank at a rate of 8% pa, and you expect to start work and have to pay off all of your debt in a single payment in 6 years. Should you pay your fees now or in 6 years? Not to be reproduced without the permission of the authors. 1-6 Answer: Option 1: Pay your uni fees in 6 years: The future value of the uni fees in 6...
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...Chapter 2 Time Value of Money MINI CASE Assume that you are nearing graduation and that you have applied for a job with a local bank. As part of the bank's evaluation process, you have been asked to take an examination which covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a. Draw time lines for (a) a $100 lump sum cash flow at the end of year 2, (b) an ordinary annuity of $100 per year for 3 years, and (c) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of years 0 through 3. Answer: (Begin by discussing basic discounted cash flow concepts, terminology, and solution methods.) A time line is a graphical representation which is used to show the timing of cash flows. The tick marks represent end of periods (often years), so time 0 is today; time 1 is the end of the first year, or 1 year from today; and so on. 0 1 2 year | | | lump sum 100 cash flow 0 1 2 3 | | | | annuity 100 100 100 0 1 2 3 | | | | uneven...
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...Chapter 5 5.1 Fixed costs are not related to the volume of services delivered. Semi-fixed costs are fixed at two or values within relevant ranges. 5.2 Total fixed costs and total variable costs. 5.3 a) The cost-volume profit analysis is applied to organization’s costs and revenue structure that analyzes the effect of volume changes on cost and profits.b) It’s useful because they evaluate causes of action regarding pricing and introduction of new services. 5.4 a) The differences between per-unit cost (variable cost rate) and hence the amount that each unit of outpit contributes to cover fixed costs and ultimately flows to profit.b) They contribute to cover fixed costs and ultimately flows to profit. 5.5a)Total Revenue-Total Variable Costs-Fixed Costs=Profit. b) The volume breakdown partially has the volume cost rate of the contribution margin. 5.6a) If high proportion of a business total costs are fixed. b) It’s measured by the degree of operating level. 5.7 When a provider moves from a fee-for-service to a discounted fee-for-service environment the element of capitated environment dramatically differs. 5.8 A capitated environment vs. a fee-for-service environment have critical differences in profit analysis. Mainly a capitated provider takes on the insurance function. 5.9 By the number of lives being treated rather than the number of treatments being given to one life. Instead of trying to see more patients to increase revenue a capitated environment would push the...
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...Lecture Notes on Time Value of Money Stefan Arping Amsterdam Business School University of Amsterdam 1 Roadmap • compounding and discounting • annuities and perpetuities • growing annuities and perpetuities • net present value • internal rate of return • real world complexities 2 Compounding • suppose you invest $100 for four years at 10% interest • how does your investment evolve over time? beginning year balance year 1 year 2 year 3 year 4 100.00 110.00 121.00 133.10 interest 10.00 11.00 12.10 13.31 end year balance 110.00 121.00 133.10 146.41 =100 × (1 + 0.10) =100 × (1 + 0.10)2 =100 × (1 + 0.10)3 =100 × (1 + 0.10)4 • the future value (FV) of $100 invested for four years at 10% is 100 × (1 + 0.1)4 • general principles of compounding: – convert dollars today into dollars in N years: multiply with (1 + r)N – convert dollars in N years into dollars in N + m years: multiply with (1 + r)(N +m)−N = (1 + r)m 3 Discounting • conversely, the present value (PV) of $146.41 to be received in four years is 146.41 = 100 (1 + 0.10)4 • general principles of discounting: – convert dollars in N years into dollars today: divide by (1 + r)N – convert dollars in N + m years into dollars in N years: divide by (1 + r)(N +m)−N = (1 + r)m – PV of stream of future cash flows: convert all future cash flows into cash flows today and take sum • the PV of future cash flows is equivalent in value to the future cash flows in the sense that if you had the PV today you could transform...
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...Chapter 2 Time Value of Money MINI CASE Assume that you are nearing graduation and that you have applied for a job with a local bank. As part of the bank's evaluation process, you have been asked to take an examination which covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a. Draw time lines for (a) a $100 lump sum cash flow at the end of year 2, (b) an ordinary annuity of $100 per year for 3 years, and (c) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of years 0 through 3. Answer: (Begin by discussing basic discounted cash flow concepts, terminology, and solution methods.) A time line is a graphical representation which is used to show the timing of cash flows. The tick marks represent end of periods (often years), so time 0 is today; time 1 is the end of the first year, or 1 year from today; and so on. 0 | i% 1 2 | | year lump sum 100 0 cash flow i% 1 2 3 | | | 100 | 100 100 1 2 3 | | | 75 50 annuity 0 | i% uneven cash flow stream -50 100 A lump sum is a single flow; for example, a $100 inflow in year 2, as shown in the top time line. An annuity is a series of equal cash flows occurring over equal intervals, as illustrated in the middle time line. An uneven cash flow stream is an irregular series of cash flows...
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...Assignment 1—Answer Key FIN 413, Spring 2014 Due date: May 22, 2014 Problem 1 The current price of silver is $30.00 per ounce. The storage costs are $0.35 per ounce per quarter payable at the beginning of each quarter. The risk-free rate of interest is 10 percent per annum with continuous compounding for all maturities. Jaime has just entered into a forward contract to buy 10,000 ounces of silver in six-months. a) What is the present value of the storage cost? b) What are the six-month forward price and the value of Jaime’s forward contract? c) Three months later the spot price of silver is 27.50 and the risk-free rate of interest is still 10 percent per annum with continuous compounding for all maturities. What is the value of Jaime’s forward contract? d) Explain why the forward price of silver can be calculated from its spot price and other observable variables whereas the forward price of copper cannot. a) The present value of the storage costs: b) ( ) ( ) The initial value of a forward contract is zero. c) The value of Jaime’s contract is d) Silver is an investment asset. If the forward price is too high, investors will find it profitable to hold more silver and short forward contracts. If the forward price is too low, investors will find it profitable to sell more silver and long forward contracts. Copper is a consumption asset. If forward price is too high, a strategy of buying copper and short forward contracts works. However, because...
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...Financial Planning 2 Review of time value of money Simple interest Example: A firm borrows $1,000 for a year at 10% simple interest per year. How much must the firm repay after one year? FV = future value = 1,000(1+r) = 1,000 (1.1) =1,100 What if the loan is for 3 years, at compound interest of 10% per year? If compounding is annual: FV = 1,000 (1+r)3 = 1,000 (1.1)3 = 1,331 3 Review of time value of money In general, FV = PV (1+r)t = PV * FVIF (r, t) FVIF = future value interest factor On exams, if you write FV = 1,331, this is not enough. You must write at least: FV = 1,000 FVIF (10%, 3) or FV = 1,000 (1 + 0.1)3 = 1,331 If FV = PV (1 + r)t, then 1 PV FV t (1 r ) PVIF = present value interest factor 4 Review of time value of money To find r in PVIF or FVIF We know that FV = PV (1+r)t FV (1 +r)t = [(1 PV +r)t 1 t ] (1 + r ) = = FV 1 t PV FV PV 1 t 5 Review of time value of money FV r= PV 1 t -1 To solve for t, take the log: Example: PV = 25,000; FV = 50,000; r= 12%, t =? FV = PV (1+r)t 50,000 = 25,000 (1+.12)t 50,000/25,000 = 1.12t 2 = 1.12t 6 Review of time value of money Log 2 = Log 1.12t t log 1.12 = log 2 t = log2/log 1.12 = 6.1163 ‘log’ or ‘ln’ button on financial calculator 7 Review of time value of money Annuities Draw time line ...
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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 flows...
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...information on the share prices for the mutual fund from the starting date of the period to the ending date of the period. Once I have this information, it's time for some calculation; I will add up the mutual fund's distributions per share for the chosen time period. It's vital that this calculation also includes short-term and long-term capital gain, as well as dividends. The next step in my computing is to take the total amount of distributions and then add the ending date's share price. I would then subtract the starting share price from the ending share price, and add the total distribution from the previous calculation. Finally, I would divide that figure by the starting date's share price, and multiple the rest by 100, simply to convert to a...
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...in the future and, as opposed to financial investments, like stocks and bonds, are not financial instruments that trade in the financial markets • Corporations create value for their shareholders by making good real investment decisions Valuation and Capital Budgeting Part I, HEC-ULg 2013-2014 – Marie Lambert 2 Real investments • Intrinsic price of the project? - Financial managers should use a market-based approach to value assets, whether valuing financial assets, like stocks and bonds, or real assets, like factories and machines Valuation and Capital Budgeting Part I, HEC-ULg 2013-2014 – Marie Lambert 3 Module 1 Fundamentals of discounting Valuation and Capital Budgeting Part I, HEC-ULg 2013-2014 – Marie Lambert 4 Time-value-of-money concept • Relationship between $1 today and $1 in the future - Consider the following example: A firm is contemplating investing $1 million in a project that is expected to pay out $200,000 per year for 9 years. Should the firm accept the project? We need to know the relationship between a dollar today and a (possibly certain) dollar in the future before deciding on the project Valuation and Capital Budgeting Part I, HEC-ULg 2013-2014 – Marie Lambert 5 Time-value-of-money concept • Compounding and discounting Figure 4.8 – Ross, Westerfield and Jaffe, 8th ed., page 75 Valuation and Capital Budgeting Part I, HEC-ULg 2013-2014 – Marie Lambert 6 Time-value-of-money concept • Net present value criterion ...
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...Personal Financial Planning: Chapter One Concept Checks Concept Check 1-1 (pg 9): What steps should we take in developing our financial plan?1) Determining your current financial situation 2) Developing your financial goals 3) Identifying alternative courses of action 4) Evaluating alternatives 5) Creating and implementing a financial action plan 6) Re-evaluating and revising the plan What are some risks associated with financial decisions? Economic and Product Risk: Interest rate risk- changing interest rates affect your cost when you borrow and your benefits when you invest Inflation risk- rising prices cause lost buying power Liquidity risk- Some investments may be more difficult to convert to cash or to sell without significant loss in value Product risk- products may be flawed or services may not meet your expectations. Retailers may not honor their obligations Personal Risk: Risk of Death- Premature death may cause financial hardship to family members left behind Risk of income loss- Your income could stop as a result of job loss or because you fall ill or are hurt in an accident Health Risk- Poor health may increase your medical costs. At the same time, it may reduce your working capacity or life expectancy Asset and Liability Risk- Your assets may be stolen or damaged. Others may sue you for negligence or for damages cause by your actions What are some common sources of financial planning information? Printed Materials: newsletters...
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...11/2/12 2:22 PM Page 1 Calculations for Time Value of Money TVM In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with this subject. Modern technology has made these calculations very easy. Many computer programs have built-in time-value functions, and a large assortment of handheld calculators will solve these problems using special keys. However, some people who use these methods do not understand the rationale for the answers and merely accept the results. At the other extreme, the calculations could be made using exponentials and/or logarithms. Such a procedure may provide a thorough learning experience, but it is tedious and time consuming. Compound interest tables have been developed to provide a relatively easy tool for solving time-value problems. They are found in Appendix A at the end of the textbook. Here we walk through four types of calculations, each representing one of the four tables. The Excel icons marked TVM refer to the Excel spreadsheets that can be found on the companion web site. T HE F UTURE VALUE OF A S INGLE S UM Module If you deposit $1,000 in a savings account that pays 7 percent interest annually, and 3A you do not withdraw this interest, the original amount will keep growing. (In real life, bank interest is usually compounded more frequently than once per year, but annual compounding is assumed here. In other words, the 7 percent will be...
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...credit: Dividends paid have a credit attached for tax paid by the corporation franking credit=gross div-div=div1-τc*τc * Shareholders compute tax at their own tax rate (τp) based on the corporation’s pre-tax income, then subtract the tax paid at the corporate level net shareholder tax=div1-τc*(τP-τC) Corporate Ownership versus Control * Shareholders: Own the Corp, but have no say in daily operations * Board of Directors: * Elected by shareholders * Ultimate decision-making authority * CEO: Typically delegated day-to-day decision making by Board * CFO (financial manager) * Reports to CEO * Investment decisions, financing decisions, cash management * Goal of firm to maximize shareholder value Ethics and Incentives * Agency problems: Managers may act in their own interest rather than best interest of shareholders * Use options or...
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...CHAPTER 6 TIME VALUE OF MONEY (Difficulty: E = Easy, M = Medium, and T = Tough) Multiple Choice: Conceptual Easy: PV and discount rate 1. Answer: a Diff: E You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. The discount rate decreases. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. c. The discount rate increases. d. Statements b and c are correct. e. Statements a and b are correct. Time value concepts 2. Which of the following statements is most correct? a. A 5-year $100 annuity due will have a higher present value than a 5-year $100 ordinary annuity. b. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate. c. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent. d. Statements a and c are correct. e. All of the statements above are correct. Time value concepts 3. Answer: d Diff: E Answer: e Diff: E The future value of a lump sum at the end of five years is $1,000. The nominal interest rate is 10 percent and interest is compounded semiannually. Which of the following statements is most correct? a. The present value of the $1,000 is greater if interest is compounded monthly rather than...
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