... Precise and structured reasoning is needed in all sciences including computer science. Logic is the basis of all reasoning. Computer programs are similar to logical proofs. Just as positive whole numbers are the fundamental units for arithmetic, propsitions are the fundamental units of logic. Proposition: A statement that is either true or false. E.g. Today is Monday Today is Tuesday The square root of 4 is 2 The square root of 4 is 1 2 is even, and the square of two is even, and 3 is odd and the square of 3 is odd. The Panthers can clinch a playoff berth with a win, plus a loss by the Rams, a loss or tie by the Saints and Bears, a win by the Seahawks and a tie between the Redskins and Cowboys. (Copied verbatim from the sports page 12/26/2004.) Propositions may be true or false and no preference is given one way or the other. This is sometimes difficult to grasp as we have a “natural” preference for true statements. But “snow is chartreuse” and “snow is white” are both propositions of equal standing though one is true and the other false. Non-propositions: What is today? Is today Monday? Questions are not propositions. You can’t judge whether the question itself is true or false, even though the answer to the question may be true or false. Show me some ID! Similarly, imperative statements lack a truth value. 2x=4 x=y Statements with undetermined variables do not have truth value xy=yx looks like a true proposition...
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...legibly. 4. Use of calculator is permitted, but please show how answers were obtained. A numerical answer without an explanation will be given a grade of zero. 1 1. Robinson Crusoe (RC) lives only two periods (today and tomorrow). He prefers to consume the same amount of money in each period, but his income stream is $500 today and $110 tomorrow. Assume that RC can borrow and lend at an interest rate of 10%. a) Graphically show all the possible combinations of consumption today and tomorrow available to RC. On this graph indicate how much he will spend today and how much he will spend tomorrow. ANSWER In general C 0 = 500 + C C 110 − 1 = 600 − 1 1.10 1.10 1.10 If C 0 = C1 = C then C = 600 − in other words, C , 1.10 1 ⎞ ⎛ C ⎜1 + ⎟ = 600 . ⎝ 1.1 ⎠ Therefore, C = 314.29 . If C 0 = 0 , then 0 = 600 − C1 , therefore C1 = 660 . Similarly, if C1 = 0 then 1.10 C 0 = 600 − 0 = 600. 1.10 (0, 610) C1=0 Consumption 700 Tomorrow (C1) (C 600 500 400 (314.29, 314.29) C1=C2=C 300 200 100 (600,0) C2=0 0 0 100 200 300 400 500 600 700 Consumption Today (C0) (C 2 b) An insurance company offers the following exchange (swap) to RC: RC would give the insurance company his income today and tomorrow, and in exchange would receive $320 today and tomorrow. Assume there is no default. Is RC better off taking the insurance company’s offer? Why or why not? ANSWER The present value...
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...the project today, there will be 75% chance of good market acceptance of the product and 25% chance of bad market acceptance of the product. If market reaction to the new product is good, a cash inflow of $500 will be realized each year for the next 7 years. If market reaction to the new product is bad, a cash inflow of $25 will be realized each year for the next 7 years. However, if NPC chooses to wait for 1 year to obtain more information about market tastes, the company would know definitely about the market reaction and would then either proceed with the project or not invest in it at all. The initial cost of the project is $1,500 (million). a. Assuming that all cash flows are discounted at 10%, if NPC chooses to wait a year before proceeding, how much will this increase or decrease the project's expected NPV in today's dollars (i.e., at t = 0), relative to the NPV if it proceeds today? Problem 2: a. Garner-Wagner is considering investing in a project that requires an investment of $3,000,000. The project will generate a cash inflow of 500,000 per year for the next 5 years. The cost of capital is 10%. What is the project's net present value? b. If Garner-Wagner goes ahead with this project today, it will obtain knowledge that will give rise to additional opportunities 5 years from now (at t = 5). The company can decide at t = 5 whether or not it wants to pursue these additional opportunities. Based on the best information available today, there is a...
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...both options have the same expiration time T. At T, the spot price will be equal to, above or below the strike price. If the spot price is above the strike price K, the investor will exercise the call option and buy the underlier for $500. The put will not be exercised. If the spot price is below the strike price the written put will be exercised against the investor, forcing him to buy the underlier at $500. The call will expire worthless. In either case, the underlier will be purchased at the strike price. The payoff of this combined position is max{0, S - K}- max{0, K - S} = S - K Call Put but this is actually the payoff of a long forward contract expiring at time T and with a forward price of $500. Be aware of the differences between an original long forward and a synthetic long forward: (i) the original long forward has no upfront premium payment while the synthetic long forward requires a net option premium (= abs[Call(K,T) – Put(K,T)] ) as upfront payment. (ii) At expiration at time T we pay the forward price with the original long forward, whereas with the synthetic long forward we pay the strike price. Let F0,T denote the “no‐arbitrage” forward price. This means you have to pay $0 today and at time T you are obliged to buy the asset at F0,T. The cost of the contract today is the present value of F0,T, PV(F0,T). Now we pay Call(K, T) – Put(K, T) today to buy the option on that asset for K at time T which results in a cost at time 0 of Call(K, T) – Put(K, T) + PV(K). And using the “no‐arbitrage” pricing...
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...Chapter 08 - Stock Valuation CHAPTER 8 STOCK VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The value of any investment depends on the present value of its cash flows; i.e., what investors will actually receive. The cash flows from a share of stock are the dividends. Investors believe the company will eventually start paying dividends (or be sold to another company). In general, companies that need the cash will often forgo dividends since dividends are a cash expense. Young, growing companies with profitable investment opportunities are one example; another example is a company in financial distress. This question is examined in depth in a later chapter. The general method for valuing a share of stock is to find the present value of all expected future dividends. The dividend growth model presented in the text is only valid (a) if dividends are expected to occur forever, that is, the stock provides dividends in perpetuity, and (b) if a constant growth rate of dividends occurs forever. A violation of the first assumption might be a company that is expected to cease operations and dissolve itself some finite number of years from now. The stock of such a company would be valued by applying the general method of valuation explained in this chapter. A violation of the second assumption might be a start-up firm that isn’t currently paying any dividends but is expected to eventually start making dividend payments some number of years from now. This stock...
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...NETW250 Week 1 iLab How Is the PSTN Used Today? In the lecture for this week, we discussed the history of the PSTN. In this week’s iLab, let’s examine the PSTN in a bit more detail, because it will not be going away anytime soon despite the increasing use of cellular telephones and VoIP. Keep in mind that at some point, cellular calls and VoIP traffic cross this same old PSTN. Data traffic from large organizations must continue to use landlines, because wireless connections do not have the capacity or the reliability for this. As the lecture points out, in 1984, the Bell system was broken up into parts. Today, many of these pieces have been reassembled into larger organizations. In its present form, AT&T provides service to about one half of the United States. In this iLab, you will examine the landline-based data services AT&T can provide to a large business today. To do this, go to the AT&T website at www.att.com. Websites change over time, but the AT&T website will have a listing for these services somewhere on the home page. Right now, from the AT&T home page, select the menu item that says Business. Under it, select the menu item that says Enterprise Business. On this page, look for Network Services. The Network Service page will show all of the services that AT&T can provide to a large business to connect their sites to each other, to other organizations, and to their customers. Thinking back to the basic networking courses you have taken,...
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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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...Chapter 5 1- You want to find the time value of the annuity below at end of year 3 (t=3). What should you calculate? A) PV of a 4 year annuity due B) FV of a 4 year annuity due C) FV of a 3 year annuity due D) FV of a 4 year ordinary annuity E) FV of a 3 year ordinary annuity 0 1 2 3 4 2- Moe is looking at an annuity that makes five $10,000 payments with the first annuity payment occurring 11 years from today. What is the present value of this annuity if Moe’s interest rate is 9% compounded annually? A) 16,430.30 B) 13,558.23 C) 15,987.86 D) 12,897.67 E) 17,987.89 3- You want to buy a car, and a local bank will lend you $30,000. The loan would be fully amortized over 5 years (60 months) and the nominal interest rate would be 12% with interest paid monthly. What would be the monthly loan payment? Assume payments start next period A) 430.89 B) 520.89 C) 667.33 D) 444.89 E) 430.89 4- Your sister turned 30 today and she is planning to save $4000 per year for retirement with the first deposit to be made one year from today (her last deposit will be made at age 60). She will invest in a mutual fund, which she expects to provide a return of 10% per year. She plans to retire 30 years from today, when she turns 60, and she expects to live for 30 years after retirement, to age 90. Under these assumptions, how much can she spend in each year after she retires? Her first withdrawal will be made at the end of her first retirement year (she will also make her last withdrawal...
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...interest’. Compound Interest (C.I)= [P*(1+r/100)^t – P] P=Principal amount r=Rate of interest t=Time period in years Interest may be compounded annually, semi-annually, quarterly, monthly or even daily. This is known as the compounding frequency. Greater the frequency of compounding, the greater the effective return or yield. Always adjust the ‘r’ to map to the ‘t’. That is, if the compounding is quarterly, then take the quarterly interest rate, not the annual rate. Compounded Annual Growth Rate (CAGR) If we come across a projection of say, sales or profit 3 years from now, we need to arrive at a rate at which the sales was growing each year to arrive at that future number. That growth rate, which assumes compound growth each year, is called the CAGR. CAGR = (Final Value/Initial Value)1/n- 1 It’s defined as ‘the interest rate at which a given initial value will ‘grow’ to a final value in a given amount of time.’ Time Value Concept of Money Money earns interest with time. That means, INR 100 today is worth different amounts at different points in time. Hence, money has a ‘time value’. The fundamental concepts involved in understanding the time value of money are: Future Value of Money: ‘Future value of an amount is the amount today’s money turns into at a point of time in the future (assuming a certain rate of return)’. Future value is arrived at by multiplying the principal invested today by the compounding factor (1+r)^t . ©Finitiatives Learning India Pvt. Ltd. (FLIP)...
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...True/False T F 1. After the arrival of postwar refugees in the 1940s, Jewish migration increased to record numbers between 1940 and 1969. T F 2. Most of the 17th century Jewish immigrants were small farmers from Germany and Poland. T F 3. Declining economic conditions in central Europe contributed to a dramatic increase in Jewish immigration to the U.S. after 1820. T F 4. During the 1920s and 1930s millions of Jews entered the U.S. fleeing the persecution in Europe. T F 5. Between 1930 and 1940 the number of openly anti-Semitic organizations in the U.S. sharply declined. T F 6. Jewish Americans have always supported extremist groups as a method of resisting anti- Semitism. T F 7. During the 1960s civil rights movement, Jewish American students and lawyers comprised over half of those registering African Americans to vote and defending those imprisoned. T F 8. Jews were allowed full political participation, including the right to vote and hold office, in the Atlantic coast colonies from the earliest days of their arrival. T F 9. Many Jewish voters moved from the Democratic party to the Republican party in the 1850s because of its antislavery position. T F 10. The “oppression mentality” among Jews who escaped political oppression in Europe has kept them from becoming politically active in the U.S. T F 11....
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...the indx and borrowing or lending We engage in a reverse cash-and-carry strategy. In particular we do the following: Today In 9 Months Long forward 0 ST - F0 Short index +S0 -ST Lend S0 -S0 S0erT Total 0 S0erT - F0 Specifically, with the numbers of this exercise, we have: Today In 9 Months Long forward 0 ST - 1142.03 Short index 1100 -ST Lend S0 -1100 1142.03 Total 0 0 c. Suppose a customer wishes to enter a long index futures position. If you take the opposite position, demonstrate how you would hedge your resulting short position using the indx and borrowing or lending Now we engage in cash-and-carry arbitrage: Today In 9 Months Short forward 0 F0 - ST Buy index -S0 +ST Borrow S0 +S0 -S0erT Total 0 F0 - S0erT Specifically, with the numbers of this exercise, we have: Today In 9 Months Short forward 0 1142.03 - ST Buy index -1100 +ST Borrow S0 1100 -1142.03 Total 0 0 The S&R Index psot price is 1100 and the continuously compounded risk-free rate is 5%. You observe a 9-month forward price of 1129.257. a. What dividend yield is implied by the forward price? Solve the forward rate equation for the dividend yield: F0 = S0e(r-δ)T δ = r - (1/T)ln(F0/S0) 0.015000381 b. Suppose that you believe the dividend yield over the next 9 months will be only 0.5%. What arbitrage...
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...Recommended Homework and Projects Due | R, 1/10 | Intro and Ch. 1 | 2,3,4,16,17,19,21,22 | T, 1/15 | Ch. 3 | 8,9,10,11,13,14,16,19,20,21,22,23,24,25,26,27,29,39,40, 41,44,46,47,48,49,50,52 | R, 1/17 | Ch. 3 | See previous assignment | T, 1/22 | Ch. 4 | 2,5,6,7,8,12,14,15,16,17,19,20,21,22,23,24,25, | R, 1/24 | Ch. 4 | 30,31,32,34,35,36,37,38,39,40,41,42,44,45,51 | T, 1/29 | Ch. 5 | 4,5,10,11,17,27,28,29,40,41,47 | R, 1/31 | Ch. 5 | See previous assignment | T, 2/5 | Exam #1 | R, 2/7 | Ch. 6 | 1,8,9,10,13,17,18,21,23,24,29,33,34,36,43,44,45 | T, 2/12 | Ch. 7 | 3,5,7,8,10,17,20,40,41,42,49,53,57,58,61 | R, 2/14 | Ch. 7 | See previous assignment | T, 2/19 | Ch. 8 | 1,5,7,8,24,25,26,28,29,33,35 | R, 2/21 | Ch. 8 | See previous assignment | T, 2/26 | Ch. 11 | 1,4,6,7,13,16,25,26,27,28,31,35,37 TAX RESEARCH CASE DUE TODAY | R, 2/28 | Ch. 11 | See previous assignment | T, 3/5 | Exam #2 | R, 3/7 | Ch. 9 | 1,2,6,7,9,10,19,20,23,27,28,29,32,41 | T, 3/12 | Ch. 9 | See previous assignment | R, 3/14 | Ch. 10 | 7,8,9,15,16,18,19,20,22 | T, 3/19 | Ch. 12 | 1,2,6,18,19,20,21,22 | W, 3/20 | Last day to drop a course with a grade of “W” | R, 3/21 | Ch. 13 | 3,5,9,14,15,18,19, 26, 37, 39, 43, 44 | T, 3/26 | Spring Holiday | R, 3/28 | Spring Holiday | T, 4/2 | Ch. 13 | Catch-up and review day | R, 4/4 | Exam #3 | T, 4/9 | Ch. 14 | 1,2,3,4,6,7,8,9,10,19,21,23,24,26,27,28,33,34 | R, 4/11 | Ch. 15 | 2,3...
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...DAMM Good! Lemonade Stand (DGLS) Accounting Summary Report – Season One Bus 599 - Introduction to Quantitative Principles 12 September 2010 Background The enclosed DAMM Good! Lemonade stand (DGLs) accounting summary is a quantitative snapshot of financial transactions that have occurred during the first season of operation of DGLs. This accounting summary report has two aspects: to generate common accepted financial statements that reflect the health of the business and to provide concise but insightful interpretations and necessary recommendations deduced from the data (Larson, 2008). Financial Position Summary Appendix I: Daily Seasonal Data * The seasonal data was used as an “ad hoc” journal or daily receipts record to build each of the financial worksheets. Appendix II: Financial Journal The DGLs Financial Journal is the formal recording of five aspects of a transaction that is found in the Daily Seasonal Data: (1) its date, (2) brief description of the transaction, (3) ledger account to be debited and amount, (4) ledger account to be credited and amount, and its (5) cross-reference title for other financial reports. It also includes additional data entries such as the weather condition on that day and number of hours the stand was open to help “flush out” the other factors affecting the DGLs. This approach provides an audit trail and a means of analyzing the effects of daily transactions on DGLs’s financial position. * The DGLs first season...
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...and reinvested the same amount at 7.25% (yearly) How much is available now (total)? 4) 3 years ago your parents opened a “saving account” in your favour with a bank paying a 10.75% yearly interest rate. How much do you own today for each € deposited? 5) You borrow, as an overdraft on your current account, 50 with an Italian bank charging you a nominal yearly rate of 18%. How much is your debt with the same bank two years later (Italian banks use Nominal Rates convertible quarterly)? 6) You are entitled to receive 100, 3 years from now. What is the present value of your credit discounted at 16% yearly rate? 7) Your bank charges a 16% yearly nominal rate (quarterly compounding) for a loan in your current account; how much will you pay after 3 years for a 400 loan? 8) How much do you have to invest to have 50 after 4 years with a 12% yearly return? 9) An initial bank deposit of 10 is equal to 50 after 10 years, find the yearly interest rate (compound). 10) How much should you invest today in order to have 30 after 5 years if a yearly yield of 18% is expected? 11) If 20 are invested today, yielding 14%, how long will it take to have 50? 12) How much must be invested today in order to have 250 after 4 years if the yearly yield is 16% ? 13) 50 are invested today at 13%, how long will it take...
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...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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