...project balances computed at the project’s i* values, PB(i*)n, are either less than or equal to zero throughout the life of the investment. Meaning: The investment is net in the sense that the firm does not overdraw on its return in any point and hence is not indebted to the project Contemporary Engineering Economics, 5th edition, © 2010 Pure versus Mixed Investment Pure Investment Mixed Investment Definition: An investment in Definition: An investment in which which a firm never borrows a firm borrows money from the money from the project. project during the investment period How to Determine: If the project passes the net How to determine: If a project fails investment test, it is a pure the net investment test, it is a investment. mixed investment. Relationship: A simple Relationship: If a project is a mixed investment is always a pure investment, it is a nonsimple investment. investment. (However, we can’t say that a nonsimple investment is also a mixed investment.) Contemporary Engineering Economics, 5th edition, © 2010 Example 7.6 Pure versus Mixed Investments Contemporary Engineering Economics, 5th edition, © 2010 Ex.7.6 Pure versus Mixed Investments Sample Calculation for Project B: Use 21.95% as an interest rate to find the project balances PB 21.95% 0 = $1,000. PB 21.95% 2 = +$380.50 1 + 0.2195 $300 = $164.02. PB 21.95% 3 = +$164.02 1 + 0.2195 $200 = 0. (-, +, +, 0) Mixed investment PB 21.95% 1 =...
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...Return on Equity (ROE) and Internal Rate of Return (IRR) are two very important tools which can be used in decision making in expanding and investing in overseas projects. Return on Equity (ROE) tells how much profit company is generating with shareholder's money. ROE is calculated as: ROE = Net Income/Shareholder's equity This net income is income after paying tax and preferred stock dividend but before paying common stock dividend.ROE measures profit generating efficiency of the company. (McClure, 2010) Higher the ROE, better the investment opportunity company is offering. Advantage of using ROE for investment decision is, it is easy to calculate and it tells how much profit company is generating for share holders. Ultimate goal of a company is to create value for shareholders. Thus, ROE is the right measure to find out if company is efficient in generating profit on its equity (and asset) or not. However, ROE is not the absolute indicator of investment value. If value of shareholder's equity falls, ROE will go up. Similarly, if company is taking large write-down, ROE will fall sharply. Share buyback also lowers ROE while there is no change in company's operation. (McClure, 2010) Internal Rate of Return (IRR) is an indicator of yield of an investment.IRR is widely used method in capital budgeting decisions. IRR is the discount rate where total present value of all cash inflows is equal to total present value of all cash outflows. i.e. IRR is the discount rate at which...
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...Risk and Return Concepts Prepared by: JQY Risk and Return Concepts • Measures of risk and returns • Portfolio risk and returns • CAPM Return – what is earned on an investment: the sum of income and capital gains generated by an investment. Risk – possibility of loss; the uncertainty that the anticipated return will not be achieved. Risk and Return? If you have PHP 1,000,000, will you invest in: 5% 20% Risk and Return General Rule of Thumb: More Risk = More Returns Less Risk = Less Returns It depends on the investor: Risk Seeking – prefers high risk investments Risk Neutral – willing to take on moderate risk Risk Averse – conservative, unwilling to take on high risk investments unless the returns justify and compensates for the high risk taken. Relative Risk & Returns of Asset Classes Source: http://www.weblivepro.com/articles/cpp/cppinfo.aspx Measures of Returns • Historical Returns ▫ Holding Period Return ▫ Alternative Measures Arithmetic Mean Geometric Mean Harmonic Mean • Expected Returns Measuring Historical Returns • Holding Period Return ▫ Total return on an asset or portfolio over the period during which it was held ▫ HPR = MV1 – MV0 + D MV0 MV1 = market value, end MV0 = market value, beginning D = cumulative cash distributions (at the end of period) • Annualized HPR ▫ (1 + HPR) ^ 1/n – 1 Measuring Historical Returns • Example: Mr. A bought an asset in 2005 for P100. He kept it...
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...Return Rate of Electronics I. The fact that customers tend to return purchased goods for any reason is a major frustration for the consumer electronics industry. (C. Lawton, The Wall Street Journal, May 8, 2008) Recently, it was reported that 68% of all returns were for “no trouble found”. Consider that a sample of 24 customers who returned consumer electronics purchases was selected. Answer the following questions. Round your answers to four decimal digits. 1. Show that the requirements of binomial probability distribution are satisfied. a. A fixed number of trials – 24. b. Two possible outcomes – No trouble found, yes or no c. The probability of success is the same on each trail. d. The trails are independent. e. The random variable X is represented. 1. What is the probability that exactly 18 of the 24 customers made a return for “no trouble found”? binompdf (24, 0.68, 18) = 0.1397 2. What is the probability that no more than half of the customers made a return for “no trouble found”? binomcdf (24, 0.68, 12) =0.0507 3. What is the probability that at least half of the customers made a return for “no trouble found”? binomcdf (24, 0.68, 11) = 0.0202 1-0.0202=0.9798 4. What is the expected number of customers in this sample who made a return for “no trouble found”? µx=np 24(0.68) = 16.32, 17 customers found no trouble. 5. What is the standard deviation of this binomial distribution? Ơx=√np(1-p) √24(0.68)(1-0.68)=2.2853 ...
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...CFA, FRM Strathmore University GARP Chapter Meeting 29th July 2011 Agenda 1. Background 2. Credit Risk and the Case of Washington Mutual 3. Operational Risk and the Case of Rogue Brokers in Kenya and Barings 4. Market Risk and the Case of LTCM 5. Liquidity Risk and the Case of Northern Rock 6. Q&A BACKGROUND Main Types of Financial Risk Risk Type Definition Credit Risk The potential that a bank's borrower or counterparty will fail to meet its obligations in accordance with agreed terms. Market Risk The risk that movements in market prices will adversely affect the value of on- or off-balance sheet positions. The risk is attributable to movements in interest rates, foreign exchange (FX) rates, equity prices or prices of commodities. Operational Risk Risk of loss resulting from inadequate or failed internal processes, people and systems, or from external events. The definition includes legal risk, but excludes reputational and strategic risk. Liquidity Risk Liquidity is the ability to fund increases in assets and meet obligations as they become due. It is crucial to the ongoing viability of any organization. Source: Financial Stability Institute CREDIT RISK AND THE CASE OF WASHINGTON MUTUAL Sources of Credit Risk Apart from traditional types of loans, credit risk can also be found in a bank's: Investment portfolio Overdrafts Letters of credit Credit risk also exists in a variety...
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...Required Rate of Return on stocks Name: Course: Instructor: Date: REQUIRED RATE OF RETURN ON STOCKS Introduction The full amount of risks that any investment faces is composed of the summation of the diversifiable and the non-diversifiable risks. As shown in the formula below. Total Risk = Systematic (non-diversifiable) Risk + Diversifiable Risks The Systematic risk is defined as the effect of risk that every type of investment will come across owing to the geo-political factors such as inflation. The unsystematic risk is attributed to factors such as poor leadership, labor factors among others. Unlike the systematic risk, it can be lowered by spreading the investment portfolio to different firms in diverse sectors or by investing in the different classes of assets. Total Risk = Systematic Risk + Diversifiable Risks Required Return = Risk-Free Rate + Risk Premium = Risk-Free Rate + [Beta × (Market Return – Risk-Free Rate)] Beta (Year = 2008) MNQ Company's common stock 0.85 Stock #1 1.5 Stock #2 0.27 Stock #3 1.1 Stock #4 2.15 Stock #5 -0.5 Stock #6 0.7 Stock #7 1.4 Stock #8 1.2 Stock #9 0.65 Risk-Free Rate of Return = 5% Market Risk Premium = 6% Required rate of return MNQ Company's common stock 5% + [0.85 × (6% - 5%)] = 5.85% Stock #1 ...
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...Required Rate of Return on stocks Name: Course: Instructor: Date: REQUIRED RATE OF RETURN ON STOCKS Introduction The full amount of risks that any investment faces is composed of the summation of the diversifiable and the non-diversifiable risks. As shown in the formula below. Total Risk = Systematic (non-diversifiable) Risk + Diversifiable Risks The Systematic risk is defined as the effect of risk that every type of investment will come across owing to the geo-political factors such as inflation. The unsystematic risk is attributed to factors such as poor leadership, labor factors among others. Unlike the systematic risk, it can be lowered by spreading the investment portfolio to different firms in diverse sectors or by investing in the different classes of assets. Total Risk = Systematic Risk + Diversifiable Risks Required Return = Risk-Free Rate + Risk Premium = Risk-Free Rate + [Beta × (Market Return – Risk-Free Rate)] Beta (Year = 2008) MNQ Company's common stock 0.85 Stock #1 1.5 Stock #2 0.27 Stock #3 1.1 Stock #4 2.15 Stock #5 -0.5 Stock #6 0.7 Stock #7 1.4 Stock #8 1.2 Stock #9 0.65 Risk-Free Rate of Return = 5% Market Risk Premium = 6% Required rate of return MNQ Company's common stock 5% + [0.85 × (6% - 5%)] = 5.85% Stock #1 ...
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...CHAPTER 1—THE INVESTMENT SETTING TRUE/FALSE 1. The rate of exchange between certain future dollars and certain current dollars is known as the pure rate of interest. ANS: T PTS: 1 2. An investment is the current commitment of dollars over time to derive future payments to compensate the investor for the time funds are committed, the expected rate of inflation and the uncertainty of future payments. ANS: T PTS: 1 3. The holding period return (HPR) is equal to the holding period yield (HPY) stated as a percentage. ANS: F PTS: 1 4. The geometric mean of a series of returns is always larger than the arithmetic mean and the difference increases with the volatility of the series. ANS: F PTS: 1 5. The expected return is the average of all possible returns. ANS: F PTS: 1 6. Two measures of the risk premium are the standard deviation and the variance. ANS: F PTS: 1 7. The variance of expected returns is equal to the square root of the expected returns. ANS: F PTS: 1 8. The coefficient of variation is the expected return divided by the standard deviation of the expected return. ANS: F PTS: 1 9. Nominal rates are averages of all possible real rates. ANS: F PTS: 1 10. The risk premium is a function of the volatility of operating earnings, sales volatility and inflation. ANS: F PTS: 1 11. An individual who selects the investment that offers greater certainty when everything else is the same is known as a risk averse...
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... Concepts Covered Cost of Equity: Cost of Equity is the minimum rate of return a firm must offer to the shareholders. This is necessary as the shareholders who have taken a risk in investing would be waiting for returns. The formula for Cost of Equity is given by: Cost of Equity = (Dividend per share/ Current Market Value of Stock) * Growth rate of Dividends Cost of debt: - Cost of debt is the effective interest rate that a company pays on its debt. Cost of debt is usually calculated after the interest expenses are deducted Cost of debt = Cost of Debt before tax (i.e. Interest rate) * (1-Tax Rate) WACC: Weighted average cost of capital is one of the measures to calculate the cost of capital of the firm. Weighted Average Cost of Capital is the minimum return a firm must earn on existing assets to keep its stock price constant and satisfy its creditors and owners. [pic] c = weighted average cost of capital y = Expected rate of return on equity (cost of equity) b = Expected rate of return on debt (cost of debt) E = Total market value of equity D = Total debt and leases K = E+D = Total capital invested Tc = Corporate Tax Rate Capital Asset Pricing Model (CAPM) • Asset Pricing Equation: E(ri) = rrf + bi[E(rm)-rrf] , where E(ri) is the expected return on the security. rrf is the risk free rate...
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...the stock return would be affected when the factor of your choice changes. d) Describe a scenario where one can benefit from trading on the factor of your choice. a) There is a variety of factors that can determine the returns on security. The market based factor is the return on the broad market index such as S&P 500. This market return is one of the factors in the model. Other factors include the following: • GDP growth rate. This factors shows overall macroeconomic conditions that tend to affect a stock’s performance. • Risk free rate of return. • 10 year T-bond interest rate that shows the required return on 10-year government bonds. • A company’s ROE as an indicator of its profitability. Therefore, the model will look like this: [pic], where betas show the sensitivity of return to the factor, rm is the market rate of return, rf is the risk-free rate, T-bond is the 10-year T-Bond rate and ROE is the return on equity (ROE). Generally, GDP has a positive effect on a stock return. Higher economic growth leads to more business opportunities and potentially higher profits. This positively affects a stock’s return. Market rate of return has a positive effect assuming a positive beta. Risk-free rate has a negative impact on a stock’s performance. Higher rate leads to lower return on a company’s stock. The same effect comes from 10-year T-Bond rate. Higher rate leads to lower expected return on a stock...
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...CHAPTER 1 THE INVESTMENT SETTING Answers to Questions 1. When an individual’s current money income exceeds his current consumption desires, he saves the excess. Rather than keep these savings in his possession, the individual may consider it worthwhile to forego immediate possession of the money for a larger future amount of consumption. This trade-off of present consumption for a higher level of future consumption is the essence of investment. An investment is the current commitment of funds for a period of time in order to derive a future flow of funds that will compensate the investor for the time value of money, the expected rate of inflation over the life of the investment, and provide a premium for the uncertainty associated with this future flow of funds. 2. Students in general tend to be borrowers because they are typically not employed so have no income, but obviously consume and have expenses. The usual intent is to invest the money borrowed in order to increase their future income stream from employment - i.e., students expect to receive a better job and higher income due to their investment in education. 3. In the 20-30 year segment an individual would tend to be a net borrower since he is in a relatively low-income bracket and has several expenditures - automobile, durable goods, etc. In the 30-40 segment again the individual would likely dissave, or borrow, since his expenditures would increase with the advent of family life, and conceivably...
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...FFinance: principles of Finance (part 1) Financial markets and management Valuation of investment Value of investment = value of investment’s cash flows * Concept of present value: value of investment = PV(CF°, CF1, CF2…) Important characteristics of cash flows: * Time: for the same amount of money, now is preferred to tomorrow * Uncertainty: risk and return (1 for sure is preferred to half a chance to get 2) Opportunity cost of capital: Definition: opportunity cost of capital is the expected rate of return offered by equivalent investments in financial markets Net present value (investment rule) Definition: NPV of an investment is the current market value of its cash flows * accept project if its NPV is positive Arbitrage pricing An arbitrage is an investment opportunity such that: * It requires no positive investment today but yields positive payoffs in the future (type 1) * Yields positive payoff today without requiring positive payment in the future (type 2) Present value Valuing cash flows The future value of a cash flow of C dollars in T years when invested at a rate-of-return r is: FV(C) = $C * (1+ r)T We can deduce of this the present value of an amount of money received in T years: PV(C) = $C(1+r)T=$C*[discount factor at r, maturity T] Discount factor at r, maturity T = 1(1+r)T Project evaluation {Cfi, I ϵ [0;T]}: NPV = ∑ Cfi(1+r)i * Positive (<0) NPV projects increases (decrease) the value of a firm by the amount of...
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...at a rate of 5 percent per year in the future. Determine the value of the stock: Dividend * (1 + growth) / (overall return – growth) a. If the required rate of return is 12 percent.: 1.90 * (1.05 / 0.07) = $28.50 b. If the required rate of return is 15 percent. 1.90 * (1.05 / 0.10) = $19.95 c. Given your answers to Parts a and b, how are stock prices affected by changes in investor's required rates of return? When the higher overall return is the lower the stock is. When the anticipated price goes down the return rate goes up. Bond Garnett Corporation has also issued bonds which have a face value of $1,000, will mature in 10 years, and carry a coupon rate of 16 percent. Assume interest payments are made semiannually. a. Determine the present value of the bond's cash flows if the required rate of return is 16.64 percent. Present value= $785.45 b. How would your answer change if the required rate of return is 12.36 percent? $917.59 Paying less for the same payment gives you a higher yield, so when the bond rates go down the present value goes up. Beta Calculate the beta by assuming that the risk-free rate designated by r RF = 5%, the market risk premium designated by r M = 10%, and the expected rate of return for stock A is designated by r A = 12%. a. What is the beta for Stock A? E(R) is 12%, Rf = 5% and Rm = 10% 0.12 = 0.05 + B(0.10 - 0.05) = 0.05B = 0.07. So B = 1.4 b. If Stock A's beta was 2.0, what would be A's new required rate of return...
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...interest rate is 10% per year. Mr. Dell also has an investment opportunity—having the same risk as the market in which he can invest $50 this year and receive $80 next year. Suppose Mr. Dell consumes $50 this year and invests in the project. What is the NPV of the investment opportunity? NPV = (80/1.1) - 50 = + 22.73. | 7. (11) | Ms. Anderson has $60,000 income this year and $40,000 next year. The market interest rate is 10% per year. Suppose Ms. Anderson consumes $80,000 this year. What will be her consumption next year? Borrow $20,000 this year to consume 60,000 + 20,000 = 80,000. Consumption next year = 40,000 - (20,000 × 1.1) = 18,000. | 9. (13) | Mr. Smith has an income of $40,000 this year and $60,000 next year. He can invest in a project that costs $30,000 this year, which generates an income of $36,000 next year. The market interest rate is 10%. What will be his consumption next year if Mr. Smith invests in the project and consumes $50,000 this year? Consumption next year = [40,000 - 30,000 - 50,000] × 1.1 + (60,000 + 36,000) = 52,000. | 14. | Given the following data for Project M: NPV = -200 + 150/1.05 + 120/(1.05^2) = 51.70. | 15. | Your firm expects to receive a cash flow in two years of $10,816 in nominal terms. If the real rate of interest is 2% and the inflation rate is 4%, what is the real cash flow for year 2? Real cash flow = 10,816/(1.04^2) = 10,000. | 16. | The real cash flow occurring in year 2 is $60,000. If the inflation rate is 5% per...
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...Chapter 6. Risk, Return, and CAPM Dollar return: Amount to be received-Amount invested Rate of return: Amount received-Amount investedAmount invested Stand-alone risk is the risk an investor has in just holding the one asset Expected rate of return: r=i=1npiri Where P is probability of i outcome and r is the rate of return The more leptokurtic the distribution, the more likely the actual outcome will be closer to the expected return. Measuring Standalone Risk: Standard Deviation 1. Expected Rate of return 2. Deviationi= ri-r 3. Variance=σ2=i=1n( ri-r)2Pi 4. Standard Deviation=σ=Variance 5. Or use Excel of Financial calculator Using Historical Data to Measure Risk: Realized Rates of Return: rAvg=t=1nrtn Standard Deviation of the Sample Returns: σ=S=t=1n(rt-rAvg)n-1 In Excel use =Average and =STDEV functions Measuring Standalone Risk: Coefficient of Variation Coefficient of variation = CV=σr Risk Aversion and Required Rate of Return Assume risk aversion for investors Textbook Example: Basic Food’s Price up to $150 from $100 Sale.com Price down to $75 from 100. Difference in return, 20%-10%= Risk Premium Risk in Portfolio Context Expected return on portfolio=Weighted expected return=rp=i=1nwiri Portfolio Risk Stocks can be combined into portfolios which then become less risky to riskless depending on the correlation of the assets. Stocks with a ρ=-1 are perfectly negatively correlated. The inverse is positively correlated. Expected...
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