Gordon Guides For the MT Exam. Financial Math

Transcription

1 Financial Math For the IMT Exam, candidates are expected to have a high degree of understanding of time value of money principles, security valuation and basic statistics. Formulas are provided on at the beginning of the exam booklet. Therefore, do not memorize them, know how to use them! Candidates report that a lot of relatively easy marks are often missed because of a lack of familiarity with basic Math skills and most surprising simply not knowing how to use a financial calculator correctly. If you are weak in Math and have never used a financial calculator, we suggest you use the Texas Instruments BA II PLUS.do not buy the HP 10B or 12C.you will spend weeks just learning how to turn it on! The BA II PLUS is a much simpler machine to operate, it can do all of the required calculations and it costs about one half the price of the HPs info@examsuccess.ca

2 3. Net present value (NPV) In investment theory NPV analysis indicates whether or not a potential investment will increase an investor s wealth or decrease an investor s wealth. Investments that have a positive NPV are said to be wealth enhancing, while investments that have a negative NPV are said to be wealth reducing. Thus a rational investor would only select investments that have positive NPVs! Using a financial calculator, use the cash flow keys to calculate NPV. To calculate NPV without a financial calculator, use the following formula: NPV = CF 0 + CF 1 + CF CF n Where: CF = Cash flow (1+k) 1 (1+k) 2 (1+k) n k= discounting rate 4. Internal rate of return (IRR) The IRR is another investment evaluation tool that allows investors to identify wealth enhancing investments. The IRR is the rate which sets the NPV equal to zero, it is often considered to be similar to a break even rate of return. Candidates should know how to use a financial calculator to find it otherwise they must use trial and error. The decision rule is as follows: If the IRR is greater than the cost of your capital (ie. the discount rate), then the investment will be wealth enhancing, so a rational investor would select it. If the IRR is less than the cost of your capital (ie. the discount rate), then the investment will be wealth reducing, so a rational investor would not select it info@examsuccess.ca

3 An investment is estimated to cost $150 million. It is assumed that the investment will yield the following end of year cash flows: year net cash flow ($ million) Calculate the project's NPV and IRR assuming the cost of capital is 10%: Using the formula: NPV = (150) = Using the cash flow keys on your financial calculator: CF0 = (150), CF 1 = 25, CF 2 = 50, CF 3 = 55, CF 4 = 40, CF 5 = 60, I = 10, Solve for NPV = Use the calculator to solve for IRR = 14.59% Your client has $10,000 and is looking to invest in a private equity deal. You present your client with the following investment opportunity, invest $10,000 today and receive the following year end cash flows. Year Cash Flow ($10,000) $3,500 $4,500 $5,000 $5,000 What is the NPV of this investment, assuming a discount rate of 12% is applied? What is the IRR? The answer is $3, The answer is 26.51% Exam Tip: NPV and IRR calculation questions and theory questions are low probability for the exam. Just know the basic decision rules info@examsuccess.ca

4 5. Compounding periods Compounding periods represent the number of time periods over which your money accrues interest. Candidates should remember the following trivial points about compounding: 1. The greater the number of compounding periods (ie. longer time), the greater the amount of interest, and thus the greater the ending value. 2. The more frequently the compounding, the greater the amount of interest, and thus the greater the ending value. 6. Interest rate In economic terms, the interest rate represents the cost of money. The interest rate reflects the riskiness of an investment the higher the risk, the higher the interest rate charged. For the exam, you can also think of the interest rate as the rate at which your money grows. Exam Tip: Stated Interest Rate Nominal annual rate or the contractual rate (ie. Coupon) Periodic Rate Rate of interest earned over 1 compound period (ie. Semi-annual) Effective Annual Rate Rate of return actually being earned after adjustments for compounding frequency 7. Simple annuities (ordinary and annuity due) A simple annuity is any investment that pays an investor the same amount of money (the payment) on a regular basis (equal time periods), for a specific period of time. An ordinary annuity makes it payments at the end of the time periods, while an annuity due makes its payments at the beginning of the time period. Remember the future value of an annuity is always zero! info@examsuccess.ca

5 Examples: An annuity offered by Big Life Insurance Co. will pay Ron Smith $242,500 at the end of every year for 20 years. What is the cost (or present value) of this annuity assuming the interest rate per year is 7%? The answer is $2,569, An annuity offered by Big Life Insurance Co. will pay Ron Smith $242,500 at the beginning of every year for 20 years. What is the cost (or present value) of this annuity assuming the interest rate per year is 7%? The answer is $2,748, Michelle wants to retire in 17 years. She estimates that she will need $300,000 in RRSP savings at the time she retires. If her investments earn 11.5% annually, what is the difference in required annual savings if she invests at the beginning of each year rather than at the end of each year? A an additional $ C no difference B a savings of $ D a savings of $6, The answer is B END: n = 17, I = 11.5%, PV = $0, FV = $300,000, CPT PMT = $6, BGN: n = 17, I = 11.5%, PV = $0, FV = $300,000, CPT PMT = $5, Difference: $6, $5, = $ savings Exam Tip: Read the questions carefully, so you can recognize the indicator words used on the exam. Indicator words give you clues and tell you when you need to adjust your calculator to BEG or END MODE! Indicator words: Annuity Due, set your calculator to BGN if you read: payments on your birthday, anniversary, at the beginning of the year, on January 1 st, starting today, etc. Ordinary Annuity, set your calculator to END if you read: at the end of the year, starting next month, etc info@examsuccess.ca

6 18. Time-weighted return (TWRR) The TWWRR is used to calculate the annualized compound growth rate of an investment over a specific time period, by geometrically linking the holding period returns. One trivial note, the TWRR is the preferred measure of performance for Mutual Fund Portfolio Managers, because it isolates the period to period growth of the fund, and is unaffected by unitholder contributions or redemptions! To calculate the TWRR (or Geometric Average): TWRR = [ (1+R 1 )(1+R 2 )(1+R 3 ).(1+R n ) ] 1/n 1 Be aware that in math x y is the same as y 1/x ( Prof. Gordon if you need an explanation) Calculate the time weighted rate of return given the following series of returns for the BZG Growth Fund: Year Return 10% 15% -10% 20% 5%. 19. Risk-free return (R f ) The risk-free return is the rate of return earned on an investment that has no risk! The answer is 7.48% The most common proxy for the risk-free rate of return is the Government T-Bill rate, because T-Bills are considered to be risk-free investments. 20. Standard deviation (SD) In investment theory standard deviation represents a measure of the level of risk, the higher the standard deviation, the higher the risk. (Link to Investment Management) Professional money managers look back over the historical performance of an investment and from this data they calculate the average return. This forms a starting point regarding their expectations for the future performance of the investment. By calculating the Standard Deviation, a manager can gain an idea of how far a return may deviate, above or below, the expected return on an investment, and thus the risk associated with an investment info@examsuccess.ca

7 Standard Deviation (for a sample) Where: x = actual return Standard Deviation = (x x ) 2 x = expected return N - 1 N = number of observations The BT Hedge Fund has posted the following annual returns 15%, 21%, 26%, and 35% in the last four years. Using the information above, calculate the standard deviation for the BT Hedge Fund. First calculate the expected return (or the average) = 15% + 21% + 26% + 35% = 24.25% 4 Now calculate the standard deviation: SD = ( ) 2 + ( ) 2 + ( ) 2 + ( ) 2 = = 2.44% A Financial Planner gathers the following sample of data for a client s stock portfolio: Year Return 8% -5% 0% 9% Based on this information calculate the standard deviation of returns. First calculate the expected return (or the average) = 8% - 5% + 0% + 9% = 3% 4 Now calculate the standard deviation: SD = (8-3) 2 + (-5-3) 2 + (0-3) 2 + (9-3) 2 = 134 = 6.68% The answer is 6.68% info@examsuccess.ca

8 Portfolio Return and Variance (Standard Deviation) Expected Return The expected return for a portfolio of securities is simply the weighted average of the expected returns for each individual asset. E(r) = ( w 1 ) ( Ex. Return Asset 1 ) + ( w 2 )( Ex. Return Asset 2 ) ( w n )( Ex. Return Asset n ) Where: w n = the weighting of the asset Asset weightings are calculated using the following formula: W n = Market value of Asset n _ Total market value of the Portfolio Your firm s quantitative research department has published the following information regarding expected rates of return for the various asset classes: Expected Return Equities 16% Bonds 8% Cash 5% You have allocated your client s assets according to the following breakdown: $60,000 in Equities, $30,000 in Bonds, and $10,000 in Cash. What return should your client expect to earn on his portfolio? First calculate the asset weightings: Weighting in Equities = $60,000 = 60% $100,000 Weighting in Bonds = $30,000 = 30% $100,000 Weighting in Cash = $10,000 = 10% $100,000 Next, calculate expected return using the formula: E(r) = ( 0.6 )( 16 ) + ( 0.3 )( 8 ) + ( 0.1 )( 5 ) = 12.5% info@examsuccess.ca

9 Instructor/Author Profile: Brian Y. Gordon, CFA, CFP, CIM, MBA, FCSI, is a tenured Professor in the School of Business at Centennial College in Toronto where he teaches Economics, Financial Accounting, Corporate Finance, the Canadian Securities Course, Personal Financial Planning and Investment Management. Prof. Gordon is also a part-time faculty member at Concordia University in Montreal, where he teaches Economics and Investment Management courses at the MBA level. Prof. Gordon has also lectured at Ryerson University in Toronto teaching Corporate Finance. Since 1999, Prof. Gordon has been a featured lecturer and workshop facilitator for CFP and CFA review programs offered across Canada. Prior to entering academia, Prof. Gordon developed his expertise in the discount brokerage, full service brokerage and banking industries, specializing in investment management, business development, strategic sales and marketing, and wealth management training. Prof. Gordon holds a BA in Economics from the University of Toronto, an MBA from Heriot-Watt University in the UK, and was awarded his CFA charter in In 1995, Prof. Gordon was granted a fellowship from the Canadian Securities Institute, earning the prestigious FCSI designation. Prof. Gordon successfully challenged the CFP Professional Proficiency Examination and was awarded the right to use the CFP designation in info@examsuccess.ca