FI 4000 1st Edition Exam 1 Study Guide Time Value of Money Present and Future Value ex Deposit 5000 today in account that earns 10 in the first two years 12 for every year for three years after that and 10 for the last year How much will it amount to in 6 years FV 6 years 5000 1 10 2 1 12 3 1 1 1 9350 add up number of years to equal 6 ex If you want to have 1000 after 3 years in an account that pays 5 interest in year 1 7 in year 2 and 3 in year 3 how much must you have in it today 1000 1 03 1 07 1 05 PV 864 15 Multiple cash flows ex Year 1 CF 100 years 2 and 3 CF 200 years 4 and 5 CF 300 The required discount rate is 7 for the first two years and 5 for the last three years What is the value of the cash flows at the end of year 5 What is the value of the cash flows today 300 300 1 05 1 200 1 05 2 200 1 05 3 100 1 07 1 05 3 Year 5 year 4 compounded year 3 future value end of year 2 rate year 1 rate up to year 2 1190 89 Because we are compounding and moving forward to the next years year 2 has already been accounted for in the compounding of year 1 Accept or reject investment opportunity discount cash flows of project if present value is less than the cost of the project today should be rejected if it is greater should accept Annuities ex Bill just turned 40 and decides he wants to start investing to someday open up his own Playboy club He wishes to accumulate 1 million by the time he turns 65 through an interest account earning 10 compounded annually If he begins making annual deposits in one year with his last deposit made at age 65 how much should these be for FV 1000000 C 1 10 25 1 0 10 solve for constant C 1000000 98 35 C 10167 77 When dealing with future expenses accumulating and determining how much to invest today to earn that amount in the future solve for PV with C given and use equation 1 1 1 r t r Then discount that amount to the value at time 0 Add 1 if to find deposit amount with present value of future annual deposits If there is both a lump sum and annual payment ex healthcare fund identify discount rates throughout period if it is different subtract the smaller period of years from the larger period discount lump sum as 120000 1 09 6 1 05 59 and annual payments deposits should be discounted accounting for each year 1st year is not discounted so it is just the amount value compare present value of lump sum and payments is it less go for the fund Effective Annual Rate EAR used to compare two alternative investments with different compounding periods annual percentage rate is just multiplying the rate by whichever number will make it annual compounding for instance semi annual rate 2 annual legal rate monthly compounding 12 but same method cannot be used for semiannual which would require the semiannual APR ex You are choosing between two savings accounts One pays 5 25 compounded daily and the other 5 3 compounded semi annual Which one will be better for you to choose has higher EAR1 1 0525 365 365 1 05389 or 5 39 better choice EAR2 1 053 2 2 1 0537 or 5 37 in calculating how much interest can be saved from one credit application choice versus another multiply the amount of credit extended by the EAR 1 or by 1 APR m m remember to choose the alternative that has the lower effective rate Risk and Return Measuring Investment Returns over Multiple Periods arithmetic average sum of returns in each period divided by number of periods useful in determining performance for future quarters but does not represent single quarterly rate for year no compounding ra 10 25 20 25 4 10 geometric average single per period return and same cumulative performance as sequence of actual returns known as time weighted average and ignores variation in funds under management rG 1 10 1 25 1 20 1 25 1 4 1 8 29 Expected Return IRR internal rate of return of investment considers changes in assets under management compare discount rate as result of present value of future cash flows being investment amount expected mean return average HPR if repeat investment in asset many times weighted average of possible returns of future reward from investment surprise return difference between actual and expected return uncertainty of investment is function of magnitudes of possible surprises ex Predicted returns for Stocks C and T in three possible states of nature What are the expected returns What is the volatility variance Risk State Probability C T Boom 0 3 0 15 0 25 Normal 0 5 0 10 0 20 Recession 0 2 0 02 0 01 E r C 0 3 0 15 0 5 0 10 0 2 0 02 099 E r T 0 3 0 25 0 5 0 20 0 2 0 01 177 var C 0 3 15 099 2 0 5 10 099 2 0 2 02 099 2 sqrt 0020305 4 5 var T 0 3 25 177 2 0 5 10 177 2 0 2 01 177 2 sqrt 0074403 8 6 variance expected value of the squared deviation from the mean deviations of returns from the mean squared because otherwise negative deviations will offset positive ones resulting in zero for expected deviation from mean square rooted variance is standard deviation risk premiums difference between the expected Holding Period Return or the uncertain future holding periods and the risk free rate or the rate of return that can be earned with certainty E rp rf will be higher with more risk aversion in analyzing Annual Holding Period returns subtract difference between Arithmetic mean and Arithmetic mean of T bill from first percent to get historical risk premium do the same for another stock the average of the two provides standard deviation Scenario Analysis used to quantify risk and estimate possible HPR s and likeliness of them occurring process by which devise list of possible economic scenarios and specify likelihood of each and the HPR that will be realized in each case probability distribution list of possible outcomes HPR s with their associated probabilities allows us to derive measurements for both the reward and risk of investment characterized by most likely value mean variance standard deviation both of which are charact of normal distribution or skewness ex What are expected returns for stocks X and Y What are the standard deviations Bear Market Normal Market Bull Market Probability 2 5 3 Stock X 20 18 50 Stock Y 15 20 10 E r X 0 2 20 0 5 18 0 3 50 20 E r Y 0 2 15 0 5 20 0 …