CAIIB -Financial Management - Transcript

1.CAIIB -Financial Management Module A -Quantitative Techniques and Business 2.Agenda Time Value of Money Bond Valuation Theory Sampling Regression and Correlation4.Objectives What do we mean by Time value of money Present Value, Discounted Value, Annuity5.Time Value of Money What is Time Value of Money? Future Value Present Value Future Value: Compounding:6.Compounding Compounding Formula What if compounding is done on monthly basis?7.Compounding Exercise Exercise: Prepare a table showing compounding as per following conditions: Rate of Interest - 5%, 12% and 15% Compounding 2 & 4 times in a year Principal Rs.100,000/-8.Discounting Present Value You have an option to receive Rs. 1,000/- either today or after one year. Which option you will select? Why? Decision will depend upon the present value of money; which can be calculated by a process called Discounting (opposite of Compounding) Interest Rate and Time of Receipt of money decide Present Value What is the present value of Rs. 1,000/- today and a year later?9.Discounting contd Formula to find Present Value of Future Cash Receipt Where PV = Present Value, P = Principal, i = Rate of Interest, n = Number of Years after which money is received Assuming Rate of Interest is 10%, value of Rs. 1,000/- to be received after 1 year will be, Whereas the value of money to be received today will be Rs. 1,000/-10.Discounting of a Series contd How discounting is done for a series of cashflow? e.g. Receive Rs. 1,000/- at the end of every year for 3 years OR Receive Rs. 2,500/- today Assume Rate of Interest @10%11.Periodic Discounting What if the receipts are over six months interval ? Find Present Value of the money receipts Periodic Discounting Formula12.Periodic Discounting Formula13.Charting of Cashflow For any financial proposition prepare a chart of cashflow: e.g.14.Net Present Value Net Present Value means the difference between the PV of Cash Inflows & Cash Outflows How do you compute NPV? Prepare Cashflow Chart Net off Inflow & Outflow for each period separately If Inflow > Outflow, positive cash If Inflow < Outflow, negative cash Find present values of Inflows & Outflows by applying Discount Factor (or Present Value Factor) NPV = (PV of Inflows) LESS (PV of Outflows); Result can be +ve OR -ve Continuing with our example of Bond Investment:15.NPV contd If Cashflows are discounted at say 10%, the sum of PV is 25.05, a positive number & therefore the IRR has be higher than 10% to make Net Present Value to zero16.Internal Rate of Return (IRR) Definition: The Rate at which the NPV is Zero. It can also be termed as Effective Rate If we want to find out IRR of the bond investment cashflow:17.IRR Contd To prove that at IRR of 11.38% the NPV of Investment Cashflow is zero, see the formula & table:18.IRR - Additional Example You buy a car costing Rs. 600,000/- Banker is willing to finance upto Rs. 500,000/- The loan is repayable over 3 years, in Equated Monthly Installments (EMI) of Rs. 15,000/- Installments are payable In Arrears What is the IRR? How do you express this mathematically? What are the values of each component in the formula? What will be the impact on IRR if the EMIs are payable In Advance? Can we use IRR for computing Interest & Principal break-up?19.IRR - Additional Example contd Plot the cashflow: EMI in Arrears20.IRR - Additional Example contd21.BOND VALUATION22.Objectives Distinguish bonds coupon rate, current yield, yield to maturity Interest rate risk Bond ratings and investors demand for appropriate interest rates23.Bond characteristics Bond - evidence of debt issued by a body corporate or Govt. In India, Govt predominantly A bond represents a loan made by investors to the issuer. In return for his/her money, the investor receives a legaI claim on future cash flows of the borrower. The issuer promises to: Make regular coupon payments every period until the bond matures, and Pay the face/par/maturity value of the bond when it matures24.How do bonds work? If a bond has five years to maturity, an Rs.80 annual coupon, and a Rs.1000 face value, its cash flows would look like this: Time 0 1 2 3 4 5 Coupons Rs.80 Rs.80 Rs.80 Rs.80 Rs.80 Face Value 1000 Market Price Rs.____ How much is this bond worth? It depends on the level of current market interest rates. If the going rate on bonds like this one is 10%, then this bond has a market value of Rs.924.18. Why?26.Bond prices and Interest Rates Interest rate same as coupon rate Bond sells for face value Interest rate higher than coupon rate Bond sells at a discount Interest rate lower than coupon rate Bond sells at a premium

27.Bond terminology Yield to Maturity Discount rate that makes present value of bonds payments equal to its price Current Yield Annual coupon divided by the current market price of the bond Current yield = 80 / 924.18 = 8.66%28.Rate of return Rate of return = Coupon income + price change ---------------------------------------- Investment e.g. you buy 6 % bond at 1010.77 and sell next year at 1020 Rate of return = 60+9.33/1010.77 = 6.86%29.Risks in Bonds Interest rate risk Short term v/s long term Default risk Default premium30.Bond pricing The following statements about bond pricing are always true. Bond prices and market interest rates move in opposite directions. When a bonds coupon rate is (greater than / equal to / less than) the markets required return, the bonds market value will be (greater than / equal to / less than) its par value. Given two bonds identical but for maturity, the price of the longer-term bond will change more (in percentage terms) than that of the shorter-term bond, for a given change in market interest rates. Given two bonds identical but for coupon, the price of the lower-coupon bond will change more (in percentage terms) than that of the higher-coupon bond, for a given change in market interest rates.31.SAMPLING32.Objectives Distinguish sample and population Sampling distributions Sampling procedures Estimation data analysis and interpretation Testing of hypotheses one sample data Testing of hypotheses two sample data33.Pouplation and Sample34.Types of sampling Non random or judgement Random or probability35.Methods of sampling Sampling is the fundamental method of inferring information about an entire population without going to the trouble or expense of measuring every member of the population. Developing the proper sampling technique can greatly affect the accuracy of your results.36.Random sampling Members of the population are chosen in such a way that all have an equal chance to be measured. Other names for random sampling include representative and proportionate sampling because all groups should be proportionately represented.37.Types of Random sampling Simple random sampling Systematic Sampling: Every kth member of the population is sampled. Stratified Sampling: The population is divided into two or more strata and each subpopulation is sampled (usually randomly). Cluster Sampling: A population is divided into clusters and a few of these (often randomly selected) clusters are exhaustively sampled. Stratified v/s cluster Stratified when each group has small variation withn itself but if there is wide variation between groups Cluster when there is considerable variation within each group but groups are similar to each other38.Sampling from Normal Populations Sampling Distribution of the mean the probability distribution of sample means, with all samples having the same sample size n. Standard error of mean for infinite populations sx = s/n1/2 Standard Normal probability distribution39.Density Curve (or probability density function) the graph of a continuous probability distribution The total area under the curve must equal 1. Every point on the curve must have a vertical height that is 0 or greater. Remind students that the area of a probability density curve must equal 1 as the total of all probabilities of a probability distribution equals 1. Remind students that the area of a probability density curve must equal 1 as the total of all probabilities of a probability distribution equals 1.40.Because the total area under the density curve is equal to 1, there is a correspondence between area and probability. page 228 of text This is an important fact for students to understand.page 228 of text This is an important fact for students to understand.41.Definition Standard Normal Deviation a normal probability distribution that has a mean of 0 and a standard deviation of 1 Again showing this graph with a graphing calculator will be very a very effective illustration for students. Changing one or both of the parameters, ? or ?, while leaving the standard normal curve in place, makes a good demonstration.Again showing this graph with a graphing calculator will be very a very effective illustration for students. Changing one or both of the parameters, ? or ?, while leaving the standard normal curve in place, makes a good demonstration.42.Definition Standard Normal Deviation a normal probability distribution that has a mean of 0 and a standard deviation of 1 page 229 and 231 of text The areas have been calculated by mathematicians using the calculus of the area between the curve and the x-axis. Fortunately, for the students in this course, the calculus knowledge is not necessary with the inclusion of Table A-2 (z-distribution) in the book. page 229 and 231 of text The areas have been calculated by mathematicians using the calculus of the area between the curve and the x-axis. Fortunately, for the students in this course, the calculus knowledge is not necessary with the inclusion of Table A-2 (z-distribution) in the book.43.Table A-2 Standard Normal Distribution = 0 ? = 1 Emphasize that Table A-2 gives the area (probability) from the mean (=0) to the z-score only. Students will need to be reminded of this often in the initial stages of this topic. Emphasize that Table A-2 gives the area (probability) from the mean (=0) to the z-score only. Students will need to be reminded of this often in the initial stages of this topic.44.Practice finding some areas (probabilities) for various z scores. Again remind students that these areas will be from the mean to the particular z score. Drawing the correct graph and shaded area is very helpful in learning this concept. Practice finding some areas (probabilities) for various z scores. Again remind students that these areas will be from the mean to the particular z score. Drawing the correct graph and shaded area is very helpful in learning this concept.45.Example: If a data reader has an average (mean) reading of 0 units and a standard deviation of 1 unit and if one data reader is randomly selected, find the probability that it gives a reading between 0 and 1.58 units. That is 44.29% of the readings between 0 and 1.58 degrees. Another interpretation that will be important to discuss. Another interpretation that will be important to discuss.46.Central Limit Theorem 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation ?. 2. Samples all of the same size n are randomly selected from the population of x values. page 257 of textpage 257 of text47.Central Limit Theorem48.Practical Rules Commonly Used: 1. For samples of size n larger than 30, the distribution of the sample means can be approximated reasonably well by a normal distribution. The approximation gets better as the sample size n becomes larger. 2. If the original population is itself normally distributed, then the sample means will be normally distributed for any sample size n (not just the values of n larger than 30).49.REGRESSION - CORRELATION50.Objectives Relationship between two or more variables Scatter diagrams Regression analysis Method of least squares51.Regression Definition Regression Equation page 525 of textpage 525 of text52.Regression Definition Regression Equation53.The Regression Equation x is the independent variable (predictor variable)54.Notation for Regression Equation y-intercept of regression equation ?0 b0 Slope of regression equation ?1 b1 Equation of the regression line y = ?0 + ?1 x y = b0 + b155.Assumptions 1. We are investigating only linear relationships. 2. For each x value, y is a random variable having a normal (bell-shaped) distribution. All of these y distributions have the same variance. Also, for a given value of x, the distribution of y-values has a mean that lies on the regression line. (Results are not seriously affected if departures from normal distributions and equal variances are not too extreme.)56.Definition Correlation exists between two variables when one of them is related to the other in some way57.Assumptions 1. The sample of paired data (x,y) is a random sample. 2. The pairs of (x,y) data have a bivariate normal distribution. page 507 of text Explain to students the difference between the paired data of this chapter and the investigation of two groups of data in Chapter 8. page 507 of text Explain to students the difference between the paired data of this chapter and the investigation of two groups of data in Chapter 8.58.Definition Scatterplot (or scatter diagram) is a graph in which the paired (x,y) sample data are plotted with a horizontal x axis and a vertical y axis. Each individual (x,y) pair is plotted as a single point. Relate a scatter plot to the algebraic plotting of number pairs (x,y). Relate a scatter plot to the algebraic plotting of number pairs (x,y).59.Positive Linear Correlation page 508 of textpage 508 of text60.Negative Linear Correlation61.No Linear Correlation Emphasize that graph (h) does have a correlation - just not linear. Other types of correlation, such as (h), will be briefly discussed in Section 9-6. Emphasize that graph (h) does have a correlation - just not linear. Other types of correlation, such as (h), will be briefly discussed in Section 9-6.62.TIME SERIES63.Objectives Understanding four components of time series Compute seasonal indices Regression based techniques64.Time series Group of data or statistical information accumulated at regular intervals65.Variations in Time series Secular trend A persistent trend in a single direction. A market movement over the long term which does not reflect cyclical seasonal or technical factors. Cyclical fluctuation The term business cycle or economic cycle refers to the fluctuations of economic activity (business fluctuations) around its long-term growth trend. The cycle involves shifts over time between periods of relatively rapid growth of output (recovery and prosperity), and periods of relative stagnation or decline (contraction or recession). Seasonal variation Pattern of change within a year Irregular variation Unpredictable, changing in a random manner66.Trend analysis To describe historical patterns Past trends will help us project future67.LINEAR PROGRAMMING68.Objectives Understanding Linear programming basics Graphic and Simplex methods69.Linear Programming Problem formulation if All equations are linear Constraints are known and deterministic Variables should have non negative values Decision values are also divisible70.Types of LP problems Maximisation Minimisation Transportation Decision making