CMA Accelerated Program MODULE 3. Financial Management and Management Accounting 1

Transcription

1 CMA Accelerated Program MODULE 3 Financial Management and Management Accounting 1

2 Table of Contents Financial Management 1. Scope and Environment of Financial Management 3 2. Valuation Financial Planning and Dividend Policy Decisions Special Topics in Corporate Finance Problems with Solutions 53 Management Accounting 1 1. Role of the Management Accountant Cost Classifications Job Order Costing Process Costing and Spoilage Cost Behaviour Activity Based Costing Service Department Cost Allocations Joint and By-Product Costing Cost-Volume-Profit Analysis Pricing Budgeting 426 Page 2 CMA Ontario, 2011

3 FINANCIAL MANAGEMENT 1. Scope and Environment of Financial Management Introduction The financial manager is an intermediary between investors (the market) and the firm's need for financing. Financial managers typically make two major types of decisions: financing decisions relate to generating funds and managing the liabilities/equity side of the balance sheet while investing decisions are concerned with the allocation of funds and the asset side of the balance sheet. In large part, investing decisions are dealt with through the capital budgeting model that will be addressed in Lesson 18 of this course. The major emphasis in this lesson, therefore, will be on financing decisions. The financial manager must understand how wealth is created and measured. This requires an understanding of how financial assets are valued and how the value of productive assets are measured. Also required is a thorough understanding of the time value of money, uncertainty, taxation, and capital markets. It is generally assumed that the overall goal of all financial management decisions is to maximize shareholder wealth. While at first this may seem to be relatively straightforward, in reality the maximization of shareholder wealth is highly dependent on assumptions which are made regarding the timing, risk and expected value of future earnings. Finally, it must be noted that finance is a living discipline that is constantly undergoing refinement. There is much discussion on the part of financial experts regarding many of the theoretical issues discussed in this lesson. Although definitive answers to many questions may not be possible, the theories discussed will help illustrate the issues that financial managers must deal with and identify approaches for problem solving. This lesson attempts to cover a fairly wide spectrum of material that would ordinarily cover 600 or so pages in a textbook. Consequently, the discussion is abridged and aimed at addressing the main concepts. Students wishing to develop a more in-depth understanding of the topic are encouraged to refer to an introductory Corporate Finance textbook. a. Objectives of Financial Management As stated above, the objective of financial management is the maximization of shareholder wealth. In order to measure shareholder wealth, we must be able to measure the size of future cash flows, when these cash flows are expected to be received and the Page 3 CMA Ontario, 2011

4 amount of risk or uncertainty that is involved. Note that the emphasis is on cash flows not income flows; financial management is concerned with the long-term flow of resources and, therefore, need not restrict itself to accounting measures of income based on generally accepted accounting principles. Essentially managers maximize shareholder wealth (and by definition, maximize firm value) by making the following three decisions: 1. The Investment Decision - investing in projects that yield a return greater than the minimum acceptable return, 2. The Financing Decision - choosing a financing mix that will maximize the value of the firm and that will match the assets being financed, and 3. The Dividend Decision - if there are not enough investments that meet the Investment Decision criteria, returning the cash to the shareholders. b. The Canadian Financial System The Canadian financial market is comprised of participants and conventions that govern the exchange of financial assets. The market functions to: expedite the allocation of funds from surplus units (those with excess funds) to deficit units (those that need more funds than they presently have), provide a system where exchanges of resources can be performed efficiently, increase the liquidity of non-monetary instruments, facilitate the implementation of monetary policy, and provide a means of placing a value on financial assets. The term financial market is generally used to denote the total market for financial instruments. This market can then be subdivided into the primary and secondary markets. The primary market is the usual place where instruments are sold to provide funds for investments in plant and equipment. It is also where a firm selling a bond or share issue would offer its securities for sale. The primary market is comprised of both public offerings and private placements of securities. The secondary market deals with previously issued securities. The purchase or sale of existing shares on the Toronto Stock Exchange (TSE) is an example of trading in the secondary market. The importance of the secondary market cannot be stressed enough as it brings together buyers and sellers in an efficient setting. Without the secondary market, the liquidity of most financial instruments would decline substantially; who, for example, would want to invest in 20- year bonds or buy shares in a corporation if they knew that they could not sell these securities when they needed cash resources? Page 4 CMA Ontario, 2011

5 A second method of looking at the financial market is to classify investments based on the average length of time from initial investment to maturity. Generally, we think of the money market as encompassing short-term securities, such as treasury bills, commercial paper and certificates of deposit. Treasury bills (or T-bills), for example, are sold by the government through the Bank of Canada and are highly liquid (easily convertible to cash without significant loss). The terms capital market and bond market refer to instruments which are long-term in nature such as stock and bonds. In order to facilitate the functions of the markets, various financial intermediaries exist to bring together borrowers and suppliers of funds. The major financial intermediaries or institutions in Canada include: banks and trust companies, insurance companies and pension funds, investment brokers, and financial cooperatives. c. Agency Theory There are basically two agency relationships that matter to corporate finance: the relationship between managers and shareholders and the relationship between managers and creditors. We will limit our discussion in this section to the agency relationship between managers and shareholders. The agency relationship between managers and creditors will be discussed in Section 3 of these notes. The basic assumption we make is that shareholders, by virtue of their capacity to hire and fire managers and to design their compensation packages, exercise control over the managers. In return, managers consider the maximization of shareholder wealth as their primary objective in making decisions, even if it conflicts with other objectives managers may have. This assumption is subject to debate. Three major types of potential conflict can occur: 1. Managers may use corporate resources to provide themselves with 'perks' or to embark upon expansions (empire-building) that are not in the shareholders' best interests. 2. Managers may have shorter time horizons than shareholders. For example, managers may make decisions that increase short-run profitability at the expense of maximizing firm. 3. Managers and shareholders may have a different evaluation of risk. There are several means available to reduce these potential conflicts: - establish incentive compensation plans that are tied directly to shareholder interests (i.e. maximize firm value), - establish a strong corporate governance model, - monitor managerial effort, and - threat of takeover - firms whose share prices are below potential are much more likely to invite a takeover attempt. Takeovers usually result in the replacement of management. Page 5 CMA Ontario, 2011

6 d. Market Efficiency and the Efficient Market Hypothesis An efficient capital market is defined as one where prices reflect all available information. Technically, in an efficient capital market, an investor purchasing a security will receive a normal return that is commensurate with the risky nature of that security and will not receive any abnormal returns. What makes a market efficient is the level of competition between investors. If a stock is considered to be underpriced, informed investors will buy this stock putting upward pressure on the price until the price reaches an equilibrium where it is neither under- or over-priced. The Efficient Market Hypothesis (EMH) states that it is impossible to obtain abnormal returns consistently with either fundamental or technical analysis. Fundamental analysis is the evaluation of a security's future price movement based upon sales, internal developments, industry trends, the general economy, and expected changes in each factor. Technical analysis is the evaluation of a security's future price based on the sales price and number of shares traded in a series of recent transactions. Technical analysis, when applied to the stock market, attempts to predict future share prices based on the movement of past share prices. Under the EMH, the expected return of each security is equal to the return required by the marginal investor given the risk of the security. Moreover, the price equals its fair value as perceived by investors. In actuality, certain information impacts stock prices more quickly than other information. As such, the EMH has three forms: Strong form efficiency. All public and private information is instantaneously reflected in securities' prices. Thus, insider trading is assumed not to result in abnormal returns. Semi-strong form efficiency. All publicly available data is reflected in security prices, but private or insider data is not immediately reflected. Accordingly, insider trading can result in abnormal returns. Most experts conjecture that it is reasonable to assume that the market is semi strong efficient. Weak form efficiency. Current securities prices reflect all recent past price movement data, so technical analysis will not provide a basis for abnormal returns in securities trading. Some implications of market efficiency: changing accounting policies that increase income will have no impact on share prices managers cannot time the issue of securities, (i.e. the market will always price the securities correctly). large blocks of stock can be purchased and sold without affecting the price Page 6 CMA Ontario, 2011

7 e. Interest Rates An interest rate is a price, and like all prices it is determined by the laws of supply and demand (see Figure 1). Unfortunately, the market that determines interest rates is very complex, resulting in various theories regarding how interest rates are determined. Included in the list of complicating factors are inflationary forces and a host of risk factors, including maturity risk, default risk and foreign exchange risk. Interest % Supply of Money Nominal Rate Demand for Money Supply = Demand Amount of Money Available Figure 1: Supply and Demand for Money and Interest Rates Maturity risk refers to the duration of the investment. The longer that funds will be locked into the security, the greater is the risk that interest rates will change significantly over the life of the investment. Default risk measures the likelihood that the borrower may become unable to meet the terms of the investment agreement. Exchange rate risk deals with the chance that the real return will change due to fluctuations in the foreign exchange rate between two or more countries. As a general rule, one can describe the interest rate that will prevail in any situation as follows: Nominal Rate = real rate + expected rate + risk of Interest of interest of inflation premium It is important to note two things at this point. First, the expected rate of inflation is built into the interest rate that is quoted on the market. If the real rate of interest is 4% and the Canadian government sells T-bills to yield a return of 9%, it is reasonable to assume that the expected rate of inflation must be in the neighborhood of 5% because the risk premium is likely close to zero (there is little chance that the federal government will not pay the stated interest and principle at maturity). In fact, most financial analysts refer to the return on federal government T-bills as being the risk-free rate. Secondly, the greater the risk that is associated with a particular investment, the greater will be the required rate of return. As an investor, we would desire a higher return from a Page 7 CMA Ontario, 2011

8 speculative gold mining stock than from an investment in federal T-bills. This fact is one of the fundamental rules by which financial management decisions are governed. The risk premium is generally comprised of the following: the default risk premium the risk that the issuer of the security will default on either the interest payments or the repayment of principal. It is generally assumed that debt issued by governments has a default risk premium of zero, the maturity risk premium the longer the maturity, the higher the risk, and the liquidity risk premium if the security can be sold promptly, then the liquidity risk premium is very low or close to zero. Note that for short term securities that are subject only to inflation risk, the relationship between real and nominal rates of return are governed by the Fisher effect: (1 + i) = (1 + r)(1 + π) where i = nominal (i.e. observed) interest rates r = real rate of return π = expected inflation rate The term structure of interest rates An interest rate curve can be obtained by graphing the interest rates (y-axis) vs. the maturities (x-axis) for debt securities of similar risk. The curve obtained is called the term structure of interest rates. More often than not, interest rates increase with maturity (due to the maturity risk premium). There are much less frequent periods when the reverse is true and the term structure is downward sloping. It will be downward sloping when investors expect interest rates to go down. The rationale for an upwards sloping yield curve is that, all else being equal, longer maturities are riskier. Much of this risk depends on inflation expectations, which are an important determinant of interest rates. This is the basis for the idea that the term structure should usually be upward-sloping. Page 8 CMA Ontario, 2011

9 f. Measurement of Risk In its simplest terms, risk is the chance that things won't turn out as expected; in other words, the return may be more or less than expected. The measurement of risk can be objectively or subjectively. In its subjective state, we see statements about organizations or individuals as being risk averse. As you have learned in previous courses, it is generally assumed that all individuals are rational, that is they behave in such a manner as to maximize their satisfaction given income, market opportunities and individual preferences. Note that we do not mean that those who are risk averse are not rational; it means only that those who are risk averse will behave in a manner consistent with that risk aversion. Risk can also be measured objectively by determining the variance of the probability distribution of expected returns from a certain investment. The greater the variance, the greater is the degree of uncertainty in the return or, in other words, the greater the risk. For example, look carefully at the expected returns for stocks A and B in Figure 2. The risk associated with Stock A is obviously greater than that for Stock B. Probability Probability Expected Return % Expected Return % Stock A Stock B Figure 2: Expected Returns for Stocks A and B If one were to calculate the standard deviation for Stock A and Stock B, one might arrive at figures of approximately 9% and 0.25% respectively (this assumes that the probabilities are 25%, 50% and 25% respectively). The larger number indicates more diversity in the distribution of Stock A's expected returns and thus indicates higher risk. A "blue chip" stock such as Bell Canada would be an example of a low risk stock; stocks in an exploratory oil-drilling venture would represent a high-risk stock. Combining the notions of risk and return, we can conclude that investors considering investing in Stock A would demand a greater expected return in order to compensate for the greater risks involved. Page 9 CMA Ontario, 2011

10 Quantitative Measures of Risk The preferences of an investor in terms of the mean-variance theory can be expressed as follows: Stock A is preferred to Stock B If E(R a ) > E(R b ) And σ a < σ b Where E(R a ) and E(R b ) are the expected returns of stock A and B respectively σ a and σ b are the standard deviations of stock A and B respectively. g. Capital Asset Pricing Model By combining securities or investments from different firms, the investor can reduce the total risk associated with various investments. This notion of risk reduction is commonly referred to as diversification. Financial models can be employed to determine the expected return for a given group of securities (or portfolio) and the degree of risk associated with such an investment strategy. The expected portfolio return is simply the weighted average of the expected returns for the individual stocks. Similarly, the portfolio risk for a two-security portfolio incorporates the risks of both securities and the degree of correlation between them. Correlation refers to the degree to which the expected returns move together. If two securities increase and decrease in value together, they would be positively correlated; if they moved in opposite directions, they would be negatively correlated. Therefore, if an investor purchased one stock that went up when inflation rose and another which went down when inflation rose, the risk associated with holding the two stocks together would likely be less than that which would exist by holding either one individually. Financial analysts use a simple model known as the Capital Asset Pricing Model (CAPM). This model (see Figure 3) shows clearly the relationship between the degree of portfolio risk, the expected return of the portfolio and the risk-free rate of return. The straight line shown on the graph is known as the Security Market Line (SML) and represents various combinations of security investments that will yield a given return for a given level of risk. If an investor acquires a set of investments that matches the proportions of risk-free and risky investments available in the market, we would refer to this as a market portfolio. The expected return from this portfolio is called the market rate of return and is often approximated by the rate of return on a broad-based stock exchange index such as the Toronto Stock Exchange (TSE) 300. Investors may reduce their risk below that which is prevalent on the market by investing in less risky securities, but their returns will fall. Additional returns beyond the market return may be earned by acquiring a higher percentage of risky investments. The main application of the Capital Page 10 CMA Ontario, 2011

11 Asset Pricing Model and portfolio theory to a financial manager is the portrayal of the relationship between risk and return and how diversification can reduce risk. Return % Market Return Security Market Line Risk-Free Rate Market Risk Risk Figure 3: Capital Asset Pricing Model and SML The idea underlying the CAPM can also be extended to individual securities as they exhibit the same relationship between risk and return. Financial analysts are able to determine the risk associated with individual securities by determining the nondiversifiable risk or beta of the security. Note here that some risk is eliminated by the formation of the portfolio (this is known as diversifiable risk ) and the remaining risk (nondiversifiable risk) captures the amount of risk remaining for the security in question. Beta is a measure of the volatility of the returns for a particular investment relative to the market portfolio. The beta of the market-based portfolio is 1.0. Securities which exhibit less volatility than the market have betas of less than 1.0 (for example, Bell Canada and Trans-Canada Pipelines); stocks which are more volatile have betas of greater than 1.0 (for example, Alcan). Furthermore, we can say that if a particular stock has a beta of 1.3 it will rise in value 30% faster than the market when the market rises and fall 30% faster than the market if the market falls. The determination of the beta for a particular security, therefore, can tell us a lot about the relationship between risk and return for that particular investment. The capital asset pricing model can be quantified as follows: E(R e ) = E(R f ) + β [E(R m ) - E(R f )] Where E(R e ) = the expected return of a given common stock E(R f ) = the expected return of a risk free security (usually a longterm government bond) β = the beta of the common stock E(R m ) = the expected return of the market (the TSE 300 is often used as a surrogate for the market return) Page 11 CMA Ontario, 2011

12 The beta value of a firm's stock can generally be calculated by regressing the firm's returns against market returns. 2. Valuation a. Time Value of Money Many financial decisions involve the comparison of a cash outlay now with cash inflows into the future. Because one dollar received now is worth more than one dollar received in the future, future cash flows have to be discounted in order to compare them with today's dollars. This section goes over the mechanics of calculating discounted cash flows. The format for solutions using a financial calculator used throughout this module and other Accelerated program modules is as follows: N I/Y PV PMT FV Enter Compute X In the above example, we are trying the calculate the present value of $1,000 to be received in 5 years from now at an interest rate of 6%. If you are using the Texas Instruments BA II Plus, you need to do the following: - set the calculator to accept one payment per year as follows: 1 2ND N You only need to do this once. - clear the Time Value of Money memory as follows: 2ND FV You should do this every time you do a time value of money calculation. - enter the numbers above in the TVM memory registers - to solve, press CPT and the TVM register you are attempting to solve for, in this case PV - the answer provided is This means that if you were to invest $ today (money out of pocket and therefore the negative sign) and invest it for 5 years at 6% compounded annually, the amount would grow to $1,000. If you are using the Hewlett Packard 10BII, you need to do the following: - set the calculator to accept one payment per year as follows: 1 then Orange Button then PMT You only need to do this once. - clear the Time Value of Money memory as follows: Orange Button C ALL Page 12 CMA Ontario, 2011

13 You should do this every time you do a time value of money calculation. - enter the numbers above in the TVM memory registers - to solve, press the TVM register you are attempting to solve for, in this case PV - the answer provided is This means that if you were to invest $ today (money out of pocket and therefore the negative sign) and invest it for 5 years at 6% compounded annually, the amount would grow to $1,000. Present Value of a Single Sum to be received in the future Say we expect to receive $100,000 in 10 years from now. What is the present value of this sum using a discount rate of 7%, i.e. what is this sum of money worth today? N I/Y PV PMT FV Enter Compute X PV = -50, Present Value of an Annuity Say we expect to receive $1,000 per year for 5 years (to be received at the end of each year). What is the present value of this stream of payments? Assume an interest rate of 8%. PV = -3, N I/Y PV PMT FV Enter Compute X Assume now that you expect to receive $10,000 per year for the next 10 years and a final payment of $100,000 at the end of the 10 th year. Assuming an interest rate of 6%, the present value of these cash flows is $129,440: N I/Y PV PMT FV Enter Compute X If you were to draw a timeline for the above, it would look as follows: ,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10, ,000 Page 13 CMA Ontario, 2011

14 So, unless you tell it otherwise, the financial calculator always assumes that the timing of the cash flows is at the end of the year. Future Value of a single sum invested today Assume you have $1,000 to invest today and want to invest it for 5 years. Assuming a discount rate of 6%, how much will you have accumulated at the end of 5 years. FV = -1, N I/Y PV PMT FV Enter Compute X Future Value of an Annuity Assume now that you are willing to invest $1,000 per year for 5 years, but starting next year. How much will you have accumulated at the end of 5 years? FV = -5, N I/Y PV PMT FV Enter Compute X The difference between an annuity and annuity due Annuities assume that cash flows occur at the end of the year whereas annuities due assume that cash flows are at the beginning of the year. Most financial calculators have the capabilities of dealing with annuities due I would recommend you not use these since the function must be cleared before doing simple annuities and often this is forgotten leading to countless errors. Page 14 CMA Ontario, 2011

15 Uneven Cash Flows Both the TI BA II Plus and the HP 10B allow you to enter cash flows that are uneven. For example, say you are offered an investment with the following cash inflows. You want to calculate the present value of these cash flows at a discount rate of 6%. Time Cash Flow 1 $20, , , , , , ,000 Using the TI BA Plus, you proceed as follows: 1. Press 2 nd RESET ENTER to clear all registers 2. Press CF 3. The first register is for CF 0 the cash flow at time=0. Press 0 and ENTER. 4. Using the and keys, find the register for C01 (the first cash flow), enter and press ENTER. 5. Using the and keys, find the register for C02, enter and press ENTER. 6. Using the and keys, find the register for C03, enter and press ENTER. 7. Because the $40,000 repeats three times, we want to make sure that the frequency for this cash flow reflects this. To do this, using the and keys, find the register for F03, enter 3 and press ENTER. (Note that the frequencies assigned to all cash flows is 1 by default so you only need to enter a frequency if it is other than Using the and keys, find the register for C04, enter and press ENTER. 9. Using the and keys, find the register for F04, enter 2 and press ENTER. 10. Press the NPV key. The calculator will ask for the interest rate. Press 6 and press ENTER. Page 15 CMA Ontario, 2011

16 11. Using the and keys, find the register for NPV= and press CPT. The calculator should give you a present value of $209, Using the HP 10BII, you proceed as follows: 1. Clear all: Orange Button C ALL 2. Enter the cash flow at time = 0: 0 and press CFj 3. Enter the cash flow at t=1: 20,000 and press CFj 4. Enter the cash flow at t=2: 30,000 and press CFj 5. Enter the cash flow at t=3: 40,000 and press CFj You now need to inform the calculator that this cash flow repeats three times: Enter 3 Orange Button Nj 6. Enter the cash flow at t=6: 50,000 and press CFj You now need to inform the calculator that this cash flow repeats twice: Enter 2 Orange Button Nj 7. Enter 6 I/YR 8. Press Orange Button NPV The calculator should give you a present value of $209, Page 16 CMA Ontario, 2011

17 Perpetuities and Growing Perpetuities A perpetuity is an infinite annuity, i.e. a constant cash flow to be received at regular intervals forever. Present value of a perpetuity = PMT 1 r Examples of perpetuities are preferred shares - they have no maturity and pay a fixed annual dividend. For example, if you were to purchase a preferred share that pays a constant dividend of $7.50 per year and you require a 12% rate of return, then the preferred share would have a value of $7.50 / 0.12 = $ A growing perpetuity is a constant cash flow growing at a constant rate at regular intervals forever. The present value of a growing perpetuity is equal to: PMT 1 r g where PMT 1 = next year's payment g = growth rate. For example, a preferred share whose dividend is growing at a rate of 5%, and generates a returns of 10% and will pay a dividend of $10 next year should have a value of: $10 / ( ) = $200 b. General Valuation Model The value of any asset is the discounted value of its expected future cash flows: V 0 = CF 1 (1+ r) + CF 2 (1+ r) CF n (1+ r) n where V 0 = Value of the asset at time 0 CF = cash flow at period 1, 2, n r = discount rate Three things should be noted with regards to this model: 1. only cash flows are relevant 2. past cash flows are irrelevant. It is the expected cash flows that determine the current value of an asset. Page 17 CMA Ontario, 2011

18 3. the discount rate must reflect the asset's underlying risk - the higher the risk, the higher the expected rate of return. c. Valuation of bonds A bond is a long-term obligation for borrowed money. It is a promise to pay interest and to repay the principal on terms specified in a contract called the bond indenture. A typical indenture will usually include the following provisions: the face value of the bond - the amount of money borrowed (usually in denominations of $1,000) the coupon - the amount of stated interest to be paid - usually semi-annually the maturity - the end of the bond life a call provision - gives the issuer the right to redeem the bonds prior to their maturity by paying a call price. A bond's market price will only be equal to its face value when market interest rates are equal to the coupon rate. If the bond pays a coupon rate that is less than the required market rate, the bond will sell at a discount (i.e. less than $1,000) since investors need to be compensated for the difference in interest rates. If the bond pays a coupon rate that is more than the required market rate, the bond will sell at a premium since investors are willing to pay more for a bond that pays higher than required interest. The required market rate is called yield to maturity. This can be shown through the bond valuation formula: Bond Price = P 0 = Present Value of the Coupon Stream (Annuity or PMT) + Present Value of the Face Value (Future Value) Example: suppose a bond has a coupon rate of 8.5%, a remaining maturity of 12 years, and a face value of $1,000. If the yield-to-maturity on this bond is 10%, what is the current price of this bond? The bond pays coupons semi-annually. Coupon = $1,000 x 8.5% / 2 = $42.50 N I/Y PV PMT FV Enter Compute X Bond Price = $ Page 18 CMA Ontario, 2011

19 Computing the Yield to Maturity Example: A bond paying a coupon of 9% with 10 years remaining to maturity sells for $1,223. What is the yield to maturity? N I/Y PV PMT FV Enter Compute X Note that: (1) the present value is entered as a negative on the assumption that we would have to outlay $1,223 to purchase this bond and then receive the coupon payments and face values and (2) the coupon payment is calculated as: $1,000 x 9% / 2 = $45. The yield-to-maturity provided by the calculator is 3% is for a six month. This converts to an annual yield of 3% x 2 = 6%. Interest Rate Risk Whenever the required return of a bond changes, the price of that bond also changes. This is referred to as interest rate risk: the inverse relationship between interest yields and bond prices. When yields increase, bond prices drop. When yields decrease, bond prices increase. This sensitivity is dependent on two things: 1. time to maturity - the lower the time to maturity the lower the interest rate risk 2. coupon rate - the lower the coupon rate the greater the interest rate risk For example - take two bonds with a face value of $1,000 with 10 years to maturity. The current yield to maturity is 8% - the only difference is the coupon rate: Bond A, with a coupon rate of 12%, will sell for $1, (N = 20, i =4%,, PMT = $60, FV = $1,000) Bond B with a coupon rate of of 6% will sell for $ (N = 20, i =4%,, PMT = $30, FV = $1,000) Now, assume that the YTM drops one percentage point to 7%, then the new price of Bond A will be $1, and Bond B will be $ The percentage increase in the price of Bond A is 6.6% and the percentage increase in the price of Bond B is 7.5%. Therefore, Bond B is riskier. Page 19 CMA Ontario, 2011

20 d. Valuation of stocks Using the general valuation model, the valuation of a stock is the present value of future dividends expected to be received over the time the stock is held plus the present value of the proceeds when the stock is sold: P 0 = D 1 (1+ r) + D 2 (1+ r) D n (1+ r) n + P n (1+ r) n where P 0 = the price of a share today D n = dividend to be received at time n P n = the price of a share at time n r = rate of return required by common shareholders Generally, however, we tend to conceptualize the value of a share as being the present value of all future dividends to be received in perpetuity: P 0 = D 1 r If we assume a constant growth rate in dividends, the equation becomes: P 0 = D 1 r g where g is the dividend growth rate and r > g This model is known as the dividend growth model (or the Gordon model). If we rework the above equation, we can solve for the required rate of return: r = D 1 P 0 + g = Dividend Yield + Capital Gain Yield Example 1: A stock currently paid a dividend of $4 which is not expected to change. If investors require a 12% rate of return, what is the selling price of the stock? P 0 = D 1 /r = $4 /.12 = $33.33 Example 2: Assume that PTH Co. just paid a cash dividend of $5.00 per share and that dividends are expected to grow at a rate of 8% per year forever. What is the current market value of a share of PTH Co. stock is the required rate of return is 12%? Page 20 CMA Ontario, 2011