| Stocks | Valuing Common Stocks - Examples and Practice |
| Preferred Stocks | The Constant (Gordon) Growth Model: Cost of Stock (RATE) = (D1 / P ) + g |
| You should know that most companies do not issue preferred stock. | Note: This method ONLY works for stock with dividends that are expected to grow at a constant rate |
| However, you still need to learn how to value it. | The firm's common stock is currently selling for $40 per share. The dividend |
| The good part is that it is very easy to calculate. | expected to be paid at the end of the coming year is $5.07. Its dividend payments have been |
| Because preferred stock receives a fixed periodic dividend - it is calculated like a perpetuity | growing at a constant rate for the last five years. Five years ago, the dividend was $3.45. It is |
| expected that to sell, a new common stock issue must be underpriced at $1 per share and the firm <<<<<<< | Note: Just like the new issue of bonds, when a problem |
| Cost/RATE = Dividend / Price | must pay $1 per share in flotation costs. | gives you costs for a new issue of stock, you will need |
| Price = Dividend / RATE | Calculate the cost (RATE) of the new issue of preferred stock | to subtract the cost from the price of the stock. |
| Common Stock | Common Stock | Computing Growth Rate |
| The value of a share of stock is equal to the PV of all future cash flows (dividends) | Price | $40 | NPER | 5 | Computing the Gordon Growth Model Equation for Yield/Cost/Rate of Stock |
| Shareholders can earn capital gains if they sell their stock for more than the purchase price but, | D1 | $5.07 | RATE | ? | Cost of Stock = (D1 / P ) + g |
| what the stockholder really pays for is the right to all future dividends | g | 8% | PV | -3.45 | (5.07 / 38) + 8% = | 21.34% |
| Stock valuation equations measure stock value at a point in time based on expected risk and return. | Cost/share | $2 | PMT | 0 | Note: You were given the expected dividend (D1) in this problem. |
| The textbook mentions several methods for valuing stock - you need to be aware of all of the various methods | Adj. Price | $38 | FV | 5.07 | The expected or future dividend is used in the formula. |
| However, in the assignments and exams, we will concentrate on the most widely used approach, The Constant-Growth Model | CPT ? | 8.00% | Always read the problem carefully to determine if it gives you the |
| and the Capital Asset Pricing Model (CAPM) | | expected or the current dividend. If you are given the current |
| You can use excel to calculate both models, however there are no excel formulas that do it automatically, so you have to enter the exact equations. | dividend, it will need to be adjusted. (See note below) |
| The constant-growth model is also called the Gordon Growth Model |
| Calculating the Price of the Stock | Calculating the RATE of the stock | The Gordon Growth Model: Current Price of Stock = D1 / (r - g) |
| P0 = D1 / (rs – g) | rs = (D1 / P0) + g | The Bradshaw Company's most recent dividend was $6.75. The historical dividend payment |
| Expected dividend divided by (rate - growth rate) | Expected dividend divided by price plus the growth rate | by the company shows a constant growth rate of 5% per year. |
| If the required rate of return is 8%, what is the price of the stock. |
| In most of the constant-growth model problems, you are not given the growth rate of the dividends - you must calculate that yourself |
| So, before you can work the Gordon Growth Model - you need to calculate the growth rate with the excel RATE formula | Common Stock | Computing the Gordon Growth Model Equation for Value/Price of Stock |
| Once you get the growth rate calculated, you can then work the equation | Price | ? | Price of Stock = D1 / (r - g) |
| One other thing to be aware of is the dividend you are given in the problem | D1 | 6.75 * (1 + g) | = 6.75 * (1 + 5%) / ( 8% - 5%) |
| The gordon growth model uses the Expected Dividend (D1), so if the problem gives you the expected or future dividend then you are good to go | Cost of Stock | 8.00% | = 7.0875 / (3%) |
| However, if the problem gives you the current dividend (D0), then you will need to multiply that by (1 + g) to get the expected dividend (D1) | growth rate | 5.00% | 236.25 |
| Note: You were given the current dividend (D0) in this problem, since you need the expected dividend in the formula, |
| The Capital Asset Pricing Model for valuing stock quantifies the relationship between risk and return | you will needed to multiply the 6.75 by (1 + g) to convert the D0 to D1. |
| When a question gives you the beta of a share of common stock, this is a signal that you will need to use the CAPM equation | |
| Rs = RF + (b * (rm – RF)) Note: The extra parenthesis in this equation are for Excel | The Capital Asset Pricing Model (CAPM) Rs = RF + (b * (rm – RF)) or kp = krf + (km - krf) x b |
| They tell Excel to calculate the Market Risk Premium (rm-RF) first, then multiply by beta, then add the RF | Note: This method is used to calculate the required rate of return of an investment given its degree of risk. |
| Note the part of the formula in the parenthesis: (rm - RF), this is called the Market Risk Premium | Note: The two formulas are the same, just stated a little different. When entering the formula in excel, you will need to add the extra parenthesis so excel knows which |
| The Market Risk Premium (rm - RF) is different from the Market Return (rm) | order to compute the components. |
| The reason I am pointing this out is because sometimes a problem will give you the Market Risk Premium | Assume the risk-free rate is 5%, the expected rate of return on the market is 15%, and the beta of your firm is 1.2. |
| instead of the Return on Market (rm). | Given these conditions, what is the required rate of return on your company's stock? |
| When this happens, you need to know that there is no need to subtract the risk free rate from the market return |
| because this part of the equation has already been calculated for you. | Computing the CAPM |
| Required Rate of Return: Rs = RF + (b * (rm – RF)) |
| = 5% + (1.2 * ( 15% - 5%)) <<<Enter this equation into excel, it will do the rest! |
| = 5% + (1.2 * (10%) |
| = 5% + 12% |
| = 17% |
| |
| Valuing Stocks - Your Turn - Please complete the problem below. |
| A firm has common stock with a market price of $100 per share and an expected dividend of $5.61 per share at the end of the coming year. |
| A new issue of stock is expected to be sold for $98, with $2 per share representing the underpricing necessary in the competitive market. |
| Flotation costs are expected to total $1 per share. Five years ago, the dividend was $4.00. Calculate the cost of the stock. |
| Computing Growth Rate | Common Stock | Gordon Growth Rate Formula |
| NPER (N) | Expected Dividend | Cost of Stock = (D1 / P ) + g |
| RATE (I/Y) | Market Price |
| PV | Fees for new issue |
| PMT | Adjusted Price | 12.78% |
| FV | Growth Rate | 7.00% |
| Compute RATE | 7.00% |
| Note: Cost, Yield, Rate all mean the same thing when computing stock. |
| You are either going to be asked to compute the cost (RATE), or compute the price. (Cost and price are two different things.) |
| Assume the risk-free rate is 8%, a market return of 12%, and a beta of 1.5. |
| Given these conditions, what is the rate of return on this investment? |
| CAPM Inputs | CAPM Formula |
| rF | Rs = RF + (b * (rm – RF)) |
| rM |
| Beta |
| 14.00% |
| Note: Any time a problem mentions a beta, you know to use the CAPM equation instead of the Gordon Growth Model. |
| *The calculations for Preferred Stock are so simple, than I don't feel you need an example and a practice problem for that. |
Maylat15
3ACapitalbudetingandcotofcapital.xlsx
