JEM034 Corporate Finance Winter Semester 2017/2018 Lecture #2 Olga Bychkova
Topics Covered Today Review of key finance concepts Valuation of stocks (chapter 4 in BMA) NPV and other investment criteria (chapter 5 in BMA)
Valuing Stocks: Topics Covered How Common Stocks Are Traded How Common Stocks Are Valued Estimating the Cost of Equity Capital The Link Between Stock Price and Earnings per Share Valuing a Business by Discounted Cash Flow
How Common Stocks Are Traded Primary market market for the sale of new securities by corporations. Secondary market market in which previously issued securities are traded among investors. Common stock ownership shares in a publicly held corporation. Exchange-traded funds (ETFs) portfolios of stocks that can be bought or sold in a single trade.
How Common Stocks Are Valued The value of any stock is the present value of its future cash flows. This reflects the DCF formula. Dividends represent the future cash flows of the firm. Discounted cash flow of comparables? Book value net worth of the firm according to the balance sheet. Dividend periodic cash distribution from the firm to the shareholders. P/E ratio price per share divided by earnings per share. Market value balance sheet financial statement that uses market value of assets and liabilities.
Balance Sheet and the Financial View of the Firm Financial View of the Firm
How Common Stocks Are Valued The cash payoff to owners of common stocks comes in two forms: 1. cash dividends and 2. capital gains or losses. Expected return (market capitalization rate) the rate of return that investors expect from a share over the next year. where Expected return = r = DIV 1 + P 1 P 0 P 0, P 0 the current price of a share, P 1 the expected price at the end of a year, DIV 1 the expected dividend per share.
How Common Stocks Are Valued Example: If Fledgling Electronics is selling for $100 per share today and is expected to sell for $110 one year from now, what is the expected return if the dividend one year from now is forecasted to be $5? Expected return = r = 5 + 110 100 100 = 0.15 or 15%.
How Common Stocks Are Valued The price of any share of stock can be thought of as the present value of the future cash flows. For a stock the future cash flows are dividends and the ultimate sales price of the stock. Price = P 0 = DIV 1 + P 1 1 + r Example: Fledgling Electronics price can be thought of as follows: Price = P 0 = 5 + 110 1 + 0.15 = $100.
How Common Stocks Are Valued Dividend discount model computation of today s stock price which states that share value equals the present value of all expected future dividends. P 0 = DIV 1 1 + r + DIV 2 (1 + r) 2 +... + DIV H + P H (1 + r) H = = H t=1 DIV t (1 + r) t + P H (1 + r) H, where H is a time horizon for your investment.
How Common Stocks Are Valued Example #1: Fledgling Electronics is forecasted to pay a $5 dividend at the end of year one and a $5.5 dividend at the end of year two. At the end of the second year the stock will be sold for $121. If the discount rate is 15%, what is the price of the stock? P 0 = 5 5.5 + 121 + 1 + 0.15 (1 + 0.15) 2 = $100. Example #2: Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.5 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return? P 0 = 3 1 + 0.12 + 3.24 3.5 + 94.48 + (1 + 0.12) 2 (1 + 0.12) 3 = $75.
How Common Stocks Are Valued Suppose we forecast a constant growth rate for a company s dividends. This does not preclude year-to-year deviations from the trend: It means only that expected dividends grow at a constant rate. Such an investment would be just another example of the growing perpetuity. P 0 = DIV 1 r g r = DIV 1 +g market capitalization rate (cost of equity capital) P 0
DCF Valuation with Varying Growth Rates Example: Phoenix produces dividends in three consecutive years of 0, 0.31, and 0.65, respectively. The dividend in year four is estimated to be 0.67 and should grow in perpetuity at 4%. Given a discount rate of 10%, what is the price of the stock? P 0 = DIV 1 1 + r + DIV 2 (1 + r) 2 +... + DIV H (1 + r) H + P H (1 + r) H, where P H = DIV H+1 r g P 0 = 0 1 + 0.1 + 0.31 (1 + 0.1) 2 + 0.65 (1 + 0.1) 3 + 1 (1 + 0.1) 3 0.67 0.1 0.04 = 9.13
Estimating the Cost of Equity Capital: Return Measurements Dividend yield = DIV 1 P 0 Expected return = r = DIV 1 P 0 + g Return on equity = ROE = EPS Book equity per share
Stock Price and Earnings Per Share If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher. Payout ratio fraction of earnings paid out as dividends. Payout ratio = DIV EPS Plowback ratio fraction of earnings retained by the firm. Plowback ratio = 1 payout ratio = 1 DIV EPS
Estimating the Cost of Equity Capital Dividend growth rate can also be derived from applying the return on equity to the percentage of earnings plowed back into operations. g = return on equity plowback ratio sustainable growth rate
Stock Price and Earnings Per Share Example: Our company forecasts to pay a $8.33 dividend next year, which represents 100% of its earnings. This will provide investors with a 15% expected return. Instead, we decide to plowback 40% of the earnings at the firm s current return on equity of 25%. In this situation, the company forecasts to pay a $5 dividend next year. What is the value of the stock before and after the plowback decision? No growth: P 0 = 8.33 0.15 = $55.56. With growth: g = 0.25 0.4 = 0.1, P 0 = 5 0.15 0.1 = $100.
Stock Price and Earnings Per Share Present value of growth opportunities (PVGO) net present value of a firm s future investments. Example: If the company did not plowback some earnings, the stock price would remain at $55.56. With the plowback, the price rose to $100. The difference between these two numbers is the PVGO: PVGO = 100 55.56 = $44.44 Thus, P 0 = EPS 1 r + PVGO.
Valuing a Business Free cash flow (FCF) is the amount of cash that a firm can pay out to investors after paying for all investments necessary for growth. The value of a business is usually computed as the discounted value of free cash flows out to a valuation horizon (H), plus the forecasted value of the business at the horizon, also discounted back to present value. The valuation horizon is sometimes called the terminal value and is calculated like PVGO. PV = FCF 1 1 + r + FCF 2 (1 + r) 2 +... + FCF H PV H (1 + r) H + (1 + r) H }{{}}{{} PV(free cash flows) PV(horizon value)
Valuing a Business Example: Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows (up to year 6), PV(horizon value), and the total value of the firm. r = 10% and g = 6% starting from year 7. PV (FCF ) = 0.8 1.1 + 0.96 1.1 2 + 1.15 1.1 3 + 1.39 1.1 4 + 0.2 1.1 5 + 0.23 1.1 6 = 3.6 PV (horizon value) = 1 1.1 6 1.59 0.1 0.06 = 22.4 PV (business) = PV (FCF )+PV (horizon value) = 3.6+22.4 = 18.8
But how much are the shares worth? George s first instinct is to look at the firm s balance sheet, which shows that the book value of the equity is $26.34 million, or $13.17 per share. A share price of $13.17 would put the stock on a P /E ratio of 6.6. That is quite a bit lower than the 13.1 P /E ratio of Reeby s larger rival, Molly Sports. Stocks: Reeby Sports Mini-Case, Chapter 4 of BMA Textbook Ten years ago, in 2001, George Reeby founded a small mail-order company selling high-quality sports equipment. Since those early days Reeby Sports has grown steadily and been consistently profitable. The company has issued 2 million shares, all of which are owned by George Reeby and his five children. For some months George has been wondering whether the time has come to take the company public. This would allow him to cash in on part of his investment and would make it easier for the firm to raise capital should it wish to expand in the future.
Stocks: Reeby Sports Mini-Case, Chapter 4 of BMA Textbook George suspects that book value is not necessarily a good guide to a share s market value. He thinks of his daughter Jenny, who works in an investment bank. She would undoubtedly know what the shares are worth. He decides to phone her after she finishes work that evening at 9 o clock or before she starts the next day at 6 a.m. Before phoning, George jots down some basic data on the company s profitability. After recovering from its early losses, the company has earned a return that is higher than its estimated 10% cost of capital. George is fairly confident that the company could continue to grow fairly steadily for the next six to eight years. In fact he feels that the company s growth has been somewhat held back in the last few years by the demands from two of the children for the company to make large dividend payments. Perhaps, if the company went public, it could hold back on dividends and plow more money back into the business.
Stocks: Reeby Sports Mini-Case, Chapter 4 of BMA Textbook There are some clouds on the horizon. Competition is increasing and only that morning Molly Sports announced plans to form a mail-order division. George is worried that beyond the next six or so years it might become difficult to find worthwhile investment opportunities. George realizes that Jenny will need to know much more about the prospects for the business before she can put a final figure on the value of Reeby Sports, but he hopes that the information is sufficient for her to give a preliminary indication of the value of the shares.
Stocks: Reeby Sports Mini-Case, Chapter 4 of BMA Textbook 1. Help Jenny to forecast dividend payments for Reeby Sports and to estimate the value of the stock. You do not need to provide a single figure. For example, you may wish to calculate two figures, one on the assumption that the opportunity for further profitable investment is reduced in year 6 and another on the assumption that it is reduced in year 8. 2. How much of your estimate of the value of Reeby s stock comes from the present value of growth opportunities?
Stocks: Reeby Sports Mini-Case, Chapter 4 of BMA Textbook
Stocks: Reeby Sports Mini-Case, Chapter 4 of BMA Textbook Earnings per share (EPS) = return on equity (ROE) starting book value per share (BVPS). EPS is divided between dividends and retained earnings, depending on the dividend payout ratio. BVPS grows as retained earnings are reinvested. The keys to Reeby Sports future value and growth are profitability (ROE) and the reinvestment of retained earnings. Retained earnings are determined by dividend payout. The spreadsheet sets ROE at 15% for the five years from 2012 to 2016. If Reeby Sports will lose its competitive edge by 2017, then it cannot continue earning more than its 10% cost of capital. Therefore ROE is reduced to 10% starting in 2017.
Stocks: Reeby Sports Mini-Case, Chapter 4 of BMA Textbook The payout ratio is set at 0.3 from 2012 onwards. The long-term growth rate, which settles in between 2017 and 2018, is ROE (1 dividend payout ratio) = 0.1 (1 0.3) = 0.07. To calculate share value, we have to estimate a horizon value at 2016 and add its PV to the PV of dividends from 2011 to 2016. Using the constant-growth DCF formula, PV H = 0.71 0.1 0.07 = $23.72. The PV of dividends from 2011 to 2016 is $3.43 at the start of 2011, so share value in 2011 is: PV = 3.43 + 23.72 1.1 6 = $16.82.
Stocks: Reeby Sports Mini-Case, Chapter 4 of BMA Textbook How much of Reeby Sports 2011 value is due to PVGO? You can check by setting ROE = 0.1 for 2012-2016 as well as 2017-2018. You should get PV = $13.82. Thus PVGO = 16.82 13.82 = $3 per share for investments made in 2011 and in later years.
NPV and Other Investment Criteria: Topics Covered The Payback Period Internal Rate of Return Choosing Capital Investments When Resources Are Limited
CFO Decision Tools Survey Data on CFO Use of Investment Evaluation Techniques
Book Rate of Return Book rate of return average income divided by average book value over project life. Also called accounting rate of return. Book rate of return = book income book assets Managers rarely use this measurement to make decisions. The components reflect tax and accounting figures, not market values or cash flows.
Payback The payback period of a project is the number of years it takes before the cumulative forecasted cash flow equals the initial outlay. The payback rule says only accept projects that payback in the desired time frame. This method is flawed, primarily because it ignores later year cash flows and the present value of future cash flows.
Payback Example: Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less. Payback Project C 0 C 1 C 2 C 3 period NPV at 10% A -2,000 500 500 5,000 3 2,624 B -2,000 500 1,800 0 2-58 C -2,000 1,800 500 0 2 50
Internal Rate of Return: Return That Makes NPV = 0
Internal Rate of Return Example: You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment? NPV = 4, 000 + 2, 000 1 + IRR IRR = 28.08% + 4, 000 (1 + IRR) 2 = 0
The Internal Rate of Return Rule The internal rate of return rule is to accept an investment project if the opportunity cost of capital is less than the internal rate of return. The rule will give the same answer as the net present value rule whenever the NPV of a project is a smoothly declining function of the discount rate.
IRR: Pitfall 1 Lending or Borrowing/Special Types of Projects? With some cash flows the NPV of the project increases as the discount rate increases. This is contrary to the normal relationship between NPV and discount rates.
IRR: Pitfall 2 Multiple Rates of Return Certain cash flows can generate NPV = 0 at two different discount rates. Consider payoffs from the following mining project in Australia:
IRR: Pitfall 2 Multiple Rates of Return The cash flows generate NPV = $A0.253 million at 10% discount rate and have both IRR of 3.5% and 19.54%. There can be as many internal rates of return for a project as there are changes in the sign of the cash flows.
Modified Internal Rate of Return Challenge question: can we modify IRR calculation in this case to get only one IRR? Companies sometimes get around the problem of multiple rates of return by discounting the later cash flows back at the cost of capital until there remains only one change in the sign of the cash flows. A modified internal rate of return (MIRR) can then be calculated on this revised series. In our example, the MIRR is calculated as follows: 1. Calculate the present value in year 5 of all the subsequent cash flows: PV in year 5 = 1 1.1 + 1 1.1 2 + 1 1.1 3 + 1 1.1 4 6.5 1.1 5 = 0.866.
Modified Internal Rate of Return 2. Add to the year 5 cash flow the present value of subsequent cash flows: C 5 + PV (subsequent cash flows) = 1 0.866 = 0.134. 3. Since there is now only one change in the sign of the cash flows, the revised series has a unique rate of return, which is 13.7%: NPV = 3 + 1 1.137 + 1 1.137 2 + 1 1.137 3 + 1 1.137 4 + 0.134 1.137 5 = 0. Since the MIRR of 13.7% is greater than the cost of capital (and the initial cash flow is negative), the project has a positive NPV when valued at the cost of capital.
IRR: Pitfall 2 Multiple Rates of Return It is possible to have a zero/non-existent IRR and a positive NPV.
IRR: Pitfall 3 Mutually Exclusive Projects IRR ignores the magnitude of the project. The following two projects illustrate that problem.
IRR: Pitfall 3 Mutually Exclusive Projects
IRR: Pitfall 4 What Happens When There is More than One Opportunity Cost of Capital Term structure assumption: We assume that discount rates are stable during the term of the project. This assumption implies that all funds are reinvested at the IRR. This is a false assumption.
Capital Rationing Capital rationing limit set on the amount of funds available for investment. Soft rationing limits on available funds imposed by management. Hard rationing limits on available funds imposed by the unavailability of funds in the capital market.
Profitability Index When resources are limited, the profitability index (PI) provides a tool for selecting among various project combinations and alternatives. A set of limited resources and projects can yield various combinations. The highest weighted average PI can indicate which projects to select.
Profitability Index Example #1: Profitability index = NPV Investment
Profitability Index Example #2: We only have $300,000 to invest. Which do we select? Project NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08 Select projects with highest Weighted Average PI: WAPI(BD) = 1.13 WAPI(A) = 1.15 WAPI(BC) = 1.13 125, 000 150, 000 + 1.08 300, 000 300, 000 = 1.01 200, 000 300, 000 = 0.77 125, 000 175, 000 + 1.11 300, 000 300, 000 = 1.12
NPV and Other Investment Criteria: Problem 8, Chapter 5 of BMA Textbook Consider the following projects: (a) If the opportunity cost of capital is 10%, which projects have positive NPV? (b) Calculate the payback period for each project. (c) Which project(s) would a firm using the payback rule accept if the cutoff period were three years? (d) Calculate the discounted payback period for each project. (e) Which project(s) would a firm using the discounted payback rule accept if the cutoff period were three years?
NPV and Other Investment Criteria: Problem 8, Chapter 5 of BMA Textbook (a) + $1, 000 NPV A = $1, 000 + = $90.91. 1.1 NPV B = $2, 000 + $1, 000 $1, 000 $4, 000 $1, 000 $1, 000 + 1.1 1.1 2 + 1.1 3 + 1.1 4 + 1.1 5 = $4, 044.73. NPV C = $3, 000+ (b) Payback A = 1 year. Payback B = 2 years. Payback C = 4 years. (c) A and B $1, 000 1.1 +$1, 000 1.1 000 000 +$1, +$1, 2 1.14 1.1 5 = $39.47.
NPV and Other Investment Criteria: Problem 8, Chapter 5 of BMA Textbook (d) PV A = $1, 000 1.1 = $909.09. The present value of the cash inflows for Project A never recovers the initial outlay for the project, which is always the case for a negative NPV project.
NPV and Other Investment Criteria: Problem 8, Chapter 5 of BMA Textbook The present values of the cash inflows for Project B are shown in the third row of the table below, and the cumulative net present values are shown in the fourth row: C 0 C 1 C 2 C 3 C 4 C 5-2,000 1,000 1,000 4,000 1,000 1,000-2,000 909.09 826.45 3,005.26 683.01 620.92-1,090.91-264.46 2,740.8 3,423.81 4,044.73 Since the cumulative NPV turns positive between year two and year three, the discounted payback period is: 2 + 264.46 = 2.09 years. 3, 005.26
NPV and Other Investment Criteria: Problem 8, Chapter 5 of BMA Textbook The present values of the cash inflows for Project C are shown in the third row of the table below, and the cumulative net present values are shown in the fourth row: C 0 C 1 C 2 C 3 C 4 C 5-3,000 1,000 1,000 0 1,000 1,000-3,000 909.09 826.45 0 683.01 620.92-2,090.91-1,264.46-1,264.46-581.45 39.47 Since the cumulative NPV turns positive between year four and year five, the discounted payback period is: 4 + 581.45 = 4.94 years. 620.92
NPV and Other Investment Criteria: Problem 8, Chapter 5 of BMA Textbook (e) Using the discounted payback period rule with a cutoff of three years, the firm would accept only Project B.