FINC2011 Tutorial BMA Ch.4 Problems 5, 6, 7, 8, 18, 20, 21, 24, 25, 27 Company Z's earnings and dividends per share are expected to grow indefinitely by 5% a year If next year's dividend is $10 and the market capitalization rate is 8%, what is the current stock price? Answer P0 = 10/(.08 - 05) = $333.33 Company Z-prime is like Z in all respects save one: Its growth will stop after year In year and afterward, it will pay out all earnings as dividends What is Zprime's stock price? Assume next year's EPS is $15 Answer First we must determine the price based on dividends per share for years 1–4 Then, we must account for the growth in earnings per share With next year’s EPS at $15 and EPS growing at 5% per year, the forecasted EPS at year is $15 x (1.05)4 = $18.23 Therefore, the forecasted price per share at year is $18.23/.08 = $227.91 Therefore, the current price is If company Z (see Problem 5) were to distribute all its earnings, it could maintain a level dividend stream of $15 a share How much is the market actually paying per share for growth opportunities? Answer Price = EPS1/r + PVGO Recall that the price = DIV1/(r – g) Therefore, price = $10/(.08 - 05) = $333.333 Therefore, 15/.08 + PVGO = 333.33; therefore PVGO = $145.83 Consider three investors: Page of a Mr Single invests for one year b Ms Double invests for two years c Mrs Triple invests for three years Assume each invests in company Z (see Problem 5) Show that each expects to earn a rate of return of 8% per year Answer With next year’s dividend at $10/share and next year’s price at $350/share (calculated by taking the current year’s price of $333.33 x a 5% growth rate), Z’s forecasted dividends and prices grow as follows: Calculate the expected rates of return: From year to 1: 10 (350 333.33) 08 333.33 From year to 2: 10.50 (367.50 350) 08 350 From year to 3: 11.03 (385.88 367.50) 08 367.50 As shown, all three investors expect an 8% return over their respective one-, two.-, and three-year investments 18 Consider the following three stocks: a Stock A is expected to provide a dividend of $10 a share forever Page of b Stock B is expected to pay a dividend of $5 next year Thereafter, dividend growth is expected to be 4% a year forever c Stock C is expected to pay a dividend of $5 next year Thereafter, dividend growth is expected to be 20% a year for five years (i.e., until year 6) and zero thereafter If the market capitalization rate for each stock is 10%, which stock is the most valuable? What if the capitalization rate is 7%? Answer PA DIV1 $10 $100.00 r 0.10 PB DIV1 $5 $83.33 rg 0.10 04 PC DIV1 DIV2 DIV3 DIV4 DIV5 DIV6 DIV7 1.10 1.10 1.10 1.10 1.10 1.10 0.10 1.106 PC 5.00 6.00 7.20 8.64 10.37 12.44 12.44 $104.50 1.10 1.10 1.10 1.10 1.10 1.10 0.10 1.106 At a capitalization rate of 10%, Stock C is the most valuable For a capitalization rate of 7%, the calculations are similar The results are: PA = $142.86 PB = $166.67 PC = $156.48 Therefore, Stock B is the most valuable at a 7% capitalization rate 20 Company Q's current return on equity (ROE) is 14% It pays out one-half of earnings as cash dividends (payout ratio = 5) Current book value per share is $50 Book value per share will grow as Q reinvests earnings Assume that the ROE and payout ratio stay constant for the next four years After that, competition forces ROE down to 11.5% and the payout ratio increases to 0.8 The cost of capital is 11.5% a What are Q's EPS and dividends next year? How will EPS and dividends grow in years 2, 3, 4, 5, and subsequent years? b What is Q's stock worth per share? How does that value depend on the payout ratio and growth rate after year 4? Answer a Plowback ratio = – payout ratio = 1.0 – 0.5 = 0.5 Page of Dividend growth rate = g= Plowback ratio × ROE = 0.5 × 0.14 = 0.07 Next, compute EPS0 as follows: ROE = EPS0 /Book equity per share 0.14 = EPS0 /$50 EPS0 = $7.00 Therefore: DIV0 = payout ratio × EPS0 = 0.5 × $7.00 = $3.50 EPS and dividends for subsequent years are: Year EPS $7.00 $7.00 × 1.07 = $7.4900 $7.00 × 1.072 = $8.0143 $7.00 × 1.073 = $8.5753 $7.00 × 1.074 = $9.1756 $7.00 × 1.074 × 1.023 = $9.3866 DIV $7.00 × 0.5 = $3.50 $7.4900 × 0.5 = $3.50 × 1.07 = $3.7450 $8.0143 × 0.5 = $3.50 × 1.072 = $4.0072 $8.5753 × 0.5 = $3.50 × 1.073 = $4.2877 $9.1756 × 0.5 = $3.50 × 1.074 = $4.5878 $9.3866 × 0.8 = $7.5093 EPS and dividends for year and subsequent years grow at 2.3% per year, as indicated by the following calculation: Dividend growth rate = g = Plowback ratio × ROE = (1 – 0.08) × 0.115 = 0.023 b P0 DIV3 DIV5 DIV1 DIV2 DIV4 4 1.115 1.115 1.115 1.115 0.115 - 0.023 1.115 3.745 4.007 4.288 4.588 7.5093 $65.453 4 1.115 1.115 1.115 1.115 0.115 - 0.023 1.115 The last term in the above calculation is dependent on the payout ratio and the growth rate after year 21 Each of the following formulas for determining shareholders' required rate of return can be right or wrong depending on the circumstances: For each formula construct a simple numerical example showing that the formula can give wrong answers and explain why the error occurs Then construct another simple numerical example for which the formula gives the right answer Answer Page of a An Incorrect Application Hotshot Semiconductor’s earnings and dividends have grown by 30% per year since the firm’s founding 10 years ago Current stock price is $100, and next year’s dividend is projected at $1.25 Thus: r DIV1 1.25 g 30 3125 31.25% P0 100 This is wrong because the formula assumes perpetual growth; it is not possible for Hotshot to grow at 30% per year forever A Correct Application The formula might be correctly applied to the Old Faithful Railroad, which has been growing at a steady 5% rate for decades Its EPS1 = $10, DIV1 = $5, and P0 = $100 Thus: r DIV1 g 05 0.10 10.0% P0 100 Even here, you should be careful not to blindly project past growth into the future If Old Faithful hauls coal, an energy crisis could turn it into a growth stock b An Incorrect Application Hotshot has current earnings of $5.00 per share Thus: r EPS1 0.05 5.0% P0 100 This is too low to be realistic The reason P0 is so high relative to earnings is not that r is low, but rather that Hotshot is endowed with valuable growth opportunities Suppose PVGO = $60: P0 EPS1 PVGO r 100 60 r Therefore, r = 12.5% A Correct Application Unfortunately, Old Faithful has run out of valuable growth opportunities Since PVGO = 0: P0 EPS1 PVGO r 100 10 0 r Therefore, r = 10.0% 24 Compost Science, Inc (CSI), is in the business of converting Boston's sewage sludge into fertilizer The business is not in itself very profitable However, to Page of induce CSI to remain in business, the Metropolitan District Commission (MDC) has agreed to pay whatever amount is necessary to yield CSI a 10% book return on equity At the end of the year CSI is expected to pay a $4 dividend It has been reinvesting 40% of earnings and growing at 4% a year a Suppose CSI continues on this growth trend What is the expected long-run rate of return from purchasing the stock at $100? What part of the $100 price is attributable to the present value of growth opportunities? b Now the MDC announces a plan for CSI to treat Cambridge sewage CSI's plant will, therefore, be expanded gradually over five years This means that CSI will have to reinvest 80% of its earnings for five years Starting in year 6, however, it will again be able to pay out 60% of earnings What will be CSI's stock price once this announcement is made and its consequences for CSI are known? Answer a Here we can apply the standard growing perpetuity formula with DIV1 = $4, g = 0.04 and P0 = $100: r DIV1 $4 g 04 08 8.0% P0 $100 The $4 dividend is 60% of earnings Thus: EPS1 = 4/0.6 = $6.67 Also: P0 EPS1 PVGO r $100 $6.67 PVGO 0.08 PVGO = $16.63 b DIV1 will decrease to: 0.20 6.67 = $1.33 However, by plowing back 80% of earnings, CSI will grow by 8% per year for five years Thus: Year DIVt 1.33 1.44 1.56 1.68 1.81 5.88 EPSt 6.67 7.20 7.78 8.40 9.07 9.80 7, Continued growth at 4% Note that DIV6 increases sharply as the firm switches back to a 60% payout policy in year 6, from a $1.81 dividend to a $5.88 dividend Forecasted stock price in year is: P5 DIV6 5.88 $147 r g 0.08 04 Page of Therefore, CSI’s stock price will increase to: P0 1.33 1.44 1.56 1.68 1.81 147 $106.22 1.08 1.08 1.08 1.08 1.08 25 Permian Partners (PP) produces from aging oil fields in west Texas Production is 1.8 million barrels per year in 2013, but production is declining at 7% per year for the foreseeable future Costs of production, transportation, and administration add up to $25 per barrel The average oil price was $65 per barrel in 2013 PP has million shares outstanding The cost of capital is 9% All of PP's net income is distributed as dividends For simplicity, assume that the company will stay in business forever and that costs per barrel are constant at $25 Also, ignore taxes a What is the PV of a PP share? Assume that oil prices are expected to fall to $60 per barrel in 2014, $55 per barrel in 2015, and $50 per barrel in 2016 After 2016, assume a long-term trend of oil-price increases at 5% per year b What is PP's EPS/P ratio and why is it not equal to the 9% cost of capital? Answer a First, we use the following Excel spreadsheet to compute net income (or dividends) for 2013 through 2017: Production (million barrels) Price of oil/barrel ($) Costs per barrel ($) 2013 1.8000 65 25 2014 1.6740 60 25 Revenue Expenses Net Income (= Dividends) 117,000,000 45,000,000 72,000,000 100,440,000 41,850,000 58,590,000 2015 1.5568 55 25 85,625,100 38,920,500 46,704,600 2016 1.4478 50 25 2017 1.3465 52.5 25 72,392,130 36,196,065 36,196,065 70,690,915 33,662,340 37,028,574 Next, we compute the present value of the dividends to be paid in 2014, 2015, and 2016: P0 58,590,000 46,704,600 36,196,065 $121,012,624 1.09 1.092 1.093 The present value of dividends to be paid in 2017 and subsequent years can be computed by recognizing that both revenues and expenses can be treated as growing perpetuities Since production will decrease 7% per year while costs per barrel remain constant, the growth rate of expenses is: –7.0% To compute the growth rate of revenues, we use the fact that production decreases 7% per year while the price of oil increases 5% per year, so that the growth rate of revenues is: Page of [1.05 × (1 – 0.07)] – = –0.0235 = –2.35% Therefore, the present value (in 2016) of revenues beginning in 2017 is: PV2012 70,690,915 $622,827,445 0.09 - (-0.0235) Similarly, the present value (in 2016) of expenses beginning in 2017 is: PV2012 33,662,340 $210,389,625 0.09 - (-0.07) Subtracting these present values gives the present value (in 2016) of net income, and then discounting back three years to 2013, we find that the present value of dividends paid in 2017 and subsequent years is: $318,477,671 The total value of the company is: $121,012,624 + $318,477,671 = $439,490,295 Since there are 7,000,000 shares outstanding, the present value per share is: $439,490,295 / 7,000,000 = $62.78 b EPS2013 = $72,000,000/7,000,000 = $10.29 EPS/P = $10.29/$62.78 = 0.164, or 16.4% This is greater than the cost of capital because production and earnings are declining 27 Mexican Motors’ market cap is 200 billion pesos Next year's free cash flow is 8.5 billion pesos Security analysts are forecasting that free cash flow will grow by 7.5% per year for the next five years a Assume that the 7.5% growth rate is expected to continue forever What rate of return are investors expecting? b Mexican Motors has generally earned about 12% on book equity (ROE = 12) and paid out 50% of earnings as dividends The remaining 50% of earnings has gone to free cash flow Suppose the company maintains the same ROE and investment rate in the long-run future What is the implication for the growth rate of earnings and free cash flow? For the cost of equity? Should you revise your answer to part (a) of this question? Answer Page of a The constant growth formula P= DIV/(r − g) can be used here: $200 = $8.5/(r-.075) Solving for r, r = 0.1175 That is, investors expect an 11.75% rate of return b Given the Mexican Motors is plowing back 50% of earnings after earning 12% on equity, the firm can expect to grow at an annual rate of only 6% (ROE x plowback = 0.12 x 0.50 = 0.06) Applying the constant growth formula again and solving for r we get: $200 = $8.5/(r-.06) r = 0.1025 That is, investors should expect only a 10.25% rate of return Page of ... 0 .5 = $3 .50 $7.4900 × 0 .5 = $3 .50 × 1.07 = $3.7 450 $8.0143 × 0 .5 = $3 .50 × 1.072 = $4.0072 $8 .57 53 × 0 .5 = $3 .50 × 1.073 = $4.2877 $9.1 756 × 0 .5 = $3 .50 × 1.074 = $4 .58 78 $9.3866 × 0.8 = $7 .50 93... 0.1 15 = 0.023 b P0 DIV3 DIV5 DIV1 DIV2 DIV4 4 1.1 15 1.1 15 1.1 15 1.1 15 0.1 15 - 0.023 1.1 15 3.7 45 4.007 4.288 4 .58 8 7 .50 93 $ 65. 453 4 1.1 15 1.1 15 1.1 15. .. 2013 1.8000 65 25 2014 1.6740 60 25 Revenue Expenses Net Income (= Dividends) 117,000,000 45, 000,000 72,000,000 100,440,000 41, 850 ,000 58 ,59 0,000 20 15 1 .55 68 55 25 85, 6 25, 100 38,920 ,50 0 46,704,600