Finance Exam 2

- Fraction of earnings paid out as dividends

payout ratio

- Fraction of earnings retained by the firm

plowback ratio

Ex: Northwest Natural Gas stock was selling for $29 per share at the start of 2025, Dividend payments for that year were expected to be $1.3 a share. What is the expected return on equity, assuming a growth rate of 8%?

r = (1.3 / 29) + .08 = 12.48%

Ex: Company Y does not plow back any earnings and is expected to produce a level dividend stream of $5 a share. If the current stock price is $40, what is the market capitalization rate?

r = Div1/P0 = 5/40 = 12.5%

The value of a project, a company, or any asset is:

- Its expected future cash flows - Evaluated at its cost of capital

Ex: Phoenix produces dividends in four consecutive years of 0.40, 12.49, 43.09, and 51.21, respectively. The dividend in year five is estimated to be 55.47 and should grow in Perpetuity at 10%. Given a discount rate of 25%, what is the price of the stock?

- 202.8

PV when 100% equity financing. Ex: Project A is expected to produce CF = $223 for each of 9 years, with additional $54 income for selling the factory at the end of the 9 years. It is pure equity financed. Given a risk-free rate of 3%, a market premium of 9%, and a beta of 1.6, what is the PV of the project?

- 3 + 1.6(9) = 17.4% - N = 9; i = 17.4; PMT = 223; FV = 54; PV = 991.8

Ex: Project A is expected to produce CF = $249 for each of 7 years, with additional $46 income for selling the factory at the end of the 7 years. It is purely equity financed. Given a risk free rate of 0%, a market premium of 10%, and beta of 1.7, what is the PV of the project?

1. 0 + 1.7(10) = 17 2. N = 7; i = 17; PMT = 249; FV = 46 - PV = 992

Ex: Company Z earnings and dividends per share will grow indefinitely by 5.1% a year if next year's dividend is $5.9. The market capitalization rate is 12.0%. If Company Z were to distribute all its earnings, it could maintain a level dividend stream of $11.5 a share. How much is the market actually paying per share for growth opportunities?

1. 5.9/(12 - 5.1) = 85.507 2. PVGO = (D1 / r-g) - (E / r) - 85.507 - (11.5 / .12) = - 10.3

Ex: Nikko has 8 million common shares outstanding priced at $14.625 each. Next year's dividend on these shares is expected to be $2.71 and will grow at 5% per year forever. Nikko has 60,000 bonds outstanding, each with a coupon rate of 12%, and are priced at $1,050 each to yield 8% to bondholders. Nikko's marginal corporate income tax rate is 34%. Compute the WACC for the Nikko Co.

1. D = 60000*1050 = 63M, E = 8000000*14.625 = 117M, V = D+E = 180 2. Cost of bound: i = 8% 3. Cost of equity: constant growth perpetuity = 2.71/14.625+5% = 23.53% 4. WACC = (1-34%)*(63/180)*8%+(117/180)* 23.53% = 17.14%

Ex: (one period) If Fledgling Electronics is selling for $200 per share today and is expected to sell for $210 one year from now, what is the expected return if the dividend one year from now is forecasted to be $8.00? Fledgling Electronics price can be thought of as follows.

1. Expected return = 8 + 210 - 200 / 200 = 0.09 2. Price = P0 = 8 + 210 / 1 + 0.09 = 200

Ex: (Putting everything for the whole semester together) A company has 70 million debt, $80 million equity, and tax rate is 40%. The debt is just one bond with face value of 1000, 10 years to maturity, coupon rate 7% and selling at 923. The risk-free interest rate is 6%, the market return is 12%, and its stock beta is 1.5. What is the WACC for the company?

1. N = 10; PV = -923; PMT = 70; FV = 1000; - i = 8.16 = cost of debt 2. According to CAPM, the required stock return is: 6 + (12 -6) x 1.5 = 15% 3. V = 80 + 70 = 150 million WACC = (1 - Tc) rD(D/V) + rE (E/V) = (1 - .4) * 8.16 * (70/150) + 15 * (80/150) = 2.28 + 8 = 10.28%

Ex: Our company forecasts to pay a $10 dividend next year, which represents 100% of its earnings. This will provide investors with an 8% expected return. Instead, we decide to plowback 37% of the earnings at the firm current return on equity of 13%. What is the present value of growth opportunities (PVGO)?

1. No Growth - P0 = 10 / .08 = $125 2. With Growth - Div. = 10 x (1 - .37) = 6.3 --- G = .13 x .37 = .0481 --- P0 = 6.3 / .08 - .0481 = $197.4921 PVGO = 197.4921 - 125 = 72.5

Ex: Our company forecasts to pay a $10 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plowback 50% of the earnings at the firm's current return on equity of 20%. What is the value of the stock before and after the plowback decision?

1. No Growth - P0 = 10 / .12 = $83.33 2. With Growth - Div. = 10 x (1 - 50%) = 5 --- g = .20 x .50 = .10 --- P0 = 5.00 / .12 - .10 = $250 PVGO = 250.00 - 83.33 = $166.67

Ex: Our company forecasts to pay an $8.33 dividend next year, representing 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%. What is the value of the stock before and after the plowback decision? What is the Present value of growth opportunities?

1. No Growth - P0 = 8.33 / .15 = $55.56 - All earnings are paid out each year, there is no increase in equity basis 2. With Growth - Div. = 8.33 x (1 - 40%) = 5 --- G = .25 x .40 = .10 --- P0 = 5.00 / .15 - .10 = $100.00 If the company did not plowback some earnings, the stock price would remain at $55.56. With the plowback, the price rose to $100.00. (PV with growth - PV without growth) is called the present value of growth opportunities (PVGO) - PVGO = 100.00 - 55.56 = $44.44

What are the return measurements for stable and still growing firms?

1. Stable firms - P0 = Div1 / r - Dividend yield = Div1 / P0 2. Growing Firms - P0 = Div1 / r - g - R = (Div1 / P0 ) + g

Ex: Consider the following two stocks: - A will provide a dividend of $10 forever. - B will pay a dividend of $5 next year. Thereafter, dividend growth will be 4% a year forever. If the market capitalization rate for each stock is 10%, which stock is the most valuable? What is the capitalization is 7%?

10% - A P0 = Div/r = 10/10% = 100 - B P0 = Div1 / (r-g) = 5/(10%-4%) = 83.33 7% - 10/7% = 142.86 - 5/(7%-4%) = 166.67

Ex: Assume the risk-free interest rate is 7% and the market return is 12%. If the beta of a stock is 1.4, according to CAPM, what is the required rate of return on the stock?

7 + (12 - 7) x 1.4 = 14%

- Net worth of the firm according to the balance sheet

Book Value

Ex: Assume the risk-free interest rate is 2% and the market return is 11%. If the beta of a stock is 1.4, according to CAPM, what is the required rate of return on the stock?

CAPM = re = rf + Be(rm - rf) = 2 + 1.4(11 - 2) = 14.60%

To determine the firm's cost of capital the second step is to estimate the marginal cost of each source of capital. Step 2: The marginal cost of common equity. To compute the return required by stockholders, we can use CAPM: What is the formula?

CAPM: re = rf + Be (rm - rf) where rj = cost of capital for project j - rf = riskless return - rm = required return on the market portfolio - rm - rf = market risk premium - Bi = beta of project j

- ownership shares in a publicly held corporation

Common Stock

Ex: Nikko has 8 million common shares outstanding priced at $14.625 each. Next year's dividend on these shares is expected to be $2.71, and will grow at 5% per year forever. What is the cost of equity?

Cost of equity = 2.71/14.625 + 5% = 23.53%

- Periodic cash distribution from the firm to the shareholders

Dividend

- Computation of today's stock price which states that share value equals the present value of all expected future dividends

Dividend Discount Model

Ex: (for already stable companies): Northwest Natural Gas stock was selling for $48 per share at the start of 2015. Dividend payments for the next year were expected to be $2.00 a share. What is the dividend yield, assuming no growth?

Dividend yield = r = 2.00 / 48 = 4.17%

Ex (for already stable companies): Northwest Natural Gas stock was selling for $49.43 per share at the start of 2015. Dividend payments for the next year were expected to be $2.00 a share. What is the dividend yield, assuming no growth?

Dividend yield = r = 2.00 / 49.43 = 0.41

Ex: If Fledgling Electronics is selling for $183 per share today and is expected to sell for $191 one year from now, what is the expected return if the dividend one year from now is forecasted to be $6?

ER = 6 + 191 -183 / 183 = 7.65%

- Portfolios of stocks that can be bought or sold in a single trade within a day, i.e. intraday

Exchange-Traded Funds (EFTs) - Biggest EFT: Vanguard.com; ishares.com

- the percentage rate of return that an investor forecasts from a specific investment over a set period of time. Sometimes called the market capitalization rate

Expected Return

Ex: 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 $5.00?

Expected Return = 5 + 110 - 100 / 100 = .15

Ex: If Fledgling Electronics is selling for $154 per share today and is expected to sell for $147 one year from now, what is the expected return if the dividend one year from now is forecasted to be $6?

Expected Return = 6 + 147 - 154 / 154 = -0.65%

Ex (for still growing companies): Northwest Natural Gas stock was selling for $49.43 per share at the start of 2015. Dividend payments for the next year were expected to be $2.00 a share. What is the expected return on equity, assuming a growth rate of 7.7%?

Expected return = r = (2.00 / 49.43) + .077 = .118

Ex: Northwest Natural Gas stock was selling for $35 per share at the start of 2025. Dividend payments for that year were expected to be $3.4 a share. What is the expected return on equity, assuming a growth rate of 10%?

Expected return = r = (3.4 / 35) + .10 = .1971

Ex: (for still growing companies): Northwest Natural Gas stock was selling for $48 per share at the start of 2015. Dividend payments for the next year were expected to be $2.00 a share. What is the expected return on equity, assuming a growth rate of 8%?

Expected return = r = 2.00 / 48 + .08 = 12.18%

What is the expected return formula?

Expected return = r = Div1 + P1 - P0 / P0

- Financial statement that uses the market value of assets and liabilities

Market Value Balance Sheet

- Portfolios of stocks that can be bought or sold in a single trade once a day or lower frequency

Mutual funds

- Price per share dividend by earnings per share; or total market cap / total book value

P/B Ratio

- Price per share dividend by earnings per share; or total market cap / total earnings

P/E Ratio

Multiple-Period Model What is the expected return/price formula for multiple periods?

P0 = Div1 / (1+r)^1 + Div2 / (1 + r)^2 + ... + DivH + PH / (1 + r)^H - H = Time horizon for your investment, after which you may sell the project to others. You can view PH as your selling price too

Ex: Company Z's earnings and dividends per share will 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?

P0 = Div1 / (r-g) = 10/(8% - 5%) = 333.33

Ex: Phoenix produces dividends in three consecutive years of 0, .40, and .70, respectively. The dividend in year four is estimated to be .75 and should grow in perpetuity at 5%. Given a discount rate of 10%, what is the price of the stock?

PV = .0 / (1 + .1)^1 + .40 / (1 + .1)^2 + .70 / (1 + .17)^3 + [ 1 / (1 + .1)^3 x .75 / (.10 - .05)] = 12.13

Ex: Phoenix produces dividends in three consecutive years of 0, .31, and .65, respectively. The dividend in year four is estimated to be .67 and should grow in perpetuity at 4%. Given a discount rate of 10%, what is the price of the stock?

PV = 0 / (1 + .1)^1 + .31 / (1 + .1)^2 + .65 / (1 + .1)3 + [ 1 / (1 + .1)^3 x .67 / (.10 - .04)] = 9.13

Ex: Phoenix produces dividends in four consecutive years of 1.00, 18.06, 41.63, and 50.59, respectively. The dividend in year five is estimated to be 54.43 and should grow in perpetuity at 6%. Given a discount rate of 17%, what is the price of the stock?

PV = 1.00 / (1 + .17)^1 + 18.06 / (1 + .17)^2 + 41.63 / (1 + .17)^3 + 50.59 / (1 + .17)^4 + [ 1 / (1 + .17)^4 x 54.43 / (.17 - .06)] = 331.1

Ex: Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 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?

PV = 3.00 / (1 + .12)^1 + 3.24 / (1 + .12)^2 + (3.50 + 94.48) / (1 + .12)^3 = $75.00

Ex: Current forecasts are for XYZ Company to pay dividends of $3.13, $5.29, and $9.68 over the next three years, respectively. At the end of three years, you anticipate selling your stock at a market price of $79.06. What is the price of the stock given a 1% expected return?

PV = 3.13 / (1 + .01)^1 + 5.29 / (1 + .01)^2 + (9.68 + 79.06) / (1 + .01)^3 = 94.4

Ex: (two periods) Fledgling Electronics is forecasted to pay a $5.00 dividend at the end of year one and a $5.50 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 155%, what is the price of the stock?

PV = 5.00 / (1 + .15)^1 + (5.50 + 121) / (1 + .15)^2 = $100.00

What is the formula to find the price of the stock with a dividend growth rate?

PV = Div1 / (1 + r)^1 + Div2 / (1 + r)^2 + Div3 / (1 + r)^3 + Div4 / (r-g) * 1/(1 + r)^n

What is the present value of growth opportunities (PVGO) formula?

PV with growth - PV without growth

The value of any stock is the present value of its future cash flows. This reflects the discounted cash flow (DCF) formula. Dividends represent the future cash flows of the firm. What is this formula?

PV(stock) = PV(expected future dividends)

Ex: Company X is expected to pay an end-of-year dividend of $3 a share. After paying the dividend, its stock is expected to sell at $82. If the market capitalization rate is 7%, what is the current stock price?

Price = (3 + 82)/(1 + .07) = 79.4

Ex: Company X is expected to pay an end-of-year dividend of $5 a share. After paying the dividend, its stock is expected to sell at $110. If the market capitalization rate is 8%, what is the current stock price?

Price = (5+110)/(1+8%) = 106.48

Ex: 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 $5.00? Expected Return = 5 + 110 - 100 / 100 = .15 Ex: Fledgling Electronics price can be thought of as follows:

Price = P0 = 5 + 110 / 1.15 = 100

The price of any share of stock can be thought of as the present value of future cash flows. For a stock, the future cash flows are dividends and the ultimate sales price of the stock. Note we just rearrange the formula on p* to obtain this formula.....what is it?

Price = P0 = Div1 + P1 / 1 + r

Infinite-period Model: Constant dividend growth. If we only focus on dividends, not the eventual selling price, we can use the perpetuity model (g = 0) / constant growth perpetuity model (g does not equal 0) to obtain the present value of the dividends, which is the stock price. What is the formula?

Price = P0 = Div1 / r - g

- Market for the sale of new securities by corporations

Primary Market

For constant dividend growth, what is the return on equity (or required or expected return on equity) formula?

R = (Div1 / P0 ) + g

Ex: A company has stocks of $14.625 each. Next year's dividend on these shares is expected to be $2.71, and will grow at 5% per year forever. What is the cost of equity?

Re = D1/P0 + g = 2.71/14.625 + 5% = 23.53%

- Market in which previously issued securities are traded among investors

Secondary Market Ex: Stock Exchanges (e.g., NYSE, Nasdaq) - Places where eshares are listed, and also traded. They are now mostly computer networks that connect traders with each other Electronic Communication Networks (ECNs) - A number of computer networks that connect traders with each other

The Calculation of the Weighted Average Cost of Capital (WACC) with Financial Claims. To determine the firm's cost of capital...

Step 1: Assign market value weights (or target weights) to each source, Step 2: Estimate the marginal cost of each source of capital Step 3: Compute the Weighted Average Cost of Capital, WACC

Ex: Stock A will provide a dividend of $6.9 forever. Stock B will pay a dividend of $4.7 next year. Thereafter, dividend growth will be 3.7% a year forever. If market capitalization rate for each stock is 8.5%, what is the value of Stock A minus the value of stock B?

Stock A = P0 = Div/r - 6.9/8.5 = 81.2% Stock B = Div1/ (r-g) - 4.7/ (8.5 - 3.7) = 97.9% 81.1 - 97.9 = -16.7%

Ex: A company has $400 million debt, $600 million equity, and tax rate is 40%. Cost of debt is 6% and cost of equity is 12%. What is the WACC for the company?

V = 400 + 600 = $1 billion D/V = 400/1000 E/V = 600/1000 WACC = (1 - Tc) rD (D/V) + rE (E/V) WACC = (1 - .4) * 6 * (.40) + 12 * (.60) = 8.64%

Ex: A company has three divisions with the following information. What is its WACC. Division - Market value - Required Return 1 - $50 million - 16% 2 - 35 million - 17% 3 - 15 million - 14%

V = 50 + 35 + 15 = 100 WACC = 16% * 50/100 + 17% * 35/100 + 14% * 15/100 = 16.05%

Ex: A company has 30% debt, 70% equity, and the tax rate is 35%. The cost of debt is 7.5% and the cost of equity is 15%. What is the WACC for the company?

WACC = (1 - TC)rD(D/V) + rE (E/V) WACC = (1 - .35) 7.5(.30) + 15(.70) = 12.0% T = tax rate

What is the Weighted Average Cost of Capital (WACC) based on both debt and equity?

WACC = (1 - Tc) r debt (D/V) + r equity (E/V) V = D + E - D = market value of debt - E = market value of equity - r debt = YTM on bonds - r equity = rf + B(rm - rf)

Ex: (WACC: Financing based on both debt and equity) A company has 50% debt, 50% equity, and tax rate is 30%. Cost of debt is 10% and cost of equity is 15%. What is the WACC for the company?

WACC = (1 - Tc) r debt (D/V) r equity (E/V) WACC = (1 - .3) 10(.50) + 15(.50) = 11.0%

PV when 100% equity financing. Ex: Project A is expected to produce CF = $100 mil for each of three years. It is pure equity financed. Given a risk-free rate of 6%, a market premium of 8%, and a beta of .75, what is the PV of the project?

r = rf + B(rm - rf ) - 6 + .75(8) - 12% - N = 3; i = 12; PMT = 100; FV = 0; PV = 240.2

Ex: (PV when 100% equity financing) Project A is expected to produce CF = $150 mil for each of five years. It is purely equity financed. Given a risk free rate of 5%, a market premium of 7%, and beta of 1.5, what is the PV of the project?

r = rf + B(rm - rf) = 5 + 1.5(7) = 15.5% N = 5 i = 15.5 PMT = -150 FV = 0 PV = 496.93

What is the constant dividend growth model formula?

re = D1 / P0 + g