# Calculating Stock Prices and Weighted Average Cost of Capital (WACC)

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## Stock Valuation and WACC Examples

### Problem 1: Constant Dividend Growth

Thomas Brothers is expected to pay a $0.35 per share dividend at the end of the year (D1 = $0.35). The dividend is expected to grow at a constant rate of 6% a year. The required rate of return is 13%. What is the stock’s current price?

P0 = D1 / (r – g) = 0.35 / (0.13 - 0.06) = $5.00

### Problem 2: Current Stock Price with Constant Growth

A stock just paid a dividend of D0 = $1.50. The required rate of return is r = 10%, and the constant growth rate is g = 4.0%. What is the current stock price?

P0 = D0(1+g) / (r – g) = 1.50(1 + 0.04) / (0.10 - 0.04) = $26.00

### Problem 3: Expected Stock Price in One Year

Using your answer for problem 2, what is the expected stock price in one year (P1)?

P1 = P0 (1 + g) = 26.00(1 + 0.04) = $27.04

### Problem 4: Multi-Stage Dividend Growth Model

Warr Corporation just paid a dividend of $1.00 a share (D0 = $1.00). The dividend is expected to grow 5% a year for the next three years and 3% thereafter. If r = 12%, what is the stock’s current value today?

Year | Dividend | Calculation |
---|---|---|

0 | $1.00 | |

1 | $1.05 | 1.00 * (1 + 0.05) |

2 | $1.10 | 1.05 * (1 + 0.05) |

3 | $1.16 | 1.10 * (1 + 0.05) |

3 (Terminal Value) | $13.28 | 1.16 * (1 + 0.03) / (0.12 - 0.03) |

NPV = $12.09 (Calculate the present value of each dividend and the terminal value, then sum them)

### Problem 5: Free Cash Flow Valuation

Smith Technologies is expected to generate $2 million in cash flow next year, $5 million in cash flow in year 2, and $7 million in cash flow in year three. After that, growth is expected to remain at 4% indefinitely. Smith has no debt, 10 million shares outstanding, and r = 10%. What is the stock’s value per share?

Year | Cash Flow (Millions) | Calculation |
---|---|---|

1 | $2 | |

2 | $5 | |

3 | $7 | |

3 (Terminal Value) | $121.33 | 7 * (1 + 0.04) / (0.10 - 0.04) |

NPV = $102.37 million (Calculate the present value of each cash flow and the terminal value, then sum them)

P0 = $10.24 ($102.37 million / 10 million shares)

### Problem 6: Cost of New Equity

Your company’s stock sells for $50 per share, its last dividend was $2.00, its growth rate is a constant 5 percent, and the company will incur a flotation cost of 15 percent if it sells new common stock. What is the firm’s cost of new equity?

r = [D0(1+g) / P0(1-F)] + g = [2.00(1 + 0.05) / 50(1 - 0.15)] + 0.05 = 9.94%

### Problem 7: Weighted Average Cost of Capital (WACC)

An analyst has collected the following information regarding Christopher Company. The company’s capital structure is 70 percent equity and 30 percent debt. The yield to maturity on the company’s bonds is 9 percent. The company’s cost of equity is 10.9%. Given this information, calculate the company’s WACC. Assume that the tax rate is 40 percent.

WACC = wdrd(1-T) + wprp + were

WACC = 0.30(9)(1 - 0.40) + 0.7(10.9)

WACC = 1.62 + 7.63

WACC = 9.25%

### Problem 8: Cost of Retained Earnings

The common stock of Anthony Steel has a beta of 1.20. The risk-free rate is 5 percent and the market risk premium is 6 percent. Assume the firm will be able to use retained earnings to fund the equity portion of its capital budget. What is the company’s cost of retained earnings?

r = rf + B(rm – rf) = 5 + 1.20(6) = 12.2%

### Problem 9: WACC with Preferred Stock

Hatch Corporation’s target capital structure is 40 percent debt, 50 percent common stock, and 10 percent preferred stock. The company’s bonds have a yield to maturity of 7 percent. The company’s preferred stock return is 9.5%. The company’s common stock sells for $28 per share and is expected to pay a dividend of $2.00 per share at the end of the year. The dividend is expected to grow at a constant rate of 7 percent per year. The firm’s tax rate is 40 percent. What is the company’s WACC?

Cost of Equity (re) = [D1 / P0] + g = [2.00 / 28.00] + 0.07 = 14.14%

WACC = wdrd(1-T) + wprp + were

WACC = 0.4(7)(1 - 0.40) + 0.1(9.5) + 0.5(14.14)

WACC = 1.68 + 0.95 + 7.07

WACC = 9.7%

### Problem 10: WACC with Retained Earnings and Debt

Helms Aircraft has a capital structure that consists of 60 percent debt and 40 percent equity. The firm will be able to use retained earnings to fund the equity portion of its capital budget. The company recently issued bonds with a yield to maturity of 9 percent. The risk-free rate is 6 percent, the market risk premium is 6 percent, and Helms’ beta is 1.5. If the company’s tax rate is 35 percent, what is the company’s WACC?

Cost of Equity (re) = rf + B(rm – rf) = 6 + 1.5(6) = 15%

WACC = wdrd(1-T) + wprp + were

WACC = 0.6(9)(1 - 0.35) + 0.4(15)

WACC = 3.51 + 6

WACC = 9.51%