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Chapter 9: Problem 7

Today is December \(31,2001 .\) The following information applies to Vermeil Airlines: \(\bullet\) After-tax, operating income \([\mathrm{EBIT}(1-\mathrm{T})]\) for 2002 is expected to be \(\$ 500\) million. \(\bullet\) The company's depreciation expense for 2002 is expected to be \(\$ 100\) million. \(\bullet\) The company's capital expenditures for 2002 are expected to be \(\$ 200\) million. \(\bullet\) No change is expected in the company's net operating working capital. \(\bullet\) The company's free cash flow is expected to grow at a constant rate of 6 percent per year. \(\bullet\) The company's cost of equity is 14 percent. \(\bullet\) The company's WACC is 10 percent. \(\bullet\) The market value of the company's debt is \(\$ 3\) billion. \(\bullet\) The company has 200 million shares of stock outstanding. Using the free cash flow approach, what should the company's stock price be today?

Short Answer

Expert verified
The stock price should be $35 per share.

Step by step solution

01

Calculate Free Cash Flow for 2002

Free Cash Flow (FCF) for 2002 is calculated using the formula:\[\text{FCF} = \text{EBIT}(1-\text{T}) + \text{Depreciation} - \text{Capital Expenditures} - \Delta \text{Net Operating Working Capital}\]Given information: EBIT(1-T) = \(500 million, Depreciation = \)100 million, Capital Expenditures = \(200 million, and no change in Net Operating Working Capital. Thus:\[\text{FCF} = 500 + 100 - 200 - 0 = \\) 400 \text{ million}\]
02

Calculate the Terminal Value at the end of 2002

The Terminal Value (TV) is calculated using the formula for the perpetuity growth model:\[\text{TV}_{2002} = \frac{\text{FCF}_{2003}}{r - g}\]Where \(\text{FCF}_{2003}\) is the FCF for 2002 grown by the constant growth rate:\(g = 6\%\). So,\[\text{FCF}_{2003} = 400 \times (1 + 0.06) = 424 \text{ million}\]The WACC \(r = 10\%\). Then,\[\text{TV} = \frac{424}{0.10 - 0.06} = \frac{424}{0.04} = \$10,600 \text{ million}\]
03

Calculate the Enterprise Value

The Enterprise Value (EV) is the sum of the present value of the FCF for 2002 and the present value of the Terminal Value. For FCF in 2002:\[\text{PV of FCF} = \frac{400}{1 + 0.10} = \frac{400}{1.10} \approx 363.64 \text{ million}\]And for the Terminal Value:\[\text{PV of TV} = \frac{10,600}{1.10} \approx 9636.36 \text{ million}\]Adding both, the Enterprise Value is:\[\text{EV} = 363.64 + 9636.36 = \$10,000 \text{ million}\]
04

Calculate the Equity Value

The Equity Value is calculated by subtracting the market value of debt from the Enterprise Value:\[\text{Equity Value} = \text{EV} - \text{Market Value of Debt} = 10,000 - 3,000 = \$7,000 \text{ million}\]
05

Calculate the Stock Price

The stock price is the Equity Value divided by the number of shares outstanding:\[\text{Stock Price} = \frac{\text{Equity Value}}{\text{Shares Outstanding}} = \frac{7,000}{200} = \$35 \text{ per share}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Free Cash Flow (FCF)
Free Cash Flow, or FCF, is an essential metric that measures a company's financial performance. It shows the cash that a company generates after accounting for capital expenditures necessary for maintaining or expanding the business. Calculating FCF can provide insight into a company's profitability and efficiency.

To calculate FCF, the formula used is:
  • \[ \text{FCF} = \text{EBIT}(1 - \text{T}) + \text{Depreciation} - \text{Capital Expenditures} - \Delta \text{Net Operating Working Capital} \]
In simpler terms, FCF starts with the company's operating income after taxes (also known as EBIT after-tax). Then, depreciation is added back because it's a non-cash expense. Next, capital expenditures, which represent the money spent on fixed assets, are subtracted because they reflect actual cash outflow. Lastly, any changes in net operating working capital are also accounted for; however, if there is no change, it won't affect the FCF.

This cash flow value is pivotal for investors as it indicates the company's capability to generate cash and utilize it for expansion, dividends, or debt reduction. In the example problem, with all values plugged in, Vermeil Airlines' FCF for 2002 was determined to be \$400 million.
Weighted Average Cost of Capital (WACC)
The Weighted Average Cost of Capital (WACC) is a calculation of a company's overall cost of capital. It reflects the average rate that a company is expected to pay to secure financing.

WACC is important because it helps in assessing investment opportunities. A project with expected returns greater than the WACC should add value to the company, while those with lower returns might detract from its worth.

The WACC is calculated by weighting the cost of each source of capital (equity and debt). Here's the formula used:
  • The cost of equity is calculated considering the expected returns demanded by shareholders.
  • The cost of debt uses the interest rate paid on debt, after adjusting for tax savings from interest deductions.
  • The weights are the proportionate values of equity and debt from the company's total financing.
In the provided scenario, Vermeil Airlines has a WACC of 10%. This is the rate used to discount future cash flows to determine the present value of expected future benefits. Therefore, it's crucial in calculating the present values of Free Cash Flow and Terminal Value.
Equity Value Calculation
Equity Value represents the value of a company available to its shareholders, and it provides a snapshot of a company's market capitalization. Calculating the Equity Value is essential when determining a company's stock price.

Here's a simple way to calculate Equity Value from Enterprise Value:
  • First, calculate the Enterprise Value (EV) by summing the present value of future cash flows, using the discounted Free Cash Flow and Terminal Value.
  • Then, subtract the market value of the company's debt from the Enterprise Value. This gives the Equity Value, which represents the residual interest in the assets of the company after settling debts.
For example, in Vermeil Airlines' case, the Enterprise Value was first calculated at \\(10,000 million. After deducting the market value of the company's debt (\\)3,000 million), the Equity Value remained \\(7,000 million.

Finally, to find the stock price, the Equity Value is divided by the number of outstanding shares. Thus, for Vermeil Airlines, the stock price came out to \\)35 per share.

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Most popular questions from this chapter

You buy a share of The Ludwig Corporation stock for \(\$ 21.40 .\) You expect it to pay dividends of \(\$ 1.07, \$ 1.1449,\) and \(\$ 1.2250\) in Years \(1,2,\) and \(3,\) respectively, and you expect to sell it at a price of \(\$ 26.22\) at the end of 3 years. a. Calculate the growth rate in dividends. b. Calculate the expected dividend yield. c. Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to obtain the expected total rate of return. What is this stock's expected total rate of return?

Harrison Clothiers' stock currently sells for \(\$ 20\) a share. The stock just paid a dividend of \(\$ 1.00\) a share (i.e., \(D_{0}=\$ 1.00\) ). The dividend is expected to grow at a constant rate of 10 percent a year. What stock price is expected 1 year from now? What is the required rate of return on the company's stock?

Fee Founders has preferred stock outstanding that pays a dividend of \(\$ 5\) at the end of each year. The preferred stock sells for \(\$ 60\) a share. What is the preferred stock's required rate of return?

Microtech Corporation is expanding rapidly, and it currently needs to retain all of its earnings, hence it does not pay any dividends. However, investors expect Microtech to begin paying dividends, with the first dividend of \(\$ 1.00\) coming 3 years from today. The dividend should grow rapidly \(-\) at a rate of 50 percent per year - during Years 4 and 5 After Year \(5,\) the company should grow at a constant rate of 8 percent per year. If the required return on the stock is 15 percent, what is the value of the stock today?

It is now January \(1,2002 .\) Wayne-Martin Electric Inc. (WME) has just developed a solar panel capable of generating 200 percent more electricity than any solar panel currently on the market. As a result, WME is expected to experience a 15 percent annual growth rate for the next 5 years. By the end of 5 years, other firms will have developed comparable technology, and WME's growth rate will slow to 5 percent per year indefinitely. Stockholders require a return of 12 percent on WME's stock. The most recent annual dividend (D) , which was paid yesterday, was \(\$ 1.75\) per share. a. Calculate WME's expected dividends for \(2002,2003,2004,2005,\) and 2006 b. Calculate the value of the stock today, \(\hat{\mathrm{P}}_{0}\). Proceed by finding the present value of the dividends expected at the end of \(2002,2003,2004,2005,\) and 2006 plus the present value of the stock price that should exist at the end of \(2006 .\) The year-end 2006 stock price can be found by using the constant growth equation. Notice that to find the December \(31,2006,\) price, you use the dividend expected in \(2007,\) which is 5 percent greater than the 2006 dividend. c. Calculate the expected dividend yield, \(D_{1} / P_{0}\), the capital gains yield expected in 2002 , and the expected total return (dividend yield plus capital gains yield) for 2002 . (Assume that \(\mathrm{P}_{0}=\mathrm{P}_{0},\) and recognize that the capital gains yield is equal to the total return minus the dividend yield.) Also calculate these same three yields for 2007 . d. How might an investor's tax situation affect his or her decision to purchase stocks of companies in the early stages of their lives, when they are growing rapidly, versus stocks of older, more mature firms? When does WME's stock become "mature" in this example? e. Suppose your boss tells you she believes that WME's annual growth rate will be only 12 percent during the next 5 years and that the firm's normal growth rate will be only 4 percent. Without doing any calculations, what general effect would these growthrate changes have on the price of WME's stock? f. Suppose your boss also tells you that she regards WME as being quite risky and that she believes the required rate of return should be 14 percent, not 12 percent. Again, without doing any calculations, how would the higher required rate of return affect the price of the stock, its capital gains yield, and its dividend yield? Again, assume that the firm's normal growth rate will be 4 percent.
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