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Chapter 9: Problem 6

Due to the highly specialized nature of the electronic industry, Barrett Industries invests a lot of money in \(\mathrm{R} \& \mathrm{D}\) on prospective products. Consequently, it retains all of its earnings and reinvests them into the firm. (In other words, it does not pay any dividends.) At this time, Barrett does not have plans to pay any dividends in the near future. A major pension fund is interested in purchasing Barrett's stock, which is traded on the NYSE. The treasurer of the pension fund has done a great deal of research on the company and realizes that its valuation must be based on the total company model. The pension fund's treasurer has estimated Barrett's free cash flows for the next 4 years as follows: \(\$ 3\) million, \(\$ 6\) million, \(\$ 10\) million, and \(\$ 15\) million. After the fourth year, free cash flow is projected to grow at a constant 7 percent. Barrett's WACC is 12 percent, it has \(\$ 60\) million of total debt and preferred stock, and 10 million shares of common stock. a. What is the present value of Barrett's free cash flows during the next 4 years? b. What is the company's terminal value? c. What is the total value of the firm today? d. What is Barrett's price per share?

Short Answer

Expert verified
Barrett's price per share is $16.735.

Step by step solution

01

Calculate Present Value of Cash Flows

To find the present value (PV) of Barrett's free cash flows for the next 4 years, we use the formula: \[ PV = \sum_{t=1}^{n} \frac{FCF_t}{(1 + WACC)^t} \]where \( FCF_t \) is the free cash flow at year \( t \), and \( WACC = 0.12 \). Calculate each year's present value:- Year 1: \( PV = \frac{3}{(1.12)^1} = 2.68 \text{ million} \)- Year 2: \( PV = \frac{6}{(1.12)^2} = 4.78 \text{ million} \)- Year 3: \( PV = \frac{10}{(1.12)^3} = 7.12 \text{ million} \)- Year 4: \( PV = \frac{15}{(1.12)^4} = 9.54 \text{ million} \)Add these together to get the total PV for the first 4 years: \[ Total\ PV = 2.68 + 4.78 + 7.12 + 9.54 = 24.12 \text{ million} \]
02

Determine the Terminal Value

Use the Gordon growth model to find the terminal value (TV) at the end of Year 4: \[ TV = \frac{FCF_5}{WACC - g} = \frac{15 \times (1.07)}{0.12 - 0.07} \]\[ TV = \frac{16.05}{0.05} = 321 \text{ million} \]Now calculate the present value of the terminal value at Year 4: \[ PV_{TV} = \frac{321}{(1.12)^4} = 203.23 \text{ million} \]
03

Calculate the Total Value of the Firm

Sum the present values of the free cash flows and the terminal value: \[ Total\ Value = 24.12 + 203.23 = 227.35 \text{ million} \]
04

Find Barrett's Price Per Share

To find the price per share of Barrett, subtract the total debt and preferred stock, and then divide by the total number of shares: \[ Equity\ Value = 227.35 - 60 = 167.35 \text{ million} \]\[ Price\ per\ Share = \frac{167.35}{10} = 16.735 \text{ per\ share} \]

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Key Concepts

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

Free Cash Flow Analysis
Free Cash Flow (FCF) is a fundamental metric in corporate valuation that represents the cash a company generates after accounting for cash outflows to support operations and maintain capital assets. For Barrett Industries, the estimated free cash flows over the next 4 years are crucial in determining the company's value.

These cash flows are projected as follows: Year 1 with $3 million, Year 2 with $6 million, Year 3 with $10 million, and Year 4 with $15 million. Each of these projections is an estimate of the cash Barrett will generate from its operations, which can be used for expansion, paying off debts, or reinvesting in R&D.

It's important to understand that Free Cash Flow shows the ability of a company to generate cash that can be used to enhance shareholder value. Calculating the present value of these cash flows involves discounting them back to their value today using the company's Weighted Average Cost of Capital (WACC).

This process essentially tells us what these future cash flows are worth at today's standards, which is instrumental for investors to make informed decisions.
Weighted Average Cost of Capital (WACC)
The Weighted Average Cost of Capital (WACC) is a measure that reflects the average rate of return a company is expected to pay its security holders to finance its assets. In simpler terms, it represents the average cost of the company's financing mix (debt and equity).

For Barrett Industries, the WACC is given as 12%. This number plays a critical role as a discount rate in valuing the company's future free cash flows and terminal value. WACC is calculated by weighting the cost of each capital component based on its proportion in the overall capital structure. This includes:
  • The cost of debt (adjusted for taxes)
  • The cost of equity
  • The proportion of each in the company鈥檚 total capital

Investors use WACC to assess the minimum acceptable return on investment to compensate for the risk. A lower WACC indicates a low risk and thus appears more attractive to investors. On the other hand, a high WACC suggests higher risk and potentially higher returns needed.

Understanding WACC helps investors gauge the feasibility of investing in a company and whether the projected returns align with their risk expectations.
Terminal Value Calculation
The terminal value is a critical component in corporate valuation, particularly for companies that have a stable growth rate expected beyond the projection period, like Barrett Industries post year 4.

The terminal value accounts for the long-term growth rate of free cash flows beyond the 4-year projections, given a perpetual growth rate of 7%. In Barrett's case, the Gordon Growth Model is used to calculate this value, which assumes that free cash flows will continue to grow at a constant rate indefinitely.

The formula: \[ TV = \frac{FCF_5}{WACC - g} \]where \( FCF_5 \) is the estimated free cash flow at Year 5, \( WACC \) is 12%, and \( g \) is the growth rate of 7%, helps us derive the terminal value.

The calculated terminal value then needs to be discounted back to present value using the WACC to reflect its worth in today鈥檚 dollars. This step ensures that the terminal value is accurately incorporated into the overall valuation analysis.

Terminal value typically makes up a significant portion of the total valuation, making it essential for capturing the long-term value prospects of a company.

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Most popular questions from this chapter

Suppose Chance Chemical Company's management conducts a study and concludes that if Chance expanded its consumer products division (which is less risky than its primary business, industrial chemicals), the firm's beta would decline from 1.2 to \(0.9 .\) However, consumer products have a somewhat lower profit margin, and this would cause Chance's constant growth rate in earnings and dividends to fall from 7 to 5 percent. a. Should management make the change? Assume the following: \(k_{M}=12 \% ; k_{R F}=9 \%\) \(\mathrm{D}_{0}=\$ 2.00\) b. Assume all the facts as given above except the change in the beta coefficient. How low would the beta have to fall to cause the expansion to be a good one? (Hint: Set \(\hat{\mathrm{P}}_{0}\) under the new policy equal to \(\hat{\mathrm{P}}_{0}\) under the old one, and find the new beta that will produce this equality.)

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.

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?

The risk-free rate of return, \(\mathrm{k}_{\mathrm{RF}},\) is 11 percent; the required rate of return on the market, \(k_{M},\) is 14 percent; and Upton Company's stock has a beta coefficient of 1.5 a. If the dividend expected during the coming year, \(D_{1},\) is \(\$ 2.25,\) and if \(g=a\) constant \(5 \%,\) at what price should Upton's stock sell? b. Now, suppose the Federal Reserve Board increases the money supply, causing the risk-free rate to drop to 9 percent and \(\mathrm{k}_{\mathrm{M}}\) to fall to 12 percent. What would this do to the price of the stock? c. In addition to the change in Part b, suppose investors' risk aversion declines; this fact, combined with the decline in \(\mathrm{k}_{\mathrm{RF}},\) causes \(\mathrm{k}_{\mathrm{M}}\) to fall to 11 percent. At what price would Upton's stock sell? d. Now, suppose Upton has a change in management. The new group institutes policies that increase the expected constant growth rate to 6 percent. Also, the new management stabilizes sales and profits, and thus causes the beta coefficient to decline from 1.5 to \(1.3 .\) Assume that \(\mathrm{k}_{\mathrm{RF}}\) and \(\mathrm{k}_{\mathrm{M}}\) are equal to the values in part c. After all these changes, what is Upton's new equilibrium price? (Note: \(D_{1}\) is now \(\$ 2,27,2\)

The beta coefficient for Stock \(C\) is \(b_{C}=0.4,\) whereas that for Stock \(D\) is \(b_{D}=-0.5\) (Stock D's beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall. There are very few negative beta stocks, although collection agency stocks are sometimes cited as an example. a. If the risk-free rate is 9 percent and the expected rate of return on an average stock is 13 percent, what are the required rates of return on Stocks \(C\) and \(D\) ? b. For Stock \(C\), suppose the current price, \(P_{0}\), is \(\$ 25 ;\) the next expected dividend, \(D_{1}\), is \(\$ 1.50 ;\) and the stock's expected constant growth rate is 4 percent. Is the stock in equilibrium? Explain, and describe what will happen if the stock is not in equilibrium.
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