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Chapter 9: Problem 21

Barrett Industries invests a lot of money in \(\mathrm{R\&D}\), and as a result it retains and reinvests all of its earnings. In other words, Barrett does not pay any dividends, and it has no plans to pay dividends in the near future. A major pension fund is interested in purchasing Barrett's stock. The pension fund manager 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 4 th year, free cash flow is projected to grow at a constant 7 percent. Barrett's WACC is 12 percent, its debt and preferred stock total to \$60 million, and it has 10 million shares of common stock outstanding. a. What is the present value of the free cash flows projected during the next 4 years? b. What is the firm's terminal value? c. What is the firm's total value today? d. What is an estimate of Barrett's price per share?

Short Answer

Expert verified
Use PV calculations for Years 1-4, Terminal Value with growth, and PV of Terminal Value to find total firm value; subtract debt for equity value; divide by shares for price/share.

Step by step solution

01

Calculate Present Value for Years 1-4

To find the present value (PV) of the free cash flows projected for the next 4 years, use the formula for Present Value: \[ PV = \frac{FCF_1}{(1 + r)^1} + \frac{FCF_2}{(1 + r)^2} + \frac{FCF_3}{(1 + r)^3} + \frac{FCF_4}{(1 + r)^4} \]Where:- \(FCF_1, FCF_2, FCF_3, FCF_4\) are the free cash flows for Years 1 to 4.- \(r\) is the discount rate, which is the WACC, 12% or 0.12.Substitute the given values:- \(FCF_1 = 3\) million, \(FCF_2 = 6\) million, \(FCF_3 = 10\) million, \(FCF_4 = 15\) million.Thus,\[ PV = \frac{3}{(1.12)^1} + \frac{6}{(1.12)^2} + \frac{10}{(1.12)^3} + \frac{15}{(1.12)^4} \]Calculate each term and sum them to find the PV for Years 1-4.
02

Calculate Terminal Value

The firm projects a constant growth rate of 7% after Year 4. Use the Gordon Growth Model (Perpetuity Growth Model) to calculate the Terminal Value at the end of Year 4:\[ TV = \frac{FCF_5}{r - g} \]Where:- \(FCF_5 = FCF_4 \times (1 + g) = 15 \times 1.07\)- \(g = 0.07\) (growth rate)- \(r = 0.12\) (discount rate)Use these values:\[ TV = \frac{15 \times 1.07}{0.12 - 0.07} \]This will give the Terminal Value at the end of Year 4.
03

Calculate Present Value of Terminal Value

Discount the Terminal Value back to present value by applying the discount formula:\[ PV_{TV} = \frac{TV}{(1 + r)^4} \]Substitute the calculated Terminal Value and discount rate:\[ PV_{TV} = \frac{TV}{(1.12)^4} \]
04

Calculate Total Firm Value

Add the present value of the free cash flows from Years 1-4 and the present value of the terminal value:\[ V_{Firm} = PV_{1-4} + PV_{TV} \]
05

Calculate Equity Value

Subtract the firm's total liabilities (debt and preferred stock) from the firm's total value to find the equity value:\[ Equity = V_{Firm} - Debt \ Debt = 60 \text{ million} \]
06

Calculate Price Per Share

Finally, divide the equity value by the number of shares outstanding to find the price per share:\[ Price \ per \ share = \frac{Equity}{\text{Number of shares}} \ \text{Number of shares} = 10 \text{ million} \]

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Key Concepts

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

Discounted Cash Flow (DCF)
The Discounted Cash Flow (DCF) method is a fundamental valuation technique used in financial management, offering a way to estimate the value of an investment based on its expected future cash flows. By projecting free cash flows over a specified period and discounting them back to their present value using the Weighted Average Cost of Capital (WACC), you can find out what the investment is worth today.

A key element to remember when using DCF is the discount rate, which in this case is the WACC. It reflects the opportunity cost, risk, and potential return an investor expects. For Barrett Industries, the free cash flows were projected as:
  • Year 1: \(3 million
  • Year 2: \)6 million
  • Year 3: \(10 million
  • Year 4: \)15 million
Each of these cash flows is discounted back to present value using the formula:

\[PV = \frac{FCF_1}{(1 + r)^1} + \frac{FCF_2}{(1 + r)^2} + \frac{FCF_3}{(1 + r)^3} + \frac{FCF_4}{(1 + r)^4} \]where \(r\) is the WACC, 12% in this scenario. This detailed process helps in determining the value of anticipated earnings from an investment today.
Terminal Value
Terminal Value represents the point at which a business's free cash flow projections start growing at a constant rate indefinitely. Typically used in valuation models, it accounts for the majority of a company's value and reflects a firm's capacity to generate cash flow over the long term.

In the case of Barrett Industries, after the first 4 years, the free cash flow is expected to grow continuously at 7% per year. Terminal Value is calculated using the Gordon Growth Model; it assumes a business will continue operating and generating cash flows well beyond the forecast period.

The formula for Terminal Value at the end of year 4 is:
\[TV = \frac{FCF_5}{r - g}\]where \(FCF_5 = FCF_4 \times (1 + g)\), \(g\) is the growth rate (7%), and \(r\) is the discount rate (12%). Calculating the Terminal Value is crucial because it allows investors to assess a company's value when it reaches a steady, perpetual growth phase.
Weighted Average Cost of Capital (WACC)
Weighted Average Cost of Capital (WACC) is a financial measure that represents a company鈥檚 average cost of capital from all sources, including equity, debt, and other funds. It is a critical component in the DCF model, acting as the discount rate to calculate the present value of expected future cash flows.

WACC is essential because it reflects the company鈥檚 cost to borrow money and thus serves as a proxy for the risk associated with its cash flows. For Barrett Industries, the WACC is 12%, suggesting that this is the required return rate for investors. It combines the cost of equity and cost of debt, weighted according to their respective use in the company鈥檚 capital structure.

The calculation of WACC involves:
  • Cost of Equity: The return required by equity investors given the risk of the company鈥檚 equity.
  • Cost of Debt: The effective rate that a company pays on its borrowed funds.
  • Proportions of each source of capital: Equity and debt weights in the company鈥檚 overall capital structure.
This measure ensures that the calculated present values in the DCF method are accurately adjusted for risk and potential return, guiding investment decisions effectively.

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Most popular questions from this chapter

Martell Mining Company's ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are rising. As a result, the company's earnings and dividends are declining at the constant rate of 5 percent per year. If \(\mathrm{D}_{0}=\$ 5\) and \(\mathrm{r}_{\mathrm{s}}=15 \%\), what is the value of Martell Mining's stock?

Assume that today is December \(31,2005,\) and the following information applies to Vermeil Airlines: \(\bullet\) After-tax operating income [EBIT(1 - T), also called NOPAT] for 2006 is expected to be \$500 million. \(\bullet\) The depreciation expense for 2006 is expected to be \(\$ 100\) million. \(\bullet\) The capital expenditures for 2006 are expected to be \(\$ 200\) million. \(\bullet\) No change is expected in net operating working capital. \(\bullet\) The free cash flow is expected to grow at a constant rate of 6 percent per year. \(\bullet\) The required return on equity is 14 percent. \(\bullet\) The WACC is 10 percent. \(\bullet\) The market value of the company's debt is \(\$ 3\) billion. \(\bullet\) 200 million shares of stock are outstanding. Using the free cash flow approach, what should the company's stock price be today?

C's beta coefficient is \(\mathrm{b}_{\mathrm{C}}=0.4,\) while Stock D's is \(\mathrm{b}_{\mathrm{D}}=-0.5 .\) (Stock \(\mathrm{D}^{\prime}\) s beta is negative, indicating that its return rises when 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 7 percent and the expected rate of return on an average stock is 11 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 would happen if the stock is not in equilibrium.

Smith Technologies is expected to generate \(\$ 150\) million in free cash flow next year, and \(\mathrm{FCF}\) is expected to grow at a constant rate of 5 percent per year indefinitely. Smith has no debt or preferred stock, and its WACC is 10 percent. If Smith has 50 million shares of stock outstanding, what is the stock's value per share?

Investors require a 15 percent rate of return on Levine Company's stock (that is, \(r_{s}=15 \%\) ). a. What is its value if the previous dividend was \(\mathrm{D}_{0}=\$ 2\) and investors expect dividends to grow at a constant annual rate of \((1)-5\) percent, (2) 0 percent, (3) 5 percent, or (4) 10 percent? b. Using data from part a, what would the Gordon (constant growth) model value be if the required rate of return were 15 percent and the expected growth rate were (1) 15 percent or (2) 20 percent? Are these reasonable results? Explain. c. Is it reasonable to think that a constant growth stock could have \(g>r_{s}\) ?
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