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Growth Opportunities Rite Bite Enterprises sells toothpicks. Gross revenues last year were \$6 million, and total costs were \(\$ 3.1\) million. Rite Bite has 1 million shares of common stock outstanding. Gross revenues and costs are expected to grow at 5 percent per year. Rite Bite pays no income taxes. All earnings are paid out as dividends. 1\. If the appropriate discount rate is 15 percent and all cash flows are received at year's end, what is the price per share of Rite Bite stock? 2\. Rite Bite has decided to produce toothbrushes. The project requires an immediate outlay of \(\$ 22\) million. In one year, another outlay of \(\$ 8\) million will be needed. The year after that, earnings will increase by \(\$ 7\) million. That profit level will be maintained in perpetuity. What effect will undertaking this project have on the price per share of the stock?

Step by step solution

01

Calculate the dividend per share

Last year's gross revenue: $6,000,000 Last year's total costs: $3,100,000 Earnings last year (since all are paid out as dividends): \(6,000,000 - \)3,100,000 = $2,900,000 Number of shares outstanding: 1,000,000 Dividend per share (DPS) = Earnings / Number of shares = $2,900,000 / 1,000,000 = \$2.9

02

Calculate the price per share

Growth rate of revenues and costs (g): 5% or 0.05 Discount rate (r): 15% or 0.15 Price per share (P) = DPS / (r - g) = \$2.9 / (0.15 - 0.05) = \$29 Now, we will find out the effect of the toothbrush project on the price per share.

03

Calculate the net present value (NPV) of the toothbrush project

Initial outlay: $22,000,000 Second outlay (in one year): $8,000,000 Increment in earnings from the second year onwards (in perpetuity): $7,000,000 We will calculate the present value of these cash flows and find the NPV. PV(Second outlay) = \(\$ 8,000,000 / (1 + 0.15) = \$ 6,956,522\) PV(Increment in earnings) = \(\$ 7,000,000 / 0.1 = \$ 70,000,000\) NPV = Initial outlay + PV(Second outlay) + PV (Increment in earnings) NPV = \((- \$ 22,000,000) + (- \$ 6,956,522) + \$ 70,000,000 = \$ 41,043,478\)

04

Adjust the price per share for the toothbrush project

The NPV of the toothbrush project is positive, which means it will add value to the firm. Increase in firm value = \(\$ 41,043,478\) Increase in price per share = Increase in firm value / Number of shares = \(\$ 41,043,478 / 1,000,000 = \$ 41.04\) Price per share after the toothbrush project = Old price per share + Increase in price per share = \(\$ 29 + \$ 41.04 = \$ 70.04\) In conclusion, the price per share of Rite Bite stock currently is \(\$ 29\). If the toothbrush project is undertaken, the price per share will increase to \(\$ 70.04\).

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Key Concepts

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

Net Present Value (NPV)

Net Present Value or NPV is a financial evaluation method that determines the profitability of an investment project.
It calculates the difference between the present values of cash inflows and outflows over a period of time. A positive NPV indicates a profitable project, while a negative NPV suggests a loss.
The formula for NPV is:\[NPV = \sum \frac{R_t}{(1 + r)^t} - C_0\]Where:

• \(R_t\) is the net cash inflow during the period \(t\)
• \(r\) is the discount rate
• \(t\) is the period number
• \(C_0\) is the initial investment cost

In the Rite Bite Enterprises scenario, the NPV of the toothbrush project was calculated as $41,043,478. This positive NPV suggested that introducing toothbrushes would add value to the company and justify increasing the stock price.

Dividend Discount Model

The Dividend Discount Model (DDM) is a method used for valuing a company's stock price based on the theory that its value equates to the sum of all future dividend payments, discounted back to their present value.
This model assumes that dividends will continue to grow at a consistent rate.
For a company paying consistent dividends, the formula is:\[P_0 = \frac{D_1}{r - g}\]Where:

• \(P_0\) is the current stock price
• \(D_1\) is the expected annual dividend next year
• \(r\) is the required rate of return
• \(g\) is the growth rate of dividends

In the context of Rite Bite Enterprises, with a perpetual growth rate of 5% and a discount rate of 15%, the stock price was determined using this model. The consistent 5% growth in revenues and costs facilitated an easier calculation of future dividends.

Perpetuity

A perpetuity is a type of financial instrument that pays a constant cash flow indefinitely. It is crucial in stock valuation as it helps in valuing cash flows that a company or investment is expected to deliver perpetually.
A perpetuity does not have an end date, unlike regular cash flows which occur over finite periods.
The formula for calculating the present value of a perpetuity is:\[PV = \frac{C}{r}\]Where:

• \(PV\) is the present value of the perpetuity
• \(C\) is the cash flow per period
• \(r\) is the discount rate

In Rite Bite's new toothbrush project, the constant increment in earnings from the second year onwards, expressed as perpetuity ($7 million), was crucial in determining the project's NPV and its contribution to the rise in stock price.

Stock Valuation

Stock valuation involves determining the intrinsic value of a company's shares to assess its current price in the market.
This evaluation helps investors make informed decisions about buying or selling stocks.
Several methods exist for stock valuation, including discounted cash flow (DCF), price-to-earnings ratio, and of course, the dividend discount model discussed earlier. For Rite Bite Enterprises, stock valuation was crucial to establish the share price based on expected cash flows, growth rates, and other strategic business decisions like the toothbrush project. It required careful calculation of future earnings and their impact on stock worth. Understanding these concepts enabled the calculation of Rite Bite's stock value, illustrating its fundamental worth with and without the new project.