Chapter 8, Problem 1Q

Define each of the following terms:

1. a. Proxy; proxy fight; preemptive right; classified stock; founders’ shares
2. b. Free cash flow valuation model, value of operations; nonoperating assets
3. c. Constant growth model; horizon date and horizon value
4. d. Multistage valuation model
5. e. Estimated value $\left({\hat{\text{P}}}_0\right)$; market price (P₀)
6. f. Required rate of return, r_s; expected rate of return, ${\hat{\text{r}}}_{\text{s}}$; actual, or realized, rate of return, ${\bar{\text{r}}}_{\text{s}}$
7. g. Capital gains yield; dividend yield; expected total return
8. h. Preferred stock

Summary Introduction

To determine: The definition of proxy, proxy fight, preemptive right, classified stock and founders shares.

Explanation of Solution

 A proxy is a document that authorizes one person to act for another, usually the power to vote common stock shares. If earnings are low and stockholders are unhappy, an outside party can use the proxies to overthrow management and take control of the business, known as a proxy struggle. The right of preemption grants the current owners the right to buy any new shares issued in proportion to their existing holdings. State law may or may not allow the right to preemption. The preemptive right, if granted, allows existing owners to retain their proportionate share of ownership and control of the company. It also prohibits the sale to new stockholders of stocks at low prices that would dilute the value of the previously issued securities. Sometimes a company creates segregated inventory to meet special needs and circumstances. Typically, one category is referred to as "Class A" when special stock classifications are used, another as "Class B," and so on. Class A can be entitled to collect dividends until Class B securities can pay dividends. Class B could be eligible to vote exclusively. Founders' shares are stock held by the owners of the company with exclusive voting rights with restricted dividends for a defined number of years.

Summary Introduction

To determine: The definition of free cash flow valuation method, value of operations, and non-operating assets.

Explanation of Solution

The free cash flow model describes a company's total value as operating value plus non-operating asset value. The operating value is the present value of all the expected future free cash flows when measured at the weighted average capital cost:

${\text{V}}_{\text{op(at}\text{time}\text{0)}}={\displaystyle \sum _{\text{t}=\text{1}}^{\infty }\frac{{\text{FCF}}_{\text{t}}}{{\left(\text{1}+\text{WACC}\right)}^{\text{t}}}}$

Investments in marketable securities and non-controlling interests in other companies ' shares and other financial instruments are non-operating assets.

Summary Introduction

To determine: The definition of constant growth model, horizon date and horizon value.

Explanation of Solution

Constant growth happens when the profits, dividends and free cash flows of a company are increasing at a steady long-term pace. The constant growth method can be used in this situation to estimate the present value of the rising cash flows or dividends. The current value of free cash flows is:

$\begin{array}{c}{\text{V}}_{\text{op}\left(\text{constant growth}\right)}=\frac{{\text{FCF}}_1}{\text{WACC}-{\text{g}}_{\text{L}}}=\frac{{\text{FCF}}_0\left(1+{\text{g}}_{\text{L}}\right)}{\text{WACC}-{\text{g}}_{\text{L}}}\\ \text{when applied to dividend, the model is:}\\ {\text{P}}_0=\frac{{\text{D}}_{\text{0}}\text{(1}+{\text{g}}_{\text{L}}\text{)}}{{\text{r}}_{\text{s}}-{\text{g}}_{\text{L}}}=\frac{{\text{D}}_{\text{1}}}{{\text{r}}_{\text{s}}-{\text{g}}_{\text{L}}}\end{array}$

The horizon date in a cash flow forecast is the last year.  During the forecast period, cash flows can rise unevenly, but are assumed to increase at a constant rate after the horizon date for all periods. The horizon price, when discounted back to the horizon date, is the value of all cash flows beyond the horizon date. The horizon value is the value of operations at the close of the defined forecast period as applied to free cash flows. It is equal to the present value of all free cash flows beyond the forecast period, calculated at the weighted average cost of capital back to the end of the forecast period. Since growth is constant after the horizon, the constant growth model can be applied at horizon date.

${\text{HV}}_{\text{T}}={\text{V}}_{\text{op(at}\text{time}\text{T)}}=\frac{{\text{FCF}}_{\text{T}+\text{1}}}{\text{WACC}-{\text{g}}_{\text{L}}}=\frac{{\text{FCF}}_{\text{T}}\text{(1}+{\text{g}}_{\text{L}}\text{)}}{\text{WACC}-{\text{g}}_{\text{L}}}\text{.}$

Once applied to dividends, the horizon value at the conclusion of the specified forecast period is the intrinsic stock price. It is equal to the present value of all dividends beyond the forecast period, discounted at the required rate of return on stock back to the end of the forecast period. Because growth is constant after the horizon, the constant growth model can be applied at the horizon date:

$\begin{array}{c}\text{Horizon value for stock}=\frac{{\text{D}}_{\text{T+1}}}{{\text{r}}_{\text{s}}-{\text{g}}_{\text{L}}}\\ =\frac{{\text{D}}_{\text{T}}\left({\text{1+g}}_{\text{L}}\right)}{{\text{r}}_{\text{s}}-{\text{g}}_{\text{L}}}\end{array}$

Summary Introduction

To determine: The definition of multistage valuation model.

Explanation of Solution

When the growth rate is stable for several years before becoming constant, a multi-stage model is used. In this case, when the growth rate has become constant, the constant growth model will be applied at the end of the forecast horizon. The cumulative present value of cash flows in the forecast periods plus the present value of the horizon value is the present value of all cash flows:

${\text{V}}_{\text{op, 0}}={\displaystyle \sum _{\text{t}=\text{1}}^{\text{T}}\frac{{\text{FCF}}_{\text{t}}}{{\text{(1}\text{}+\text{WACC)}}^{\text{t}}}}\text{+}\frac{{\text{HV}}_{\text{T}}}{{\text{(1}+\text{WACC)}}^{\text{T}}}$

When applied to dividends, the present value of dividends is:

${\text{P}}_{\text{0}}={\displaystyle \sum _{\text{t}=\text{1}}^{\text{T}}\frac{{\text{D}}_{\text{t}}}{{\text{(1}+{\text{r}}_{\text{s}}\text{)}}^{\text{t}}}}\text{+}\frac{{\widehat{\text{P}}}_{\text{T}}}{{\text{(1}+{\text{r}}_{\text{L}}\text{)}}^{\text{T}}}$

Summary Introduction

To determine: The definition of estimated value and market price.

Explanation of Solution

Estimated value is the present value of the potential cash flows expected. The market price (P0) is the price of selling an asset.

Summary Introduction

To determine: The definition of required rate of return, expected rate of return, and realized rate of return.

Explanation of Solution

The required rate of return on the common stock, denoted by rs, is the minimum acceptable rate of return, taking into account both its riskiness and other investment returns. The expected return rate, denoted by ^rs, is the expected return rate on the stock due to its current price and expected future cash flows. If the stock is in balance, the appropriate return rate will be equal to the expected return rate. The (actual) rate of return realized, denoted by ̄rs, is the rate of return actually achieved at the end of a holding period. While expected and required return rates must always be positive, realized return rates may be negative over certain periods.

Summary Introduction

To determine: The definition of capital gains yield, dividend yield, and expected total return.

Explanation of Solution

The capital gains are the product of price changes and are measured as $\frac{\left({\text{P}}_1-{\text{P}}_0\right)}{{\text{P}}_0}$. Where P0 is the price of the start of the period and P1 is the price of the end of the period. The return on capital gains is g, the constant rate of growth, for a constant growth inventory. The dividend yield on stock can either be specified as the end-of-period dividend divided by the start-of-period value, or the current dividend ratio to the current price. Using the former interpretation of valuation formulas. The estimated total return, or projected return rate, is the expected return on assets plus the expected return on an inventory of dividends. The maximum future return on a bond is the maturity yield.

Summary Introduction

To determine: The definition of preferred stock.

Explanation of Solution

Preferred stock is a hybrid—it is similar in some respects to bonds and in other ways to common stock. Until common stock dividends may be paid, preferred dividends are similar to interest payments on bonds as they are set in size and typically have to be paid. If the preferred dividend is not received, it may be withheld without the company being thrown into bankruptcy by the directors. Therefore, although preferred stock has a bond-like fixed payment, failure to make this payment will not lead to bankruptcy. Many preferred securities have the right to annual fixed dividend payments from their owners.