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Problem Set #7

Question 1Quest Financial services balance sheets report $200 million in total debt, $100 million in short-term investments, and $30 million in preferred stock. Quest has 10 million shares of common stock outstanding. A financial analyst estimated that Quest’s value of operations is $1000 million. What is the analyst’s estimate of the intrinsic stock price per share?

Question 2Lincoln Incorporated is expected to pay a $4.5 per share dividend at the end of this year (i.e., D1 = $4.50). The dividend is expected to grow at a constant rate of 5% a year. The required rate of return on the stock is, rs, is 12%. What is the estimated value per share of Boehm stock?

Question 3Assume that the average firm in Masters Corporation’s industry is expected to grow at a constant rate of 3% and that its dividend yield is 5%. Masters is about as risky as the average firm in the industry and just paid a dividend (D0) of $2.5. Analysts expect that the growth rate of dividends will be 25% during the first year (g0,1 = 25%) and 10% during the second year (g1,2 = 10%). After Year 2, dividend growth will be constant at 5%. What is the required rate of return on Masters’s stock? What is the estimated intrinsic per share?

Question 4Several years ago, Macro Riders issued preferred stock with a stated annual dividend of 5% of its $600 par value. Preferred stock of this type currently yields 10%. Assume dividends are paid annually.

What is the estimated value of Macro’s preferred stock?
Suppose interest rate levels have risen to the point where the preferred stock now yields 14%. What would be the new estimated value of Macro’s preferred stock?

Submit your answers in a Word document.

Corporate Valuation and Stock Valuation

CHAPTER 7

© 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Topics in Chapter
Features of common stock
Valuing common stock
Dividend growth model
Free cash flow valuation model
Market multiples
Preferred stock

Corporate Valuation and Stock Valuation

Common Stock: Owners, Directors, and Managers
Represents ownership.
Ownership implies control.
Stockholders elect directors.
Directors hire management.
Since managers are “agents” of shareholders, their goal should be: Maximize stock price.

Classified Stock
Classified stock has special provisions for each class, usually involving voting rights and dividend rights.
Usually named Class A, Class B, etc.
New shares in IPO sometimes have voting restrictions but full dividend rights.
Founders’ shares usually have voting rights but dividend restrictions.
Standard & Poor’s no longer allows new additions to its indices to have classified stock.

Tracking Stock
The dividends of tracking stock are tied to a particular division, rather than the company as a whole.
Investors can separately value the divisions.
Its easier to compensate division managers with the tracking stock.
But tracking stock usually has no voting rights, and the financial disclosure for the division is not as regulated as for the company.
Very few companies have tracking stock.

Different Approaches for Valuing Common Stock
Free cash flow model
Constant growth
Nonconstant growth
Dividend growth model
Constant growth
Nonconstant growth
Using the multiples of comparable firms

The Free Cash Flow Valuation Model: FCF and WACC
Free cash flow (FCF) is:
The cash flow available for distribution to all of a company’s investors.
Generated by a company’s operations.
The weighted average cost of capital (WACC) is:
The overall rate of return required by all of the company’s investors.

Value of Operations (Vop)
The PV of expected future FCF, discounted at the WACC, is the value of a company’s operations (Vop):

Sources of Value
Value of operations
Nonoperating assets
Short-term investments and other marketable securities
Ownership of non-controlling interest in another company
Value of nonoperating assets usually is very close to figure that is reported on balance sheets.

Claims on Corporate Value
Debtholders have first claim.
Preferred stockholders have the next claim.
Any remaining value belongs to stockholders.

Total Corporate Value: Sources and Claims

Value of operations= PV of FCF discounted
at WACC

Conceptually correct, but how do you find the present value of an infinite stream?

Suppose FCFs are expected to grow at a constant rate, gL, starting at t=1, and continue forever. What happens to FCF?

What is the value of operations if FCFs grow at a constant rate? See next slide.

Value of operations in terms of FCF1 and gL:

We can multiply and divide by (1+gL), for a reason that will soon be clear, as shown on the next slide.

Rewritten value of operations:

We can group , as shown on the next slide.

Value of operations with grouped terms:

We can group the terms, as shown on the next slide.

Value of operations if FCF grows
at a constant rate:

What happens toif t gets large? It depends on the size of gL relative to WACC. See next slide.

What happens to as t gets large?
If gL < WACC: Then < 1. If gL ≥ WACC: Then ≥ 1. What happens to the value of operations if gL ≥ WACC? See next slide. © 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. What happens to the value of operations if gL ≥ WACC? Vop = (Big) + (Bigger) + (Even Bigger) + …+ (Really big!) = Infinity! So g can’t be greater than or equal to WACC! © 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. What happens to the value of operations if gL ≤ WACC? Vop = (Small) + (Smaller) + (Even smaller) + …+ FCF0 (Really small!) = ? All the terms get smaller and smaller, but what happens to the sum? See next slide © 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. What is the sum of an infinite number of factors that get smaller at a geometric rate? Consider this example. The first row is t. The second row is a number that is less than 1 that is compounded to the power of t. The third row is the cumulative sum. t 1 2 3 4 . . . ∞ (1/2)t 1/2 1/4 1/8 1/16 1/∞ ≈ 0 Σ(1/2)t 1/2 3/4 7/8 15/16 ≈ 1 This sum converges to 1. Similarly, converges (although not to 1). See next slide. © 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Constant Growth Formula for Value of Operations: gL begins at Time 1 If FCF are expected to grow at a constant rate of gL from Time 1 and afterwards, and gL 8.26%
The higher ROIC causes a big increase in Vop,0.

Impact of Lower Capital Requirements
No Change Improve CR
g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
g3,4 5% 5%
gL 5% 5%
OP 4.5% 4.5%
CR 56.0% 51.0%
ROIC 8.0% 8.8%
Vop,0 $958 $1,191
WACC 9.00% 9.00%

Lower capital requirements increases the ROIC.
ROIC of 8.8% > 8.26%
The higher ROIC causes an increase in Vop,0.

Impact of Simultaneous Improvements in OP and CR
No Change Improve OP and CR
g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
g3,4 5% 5%
gL 5% 5%
OP 4.5% 5.5%
CR 56.0% 51.0%
ROIC 8.0% 10.8%
Vop,0 $958 $1,756
WACC 9.00% 9.00%

The ROIC is much higher due to the improvements in operations.

Impact of Simultaneous Improvements in Growth, OP, and CR
No Change Improve All
g0,1 10% 11%
g1,2 8% 9%
g2,3 5% 6%
g3,4 5% 6%
gL 5% 6%
OP 4.5% 5.5%
CR 56.0% 51.0%
ROIC 8.0% 10.8%
Vop,0 $958 $2,008
WACC 9.00% 9.00%

The ROIC is much higher due to the improvements in operations.
With a higher ROIC, growth adds substantial value.

Summary: Value of operations for previous combinations of ROIC and gL
ROIC ROIC ROIC ROIC ROIC
8.0% 8.8% 9.8% 10.8%
gL 5% $958 $1,191 $1,523 $1,756
gL 6% $933 $1,247 $1,694 $2,008

The ROIC is much higher due to the improvements in operations.
With a higher ROIC, growth adds substantial value.

Are volatile stock prices consistent with rational pricing?
The previous slide shows that small changes in ROIC and growth cause large changes in value.
Similarly, small changes in the cost of capital (WACC), perhaps due to changes in risk or interest rates, cause large changes in value.
As new information arrives, investors continually update their estimates of operating profitability, capital requirements, growth, risk, and interest rates.
If stock prices aren’t volatile, then this means there isn’t a good flow of information.

Value of dividend-paying stock = PV of dividends discounted at required return

Conceptually correct, but how do you find the present value of an infinite stream?

Suppose dividends are expected to grow at a constant rate, gL, forever.
D1 = D0(1 + gL)1
D2 = D0(1 + gL)2
Dt = D0(1 + gL)t
What is the present value of a constant growth Dt when discounted at the stock’s required return, rs? See next slide.

Present Value of a Constant Growth Dividend

What happens to as t gets bigger?
If gL rs?

So gL must be less than rs for the constant growth model to be applicable!!

Required rate of return: beta = 1.2, rRF = 7%,
and RPM = 5%.
Use the SML to calculate rs:

Estimated Intrinsic Stock Value:
D0 = $2.00, rs = 13%, gL = 6%

Expected Stock Price in 1 Year

Expected Dividend Yield and Capital
Gains Yield (Year 1)

Total Year 1 Return
Total return = Dividend yield + Capital gains yield.
Total return = 7% + 6% = 13%.
Total return = 13% = rs.
For constant growth stock:
Capital gains yield = 6% = gL.

Rearrange model to rate of return form:

Nonconstant Growth Stock
Nonconstant growth of 30% for Year 0 to Year 1, 25% for Year 1 to Year 2, 15% for Year 2 to Year 3, and then long-run constant gL = 6%.
Can no longer use constant growth model.
However, growth becomes constant after 3 years.

Steps to Estimate Current Stock Value
Forecast dividends for nonconstant period, which ends at horizon date after which growth is constant at gL.
Find horizon value, which is PV of dividends beyond horizon date discounted back to horizon date
Horizon value = =

Steps to Estimate Current Stock Price (Continued)
Find PV of each dividend in the forecast period.
Find PV of horizon value.
Sum PV of dividends and PV of horizon value.
Result is estimated current stock value.

Example of Estimating Current Stock Value (D0 = $2.00, rs = 13%)

Expected Dividend Yield and Capital
Gains Yield (t = 0)

Expected Dividend Yield and Capital Gains Yield (after t = 3)
During nonconstant growth, dividend yield and capital gains yield are not constant.
If current growth is greater than g, current capital gains yield is greater than g.
After t = 3, gL = constant = 6%, so the
capital gains yield = 6%.
Because rs = 13%, after t = 3 dividend
yield = 13% – 6% = 7%.

Using Stock Price Multiples to Estimate
Stock Price
Analysts often use the P/E multiple (the price per share divided by the earnings per share).
Example:
Estimate the average P/E ratio of comparable firms. This is the P/E multiple.
Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price.

Using Entity Multiples
The entity value (V) is:
the market value of equity (# shares of stock multiplied by the price per share)
plus the value of debt.
Pick a measure, such as EBITDA, Sales, Customers, Eyeballs, etc.
Calculate the average entity ratio for a sample of comparable firms. For example,
V/EBITDA
V/Customers

Using Entity Multiples (Continued)
Find the entity value of the firm in question. For example,
Multiply the firm’s sales by the V/Sales multiple.
Multiply the firm’s # of customers by the V/Customers ratio
The result is the firm’s total value.
Subtract the firm’s debt to get the total value of its equity.
Divide by the number of shares to calculate the price per share.

Problems with Market Multiple Methods
It is often hard to find comparable firms.
The average ratio for the sample of comparable firms often has a wide range.
For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers?

Comparing the FCF Model and Dividend
Growth Model
Can apply FCF model in more situations:
Privately held companies
Divisions of companies
Companies that pay zero (or very low) dividends
FCF model requires forecasted financial statements to estimate FCF
Takes more effort than just forecasting dividends, but…
Provides more insights into value drivers.

Preferred Stock
Hybrid security.
Similar to bonds in that preferred stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock.
However, unlike bonds, preferred stock dividends can be omitted without fear of pushing the firm into bankruptcy.

Value of Preferred Stock
(Dividend = $2.10; rps = 7%)

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