discussion 7

Chapter7-StocksStockValuationandStockMarketEquilibrium..pptx

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Corporate Valuation and Stock Valuation

CHAPTER 7

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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.

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!

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

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.

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<WACC:

This is the PV of all FCF from Time 1 through infinity, when discounted at WACC.

Constant Growth Formula for Value of Operations: gL begins at Time 0

If FCF are expected to grow at a constant rate of gL from Time 0 and afterwards, and gL<WACC:

This is still the PV of all FCF from Time 1 through infinity, when discounted at WACC.

Data for FCF Valuation

FCF0 = $24 million

WACC = 11%

FCF is expected to grow at a constant rate of gL = 5%

Short-term investments = $100 million

Debt = $200 million

Preferred stock = $50 million

Number of shares =n = 10 million

Find Value of Operations

Total Value of Company (VTotal)

Estimated Intrinsic Value of Equity (VEquity)

Voperations	$420.00
+ ST Inv.	100.00
VTotal	$520.00
−Debt	200.00
− Preferred Stk.	50.00
VEquity	$270.00

Estimated Intrinsic Stock Price per Share, (1 of 2)

Voperations`	$420.00
+ ST Inv.	100.00
VTotal	$520.00
−Debt	200.00
− Preferred Stk.	50.00
VEquity	$270.00
 n	10
	$27.00

Expansion Plan: Nonconstant Growth

Finance expansion financed by owners.

Projected free cash flows (FCF):

Year 1 FCF = −$10 million.

Year 2 FCF = $20 million.

Year 3 FCF = $35 million

FCF grows at constant rate of 5% after year 3.

No change in WACC, marketable securities, debt, preferred stock, or number of shares of stock.

Estimating the Value of Operations

Free cash flows are forecast for three years in this example, so the forecast horizon is three years.

Growth in free cash flows is not constant during the forecast, so we can’t use the constant growth formula to find the value of operations at time 0.

Time Line of FCF

Year	0	1	2	3	4	5	… t
FCF		−$10	$20	$35	FCF3(1+gL)	FCF4(1+gL)	FCFt(1+gL)

Free cash flows are forecast for three years in this example, so the forecast horizon is three years.

Growth in free cash flows is not constant during the forecast, so we can’t use the constant growth formula to find the value of operations at time 0.

Horizon Value

Year	0	1	2	3	4	5	… t
FCF					FCF3(1+gL)	FCF4(1+gL)	FCFt(1+gL)
				HV3	← ↵	← ↵	← ↵

Horizon value is also called terminal value, or continuing value.

Horizon Value Application (FCF3 = $35, WACC = 11%, gL = 5%)

This is the value of FCF from Year 4 and beyond discounted back to Year 3.

Value of Operations at t=0: PV of FCF1 through FCF3 plus PV of HV3

Year	0	1	2	3	4	5	… t
FCF		FCF1	FCF2	FCF3
	PV of FCF in explicit forecast	← ↵	← ↵	← ↵	FCF3(1+gL)	FCF4(1+gL)	FCFt(1+gL)
	+			HV3	← ↵	← ↵	← ↵
	PV of HV	← ↵	← ↵	← ↵
	= Value of operations Time 0

PV of HV is the PV of FCF beyond the explicit forecast. So PV of HV plus PV of FCF in explicit forecast is the PV of all future FCFs.

Application: Current Value of Operations (Nonconstant g in FCF until after Year 3; gL = 5%; WACC = 11%)

Estimated Intrinsic Stock Price per Share, (2 of 2)

Voperations	$480.67
+ ST Inv.	100.00
VTotal	$580.67
−Debt	200.00
− Preferred Stk.	50.00
VEquity	$330.67
÷ n	10
	$33.07

How much of the value of operations is based on cash flows from Year 4 and beyond?

The horizon value is the value of all FCF from Year 4 and beyond, discounted back to Year 3.

The present value of HV3 is the present value of all FCF from Year 4 and beyond.

The PV of HV3 is the percent of total value due to long-term cash flows.

Value of Operations and Present Value of Horizon Value

Value of operations: Vop = $480.67

Horizon value: HV3 = $612.5

PV of HV3 = $612.5/(1 + 0.11)3

= $447.855

Percent of Value Due to Long-Term Cash Flows

In this example, 93% of value is due to cash flows 4 or more years into the future.

For the average company, this percentage is around 80%.

Long-term versus Short-term Focus

Why focus on quarterly earnings if most value is from longer-term cash flows?

Changes in quarterly earnings can signal changes future in cash flows. This would affect the current stock price.

Managers often have bonuses tied to quarterly earnings, so they have incentive to manage earnings.

Forecasting Free Cash Flows: A Simple Approach

Forecast sales to grow at chosen growth rates.

Forecast net operating profit after taxes (NOPAT) and total net operating capital (OpCap) as a percent of sales.

Current Situation (in millions)

Most recent data:

Sales of $2,000

Total net operating capital, OpCap = $1,120

Operating profitability ratio

OP = NOPAT/Sales = 4.5%

Capital requirement ratio

CR = OpCap/Sales = 56%.

The target weighted average cost of capital (WACC) is 9%.

Initial Operating Assumptions for the No Change Scenario

Operating ratios remain unchanged from values in most recent year.

Sales will grow by 10%, 8%, 5%, and 5% for the next four years.

The long-term growth rate in sales is 5%.

The target weighted average cost of capital (WACC) is 9%.

Assumptions

	Actual	Forecast
Inputs	0	1	2	3	4
WACC	9.0%
Sales	$2,000
OpCap	$1,120
Sales growth rate		10%	8%	5%	5%
NOPAT/Sales	4.5%	4.5%	4.5%	4.5%	4.5%
OpCAP/Sales	56.0%	56.0%	56.0%	56.0%	56.0%

Examples of Forecasting Items

Sales1 = $2,000(1+0.10) = $2,200

NOPAT1 = $2,200(0.045) = $99

OpCap1 = $2,200(0.56) = $1,232

FCFt = NOPATt − (OpCapt − OpCapt-1)

ROICt = NOPATt/OpCapt

Forecasted FCF: No changes in operating ratios

Scenario: No Change	Actual	Forecast
	0	1	2	3	4
Sales	$2,000	$2,200	$2,376	$2,495	$2,620
NOPAT		$99	$107	$112	$117.879
OpCap	$1,120	$1,232	$1,331	$1,397.088	$1,466.942
FCF		−$13	$8.36	$45.738	$48.025
Growth in FCF			-164%	447.1%	5.0%
ROIC	8.0%	8.0%	8.0%	8.0%	8.0%

FCF is negative in Year 1.

ROIC of 8% is less than WACC of 9%--not good!

Note: There is no rounding in intermediate calculations.

Estimated Intrinsic Value (1 of 2)

Estimated Intrinsic Value (2 of 2)

Scenario: No Change
Horizon Value:
HV4 =	$1,260.65
Value of Operations:
Present value of HV	$893.08
+ Present value of FCF	$64.45
Value of operations ≈	$958

The Value of Operations versus the Total Net Operating Capital

The ROIC (8%) is too low compared to the WACC (9%).

The capital is not earning enough to meet investors’ required return, so:

Horizon value ($958) is less than the total net operating capital at the horizon ($1,467).

Current value of operations ($958) is less than the current total net operating capital ($1,120).

ROIC must be greater than WACC/(1+gL) for horizon value to be greater than the total net operating capital at the horizon.

Value Drivers

The ROIC (8%) is too low compared to the WACC (9%).

The capital is not earning enough to meet investors’ required return, so:

Horizon value ($958) is less than the total net operating capital at the horizon ($1,467).

Current value of operations ($958) is less than the current total net operating capital ($1,120).

ROIC must be greater than WACC/(1+gL) for horizon value to be greater than the total net operating capital at the horizon.

Impact of Higher Growth Rates

	No Change	Improve Growth
g0,1	10%	11%
g1,2	8%	9%
g2,3	5%	6%
g3,4	5%	6%
gL	5%	6%
OP	4.5%	4.5%
CR	56.0%	56.0%
ROIC	8.0%	8.0%
Vop,0	$958	$933
WACC	9.00%	9.00%

Higher growth causes Vop,0 to fall.

ROIC must be greater than WACC/(1+WACC) for growth to add value.

WACC/(1+WACC) = 8.26%

Impact of Higher Operating Profitability

	No Change	Improve OP
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%	56.0%
ROIC	8.0%	9.8%
Vop,0	$958	$1,523
WACC	9.00%	9.00%

Higher operating profitability increases the ROIC.

ROIC of 9.8% > 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: Then < 1.

So the bracket approaches zero as t gets large.

Constant Dividend Growth Model (gL<rs)

If gL is constant and less than rs, then converges to:

What happens 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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