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Class outline

- Sequential Valuation
- The Country Motel Case

Motivation

- So far, we discussed the fundamental principles of valuation
- TVM concepts, FCF analysis, etc.

- Now, we get into the details of DCF valuation, our primary valuation technique
- Topics covered in this chapter:
- Sequential valuation
- Valuation rules (“What to discount with what?”)

The concept of Sequential Valuation

- Firms issue multiple securities that differ in terms of “seniority” of their claims
- Sequential valuation:
- First, determine “intrinsic” value of the firm
- Divide this value among different security holders:
- Start with senior-most claims, move to less senior claims
- Finally, value the residual claim, namely, equity

Sequential Valuation Methodology

- To value a firm, you must project the firm’s cash flows forever
- This is typically done by dividing the firm’s life into two periods
- Non-constant growth period (Non-stable period)
- Cash flows in near-term

- Constant growth period (Stable period)
- Cash flows forever

- Non-constant growth period (Non-stable period)

Non-constant growth stage

- Volatile growth rates
- The firm may go through many different growth cycles

- When does this period end?
- Only when we can assume that growth is stable and will remain unchanged

- How to value cash flows in this period?
- Estimate cash flows for all years individually
- Discount cash flows

Constant growth stage

- Once the non-constant growth period ends, the constant growth period begins
- To value the firm in this stage, we must calculate a Terminal Value
- The value of all cash flows occurring in the constant growth period at the beginning of this period
- Then, this value must be discounted to t = 0

- How can we compute terminal value?
- If we can estimate constant growth rate – Use perpetuity formula
- If we cannot estimate constant growth rate – Use an Exit multiple

Three rules for valuing a firm’s cash flows

- Rule 1
- Different cash flows have different discount rates

- Rule 2
- Be consistent in your treatment of inflation

- Rule 3
- Consider the timing of the cash flows

Rule 1: Different cash flows have different discount rates

- A firm could have different divisions with different risk levels
- Some cash flows are certain and others are uncertain or riskier
- Example: If you know you will have $20,000 depreciation for the next 10 years and the tax rate is 30%, then the depreciation tax shield is a riskless cash flow

- General guidelines
- Use risk-adjusted discount rate to value risky cash flows
- Use risk-free discount rate to value riskless cash flows

Rule 2: Be consistent in your treatment of inflation

- The matching principle:
- Use nominal cash flows and a discount rate that accounts for inflation
- Use real cash flows and a discount rate that excluding the effect of inflation

Rule 3: Consider the timing of the cash flows

- So far we have assumed that cash flows being discounted are year-end cash flows
- In reality, a firm’s cash flows related to sales, COGS, investments and taxes are paid and received throughout the year

- Best approximation: Mid-year discounting
- i.e., assume that CFs accumulate at mid-year

In-class exercise

- A firm’s FCF is expected to grow at a nominal rate of 14% for 3 years, after which growth will stabilize at a nominal rate of 6% forever.
- Its FCF one year from now is estimated at $1,000
- The firm’s nominal cost of capital is 12%
- What is the intrinsic value of this firm?
- The firm has debt that is valued at $7,000. It also has 500 shares outstanding. What is the value per share?

In-class exercise (cont.)

- First set up timeline
- Calculate FCF in first 3 years (non-constant stage)
- Find the terminal value at year 3
- Discount first 3 years FCF and terminal value to time 0 and sum these values
- MV of equity = V – value of debt = ?
- Divide MV of equity by shares outstanding to get value per share

Sequential Valuation – Example

- How do we find the intrinsic value of the firm?
- At the end of year 3, the future FCFs to the firm resemble a growing perpetuity (g = 6%)
- Let V3 denote the firm value at the end of year 3. So,
- FCF1=1,000, FCF2=FCF1*1.14=1,140
- FCF3=FCF2*1.14=1,299.60
- FCF4=FCF3*1.06=1,377.58
- Therefore, V3 = $22,959.60

Sequential Valuation – Example

- Firm valuation – continued
- Now that we know V3, we can compute firm value at date 0, denoted, V
- Let V3 denote the firm value at the end of year 3. So,
- MV of equity = V – value of debt = $12,068.88
- So share price = $12,0688/500 = $24.14

In-class example modified

- Suppose we re-do the problem assuming that all cash flows were mid-year
- Then, firm value is:
- MV of equity = $20,180.60 - $7,000= $13,180.60
- Therefore, share price = $13,180.60/500 = $26.33

The Country Motel Case

- Case example
- Evaluating the decision to purchase a motel
- Plan to keep the motel for 10 years, after which it will be sold

- Assumptions:
- The current year’s FCF is:
- Constant room occupancy over 10 year period

The Country Motel Case…

- Assumptions:
- FCF is the same for the next 10 years
- All cash flows, except depreciation, have been projected as real cash flows
- Depreciation, of course, is nominal

- FCF is realized at the middle of the year

- Plan to keep the motel for 10 years, after which it will be sold
- The after-tax market value of the motel at the end of year 10 is estimated to be (nominal) $429,210

The Country Motel Case…

- Assumptions:
- Real risky discount rate is 20%
- Real risk-free discount rate is 7%
- Inflation is 3% per year
- Tax rate is 30.304%
- These rates are constant over the next 10 years

The Country Motel Case…

- Note that FCF has two components with different risk characteristics:
- Depreciation tax shield
= Depreciation * tax rate

- This is a nominal cash flow that is risk-free

- Non-depreciation FCF
= FCF – depreciation tax shield

- This is a real cash flow that is risky

- Depreciation tax shield
- These two components should be discounted with different discount rates

The Country Motel Case…

- Components of FCF:
- Depreciation tax shield (DTS):
- Depreciation is $20,000 per year
- Tax rate is 30.304% (given)
- DTS = $20,000×30.304% = $6,061

- Non-depreciation FCF
= $72,669 - $6,061 = $66,639

- Depreciation tax shield (DTS):
- So FCF = DTS + non-depreciation FCF
= $6,061 + $ 66,639 = $72,669

Timeline

- We have two annuity streams and a lump sum
- with different risk characteristics
- and different inflation adjustments (real versus nominal)

10

0

1&1/2

2 &1/2

9&1/2

1/2

6,061

66,639

PV?

6,061

66,639

6,061

66,639

6,061

66,639

T.V.

Computing Discount Rates

- We know the real risky and risk-free discount rates, and the inflation rate
- So using the following equation:
- we can compute
- Nominalrisky discount rate = 23.6%
- Nominalrisk-free discount rate = 10.21%

The Country Motel Case…

- Appropriate discount rates:
- DTS:
- Use nominal risk-free discount rate (10.21%)

- Non-depreciation FCF:
- Use real risky discount rate (20%)

- Terminal Value:
- Use nominal risky discount rate (23.6%)

- DTS:

The Country Motel Case…

- Valuing individual components:
- PV of depreciation tax shields (mid-year flow):
- 10-year annuity with C=$6,061 discounted at 10.21%
- Value = $38,747

- PV of non-depreciation FCF (mid-year flow):
- 10-year annuity with C=$66,639 discounted at 20%
- Value = $306,047

- PV of terminal value:
- A future lump sum of $429,210 discounted at 23.6%
- Value = $51,580

- PV of depreciation tax shields (mid-year flow):

The Country Motel Case…

- Computing intrinsic value of the motel, and the value of equity
- Intrinsic value of the motel is the sum of values of the individual components
- Intrinsic value of motel is $396,375

- Suppose the motel is financed with debt whose current value is $295,625
- Then, value of equity = ?

- (See modified Country Motel Case on the assigned problem sheet)

Forecasting sales

- Forecasting of sales is the first step in DCF valuation; everything else follows from this
- Sales forecasts have a big influence on income statement and balance sheet forecasts:

How do we forecast sales?

- There is no formula or method that you can apply to all situations!
- Here are some methods we will look at:
- Regressions against macroeconomic variables
- Time series analysis
- Theoretical estimation of growth rates

- Note: None of above methods may work perfectly!

Forecasting sales: Qualitative analysis

- Sales forecasting is not about blindly running regressions in Excel
- Have a good idea of the company’s sales mix
- What kind of products/ services does the company sell, and who does it sell it to?
- Is it heavily dependent on one product, sector or one large customer? Or is it more diversified?
- How sensitive are sales to economic conditions, energy prices, etc.? Basic necessity or luxury good? Branded product or commodity?

- Consider product life cycle effects (i.e., is it a growing, mature, or declining industry)

Forecasting sales: Adjusting for inflation

- Sales = Number of units sold * Unit price
- So sales growth can be due to:
- growth in number of units sold, i.e., growth in volume of sales (real growth in sales), or
- Increase in unit price (inflation)

- It is important to distinguish between nominal sales growth and real sales growth
- Otherwise, you will estimate relationship between sales and economic variables wrongly

Forecasting sales: Adjusting for inflation…

- Sales analysis should be done on real sales (i.e., sales expressed in constant dollars with respect to a base year)
- NOTE: You must translate all past sales to real sales first, before doing sales analysis

Example: Real vs. nominal sales

Example:

- A firm reported sales of $2 bn (in 1998), $2.2 bn (in 1999) and $2.5 bn (in 2000).
- CPI was 120 (in 1998), 125 (in 1999) and 132 (in 2000).
- Compute the firm’s real sales (in terms of year 2000 dollars) in 1998, 1999 and 2000.
- What was real sales growth in 1999 and 2000?

Method 1: Using economic indicators to forecast sales

- Sales may correlate with macroeconomic indicators:
- GDP, population, energy prices, level of industrial production, home sales, exchange rates, etc.

- Data sources for macroeconomic information:
- Index of leading economic indicators, produced monthly by Bureau of Economic Analysis (http://www.bea.doc.gov)
- Predictions of economists, published monthly by Blue Chip Economic Indicators:
- GDP growth forecasts, Inflation rate forecasts

- FRB Saint Louis (http://www.stls.frb.org/fred)

Method 1: Outline of the approach

- First, identify the macroeconomic variable that you expect sales to depend on
- Suppose you expect sales to be related to GDP:
- Convert all past sales to real sales, and compute the real sales growth
- Run a regression of real sales growth vs. real GDP growth to determine the relationship
- Use regression estimates to forecast real sales growth into the future
- Use estimates of real sales growth to obtain sales forecasts

Method 1: Economic indicators… Regression analysis

- Relationship between real sales growth (y) and real GDP growth (x)?
- Estimate relationship y = b + mx using past data

- Regression Analysis: Gives us estimates of intercept (b) and coefficient (m)
- R-square: Goodness of fit measure
- p-value: Does growth in GDP significantly explain sales growth?
- Rule for p-values:

Method 1: Forecasting sales using regression estimates

- How do we predict future sales using regression estimates (‘b’ and ‘m’)?
- For each year in future, first estimate real sales growth using the equation:
Real sales growth = b + m* real GDP growth

- Then, compute real sales and nominal sales (using inflation forecasts)
- Note: GDP growth and inflation forecasts can be obtained from sources I listed earlier

- For each year in future, first estimate real sales growth using the equation:

Example: Regression Analysis

- Real revenues and Real GDP have been computed with 1998 as the base year
- NOTE: Numbers in BLUE font are given information; the rest of the numbers have been computed

Example: Regression Analysis

- Regression model: y=mx+b, y = real sales growth, x = real GDP growth
- In Excel: Tools | Data Analysis | Regression

Example continued…

- Suppose you expect real GDP growth to be 4% in 1999, 3.5% in 2000 and 3% in 2001
- Using our regression estimates (assume p-value was less than 0.1):
- Compute real sales growth and real sales for 1999, 2000 and 2001
- Suppose you expect inflation to be 4% each year for all 3 years, compute the nominal sales for 1999, 2000 and 2001

Method 2: Time series analysis

- In time series analysis, we examine past sales to identify trends that we expect to continue in future
- i.e., we are looking for answers to questions like:
- How have firm’s real sales grown in the past – high growth or low growth?
- Has growth been exponential or linear?
- Is growth slowing down or speeding up?
- and so on…

- i.e., we are looking for answers to questions like:
- Use product life cycle to make qualitative judgment on how long trends will persist

Method 2: Time series analysis…

- Analyzing sales growth patterns:
- Stable growth
- Large established firms/ industries grow at steady rate forever (often close to GNP growth rate)
- Characteristics: Average risk and average to low reinvestment rate

- Two-stage growth
- Smaller firms/ industries grow at a high unsustainable rate initially, then settle down to a stable growth rate
- Characteristics: Moderate to high risk and moderate to high reinvestment rate

Method 2: Time series analysis…Differences in growth cycles

- Linear growth cycle (e.g., GE)
- i.e., stable growth.
- Regression equation: Y = mt+b
- ‘Y’ is real sales, and ‘t’ is a time indicator

- Exponential growth cycle (e.g., Google)
- Real sales increasing at an increasing rate
- High unsustainable growth rates
- Regression equation: Y= emt+b (or log(Y) = mt + b)

Method 2: Time Series Analysis…

- Here’s how you conduct time-series analysis:
- Suppose you have real sales from 1979-1998
- First, re-label years as t=0, t=1, t=2, t=3,…
- So 1979 is t=0, 1980 is t=1, and so on…

- Run the appropriate regression (Linear or exponential)
- Check R-square and p-value

Method 2: Time series analysis…

- Linear (stable) growth cycle: Y=mt+b
- Sales increasing at a fairly constant rate over time

Method 2: Time series analysis…

- Exponential growth cycle: Y=emt+b(or log(Y)=mt+b)
- Sales increases at an increasing rate over time

Example: Time-series analysis

- How do we conduct time-series analysis?
- Suppose you have real sales for MSFT for 1989-2001
- First, re-label years as t=0, t=1, t=2, t=3,…
- So 1989 is t=0, 1990 is t=1, and so on…

- Run the appropriate regression
- Linear growth or exponential growth

- Check R-square and p-value

Example: Time-series analysis

- Time-series Analysis – Example – MSFT sales
- You conducted time-series analysis on MSFT’s real sales, using data from 1989 (t=0) to 2001 (t=12).
- 2001 was the base year (Sales = 25296)

- You estimated an exponential growth model, (i.e., log(real sales) = a + b×T).
- The regression output is on the next slide.

- Assume past trends will continue for 2 more years:
- What are MSFT’s real sales in 2002 and 2003?
- What are its nominal sales in 2002 and 2003, if the annual inflation will be 4% in each year?

- You conducted time-series analysis on MSFT’s real sales, using data from 1989 (t=0) to 2001 (t=12).

Example: Time-series analysis Regression output

- Regression: log(real sales) = b + mt
- Regression output:

Projecting Sales – Theoretical Analysis

- A firm’s growth rate, g, depends on:
- The percentage of reinvested earnings
- The return earned on the firm’s investments
- Return on equity (ROE), Return on assets (ROA)

- High growth firms typically have low payout ratios (high reinvestment ratios)
- Payout ratio, b = Dividends/ Net income
- Reinvestment ratio = 1 – payout ratio = 1 – b

- Low payout allows these firms to reinvest in new projects, and grow faster

Projecting Sales – Theoretical Analysis

- Sustainable growth: Maximum growth feasible without external equity financing, while maintaining a constant D/E ratio
- Internal growth: Maximum growth feasible without external financing
- Note: ROE and ROA are defined in terms of end-of-year equity and assets, respectively

Projecting Sales – Theoretical Analysis

- Theoretical growth rates – Example
- In year 2000, HP has ROE of 9.76% and ROA of 4.18%. It paid out 46.377% of its earnings as a dividend
- Suppose that ROA, ROE and payout ratio stay constant
- What is the growth rate that HP can achieve without issuing equity, but maintaining its current debt to equity ratio?
- What is the growth rate that HP can achieve with no additional external financing?

Note

- In some of the examples we forecasted sales for the individual firm
- Using the exact same techniques, it is often useful to project INDUSTRY sales first
- Regressions against macroeconomic variables
- Time series analysis

- Then project the market share the firm can attain
- Consider: entry or exit of competition, marketing strategies, luxury versus necessity goods (high-cost/quality versus low-cost/quality), relative strengths weakness of firm, etc.

Next Class

- Project 1 is DUE one week from now at beginning of class
- Choose firm for Project 2 BY FRIDAY (tomorrow)
- Practice Problem Set 3 (and excel file) posted online
- Read RWJ Ch 3 and Holden Ch 15.4 & 16
- Book problems: RWJ Ch 3 Questions; Critical Thinking Questions 2,7,9,22,26, Holden Ch16

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