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Corporate Finance. Class 05 DCF Valuation Daniel Sungyeon Kim Peking University HSBC Business School. Class outline. Sequential Valuation The Country Motel Case. Motivation. So far, we discussed the fundamental principles of valuation TVM concepts, FCF analysis, etc.

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corporate finance

Corporate Finance

Class 05 DCF Valuation

Daniel Sungyeon Kim

Peking University HSBC Business School

class outline
Class outline
  • Sequential Valuation
  • The Country Motel Case
  • 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
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
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 stage
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
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
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
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
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
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
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
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
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 example1
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
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
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 case1
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 case2
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 case3
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
  • These two components should be discounted with different discount rates
the country motel case4
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

  • So FCF = DTS + non-depreciation FCF

= $6,061 + $ 66,639 = $72,669

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




2 &1/2













computing discount rates
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 case5
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%)
the country motel case6
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
the country motel case7
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 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
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
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
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 inflation1
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: Real vs. nominal sales


  • 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
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 (
    • Predictions of economists, published monthly by Blue Chip Economic Indicators:
      • GDP growth forecasts, Inflation rate forecasts
    • FRB Saint Louis (
method 1 outline of the approach
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
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
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
example regression analysis
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 analysis1
Example: Regression Analysis
  • Regression model: y=mx+b, y = real sales growth, x = real GDP growth
  • In Excel: Tools | Data Analysis | Regression
example continued
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
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…
  • Use product life cycle to make qualitative judgment on how long trends will persist
method 2 time series analysis1
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
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 analysis2
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 analysis3
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 analysis4
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
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 analysis1
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?
example time series analysis regression output
Example: Time-series analysis Regression output
  • Regression: log(real sales) = b + mt
  • Regression output:
projecting sales theoretical analysis
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 analysis1
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 analysis2
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?
  • 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
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