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ChapterTool KitChapter 710/27/15Corporate Valuation and
Stock Valuation7-4 Valuing Common Stocks—Introducing the
Free Cash Flow (FCF) Valuation ModelData for B&B
Corporation (Millions)Constant free cash flow (FCF)
=$10Weighted average cost of capital (WACC) =10%Short-term
investments =$2Debt =$28Preferred stock =$4Number of shares
of common stock =5The first step is to estimate the value of
operations, which is the present value of all expected free cash
flows. Because the FCF's are expected to be constant, this is a
perpetuity. The present value of a perpetuity is the cash flow
divided by the cost of capital:Value of operations (Vop)
=FCF/WACCValue of operations (Vop) =$100.00millionB&B's
total value is the sum of value of operations and the short-term
investments: Value of operations$100+ ST
investments$2Estimated total intrinsic value$102The next step
is to estimate the intrinsic value of equity, which is the
remaining total value after accounting for the claims of
debtholders and preferred stockholders: Value of
operations$100+ ST investments$2Estimated total intrinsic
value$102− All debt$28− Preferred stock$4Estimated intrinsic
value of equity$70The final step is to estimate the intrinsic
common stock price per share, which is the estimated intrinsic
value of equity divided by the number of shares of common
stock: Value of operations$100+ ST investments$2Estimated
total intrinsic value$102− All debt$28− Preferred
stock$4Estimated intrinsic value of equity$70÷ Number of
shares5Estimated intrinsic stock price =$14.00The figure below
shows a summary of the previous calculations.Figure 7-2B&B
Corporation's Sources of Value and Claims on Value (Millions
of Dollars except Per Share Data)Inputs:Valuation
AnalysisConstant free cash flow (FCF) =$10Value of
operations$100Weighted average cost of capital (WACC)
=10%+ ST investments$2Short-term investments =$2Estimated
total intrinsic value$102Debt =$28− All debt$28Preferred stock
=$4− Preferred stock$4Number of shares of common stock
=5Estimated intrinsic value of equity$70÷ Number of
shares5Estimated intrinsic stock price$14.00Data for Pie
ChartsShort-term investments =$2Value of operations
=$100Total =$102Debt =$28Preferred stock =$4Estimated
equity value =$70Total =$1027-5 The Constant Growth Model:
Valuation when Expected Free Cash Flow Grows at a Constant
RateCase 1: The expected free cash flow at t=1 and the expected
constant growth rate after t=1 are known.First expected free
cash flow (FCF1) =$105Weighted average cost of capital
(WACC) =9%Constant growth rate (gL) =5%When free cash
flows are expected to grow at a constant rate, the value of
operations is:Value of operations (Vop) =FCF1 / [WACC-
gL]Value of operations (Vop) =$2,625Case 2: Constant growth
is expected to begin immediately.Most recent free cash flow
(FCF0) =$200Weighted average cost of capital (WACC)
=12%Constant growth rate (gL) =7%When free cash flows are
expected to grow at a constant rate, the value of operations
is:Value of operations (Vop) =[FCF0(1+gL)]/[WACC-gL]Value
of operations (Vop) =$4,2807-6 The Multi-Stage Model:
Valuation when Expected Short-Term Free Cash Flow Grows at
a Nonconstant RateThurman Corporation's expected free cash
flows are shown below.Year01234FCF−$20$80$100$110Growth
in FCF25%10%Free cash flows are expected to grow at a 5%
rate starting at Year 4 and to continue growing at a 5% rate for
the foreseeable future. We know the free cash flow at Year 4
and we know that FCF grows at a constant rate after Year 4.
Therefore, we set the horizon date at Year 4.Free cash flow at
beginning of the constant growth phase (FCF4) =$110Weighted
average cost of capital (WACC) =15%Constant growth rate (gL)
=5%HV4 = Vop, at 4 =[FCF4 (1+gL)]/ [WACC-gL]HV4 = Vop,
at 4 =$1,155Thurman's time line of expected free cash flows
and horizon value is shown
below.Year01234FCF−$20$80$100$110Horizon
value$1,155Present value of HV4 = $660.375Present value of
free cash flows = $171.745Total value of operations at Year 0,
Vop, at t=0 =$832.120There is more than one correct way to
find the present value of the FCFs and the horizon value. For
example, you could find the total cash flows, as shown below,
which are equal to the free cash flows except for the last period,
when they are equal to the sum of the free cash flow and the
horizon value. (It is as though you received the FCF at Year 4
and then "sold" the operations and received cash equal to the
horizon value.) You could then find present value of the
combined free cash flows and horizon
value.Year01234FCF−$20$80$100$110Horizon
value$1,155Combined FCF and
HV−$20.00$80.00$100$1,265PV of combined FCF and HV =
Total value of operations at Year 0, Vop, at t=0 =$832.12Here
is a third way to find the present value of the FCFs and the
horizon value. The basic idea is to find the value of operations
at each date. For the last date, the value of operations is the
horizon value. For the previous date, the value of operations is
equal to the present value of the sum of the next date's value of
operations and FCF. For example, if you sell the operations
immediately after receiving the FCF at Year 3, then the
purchaser would receive the FCF at Year 4 plus the value of
operations at Year 4 (which is the present value of all cash
flows beyond Year 4).
Year20182019202020212022FCF−$20.00$80.00$100.00$110.00
Horizon value$1,155Vop,t =
(FCFt+1 + Vop,t+1)/
(1+WACC)$832.12$976.94$1,043.48$1,100.00$1,155.00Option
al Material. You may have noticed that we could have defined
the horizon date at Year 3 because we have an estimate of the
Year 4 free cash flow, which is expected to grow at a constant
rate thereafter. However, we recommend defining the horizon
date as the last date in the forecast period even if growth
becomes constant at or prior to this date because we have found
that this leads to fewer errors. But we illustrate this approach
below for the interested reader.Free cash flow at beginning of
the constant growth phase (FCF4) =$110Weighted average cost
of capital (WACC) =15%Constant growth rate (gL) =5%HV3 =
Vop, at 3 =FCF4 / [WACC-gL]HV3 = Vop, at 3
=$1,100Thurman's time line of expected free cash flows and
horizon value is shown
below.Year0123FCF−$20$80$100Horizon value$1,100Present
value of HV4 = $723.268Present value of free cash flows =
$108.852Total value of operations at Year 0, Vop, at t=0
=$832.120Following is a summary of the steps used in
estimating Thurman Corporation's value of operations.Figure 7-
3Thurman Corporation's Value of Operations (Millions of
Dollars)INPUTS:gL = 5%WACC
=15%ProjectionsYear01234FCF−$20.00$80.00$100.00$110.00
⟶⟶ ⟶↴ ↓↓↓↓↓FCF1FCF2FCF3FCF4HV =
Vop(t=4)────────────────────────↓(1+WACC)1(
1+WACC)2(1+WACC)3(1+WACC)4 FCF4(1+gL)↓↓↓↓
───────── ↓↓↓↓ (WACC− gL)↓↓↓↓↓↓↓↓↓$115.500PVs of
FCFs−$17.391⟵
⟵
⤶ ↓↓↓10.00%$60.491⟵
⟵
⟵
⟵
⟵
⤶ ↓↓↓$65.752⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⤶ ↓
$1,155.000$62.893⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⤶ ↓PV of
HV$660.375⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
$1,155.000 ⟵
⟵
⟵
⤶ ↓=
────── Vop =$832.12(1+WACC)47-7 Application of the
FCF Valuation Model to MicroDriveWe begin with
MicroDrive's most recent financial statements and selected
additional data.Figure 7-4 MicroDrive’s Most Recent Financial
Statements (Millions, Except for Per Share Data)INCOME
STATEMENTSBALANCE
SHEETS20152016Assets20152016Net sales$ 4,760$
5,000Cash$ 60$ 50COGS (excl. depr.)3,5603,800ST
Investments400Depreciation170200Accounts
receivable380500Other operating
expenses480500Inventories8201,000EBIT$ 550$ 500Total
CA$ 1,300$ 1,550Interest expense100120Net
PP&E1,7002,000Pre-tax earnings$ 450$ 380Total assets$
3,000$ 3,550Taxes (40%)180152NI before pref. div.$ 270$
228Liabilities and EquityPreferred div.88Accounts payable$
190$ 200Net income$ 262$ 220Accruals280300Notes
payable130280Other DataTotal CL$ 600$ 780Common
dividends$48$50Long-term bonds1,0001,200Addition to
RE$214$170Total liabilities$ 1,600$ 1,980Tax
rate40%40%Preferred stock100100Shares of common
stock5050Common stock500500Price per
share$40.00$27.00Retained earnings800970Total common
equity$ 1,300$ 1,470Weighted average
cost of capital (WACC)Total liabs. & equity$ 3,000$
3,55010.50%10.97%The first step is to calculate the key
performance measures that determine free cash flows. Figure 7-
5Key Performance Measures for MicroDrive (Millions of
Dollars)MicroDriveIndustry201520162016Calculating Net
Operating Profit after Taxes (NOPAT)NOPAT = EBIT(1 −
T)$330$300Calculating Net Operating Working Capital
(NOWC)Operating current assets$1,260$1,550− Operating
current liabilities$470$500NOWC$790$1,050Calculating Total
Net Operating Capital (OpCap)NOWC$790$1,050+ Net
PP&E$1,700$2,000OpCap$2,490$3,050Investment in operating
capital$560Calculating Free Cash Flow (FCF)FCF = NOPAT –
Investment in operating capital−$260Calculating Return on
Invested Capital (ROIC)ROIC = NOPAT/Total net operating
capital13.25%9.84%15.04%Calculating the Operating
Profitability Ratio (OP)OP =
NOPAT/Sales6.93%6.00%6.92%Calculating the Capital
Requirement Ratio (CR)CR = (Total net operating
capital)/Sales52.31%61.00%46.00%The next step is to forecast
sales, NOPAT, and total net operating capital. We do this by
estimating future sales' growth rates, operating profitability
ratios, and capital requirement ratios, as shown in Panel A in
the Figure below.Yearly sales are forecast by letting the
previous year's sales increase by the forecasted sales growth
rate. Operating profitability and total net operating capital in a
forecasted year are assumed to be proportional to sales in that
year.Figure 7-6MicroDrive's Forecast of Operations for the
Selected Scenario (Millions of Dollars, Except for Per Share
Data)Status QuoIndustryMicroDriveMicroDrivePanel
A:ActualActualForecastOperating
Ratios20162015201620172018201920202021g = Sales growth
rate15%5%10%8%7%5%5%OP =
NOPAT/Sales6.92%6.9%6%6%6%6%6%6%CR =
OpCap/Sales46.0%52.3%61%61%61%61%61%61%Tax
rate40%40%40%40%40%40%40%40%Panel
B:ActualForecastOperating
Items201620172018201920202021Net
sales$5,000$5,500$5,940$6,356$6,674$7,007.270Net operating
profit after taxes$300$330$356$381$400$420.436Total net
operating capital
(OpCap)$3,050$3,355$3,623$3,877$4,071$4,274.434FCF =
NOPAT – Investment in
OpCap−$260$25$88$128$207$216.892Growth in
FCF252%45.1%61.7%5.0%ROIC =
NOPAT/OpCap9.84%9.84%9.84%9.84%9.84%9.84%Note:
Numbers in the figure are shown as rounded for clarity in
reporting. However unrounded values are used for all
calculations. The next step is to estimate the horizon value and
the value of operations, beginning with the horizon value.Free
cash flow at beginning of the constant growth phase (FCF2021)
=$216.892Weighted average cost of capital (WACC)
=10.97%Constant growth rate (gL) =5%HV2021 = Vop, 2021
=[FCF2021 (1+gL)]/ [WACC-gL]HV2021 = Vop, 2021
=$3,814.678MicroDrive's time line of expected free cash flows
and horizon value is shown
below.Year201620172018201920202021FCF$25.000$88.000$12
7.710$206.564$216.892Horizon value$3,814.678Present value
of HV = $2,266.887Present value of free cash flows =
$452.552Total value of operations at Year 0, Vop, at t=0
=$2,719.439The figure below shows a summary of these
calculations.Figure 7-7MicroDrive Inc.'s Value of Operations
(Millions of Dollars)INPUTS:Scenario:Status QuogL =
5%WACC
=10.97%ProjectionsYear201620172018201920202021FCF$25.0
00$88.000$127.710$206.564$216.892⟶
↴ ↓↓↓↓↓↓FCF2017FCF2018FCF2019FCF2020FCF2021↓─────
─────────────────────────HV =
Vop(2021)(1+WACC)1(1+WACC)2(1+WACC)3(1+WACC)4(1+
WACC)5↓↓↓↓↓↓ FCF2021(1+gL)↓↓↓↓↓ ───────── ↓↓↓↓↓
(WACC− gL)↓↓↓↓↓↓PVs of
FCFs$22.529⟵
⤶ ↓↓↓↓$227.736$71.461⟵
⟵
⟵
⟵
⟵
⤶ ↓↓↓0.0597$93.
456⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⤶ ↓↓↓$136.217⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⤶ ↓$3,
814.678$128.889⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⤶ ↓PV of
HV$2,266.887⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
$3,814.678 ⟵
⟵
⤶ ↓=
────── Vop =$2,719.44(1+WACC)5Note: Numbers in the
figure are shown as rounded for clarity in reporting. However
unrounded values are used for all calculations. Estimating
MicroDrive's Intrinsic Stock Price per ShareValue of operations
=$2,719.44Weighted average cost of capital (WACC)
=10.97%Short-term investments =$0Short-term debt (notes
payable) =$280Long-term debt (bonds) =$1,200Preferred stock
=$100Number of shares of common stock =50MicroDrive's total
value is the sum of value of operations and the short-term
investments: Value of operations$2,719.44+ ST
investments$0Estimated total intrinsic value$2,719.44The next
step is to estimate the intrinsic value of equity, which is the
remaining total value after accounting for the claims of
debtholders and preferred stockholders: Value of
operations$2,719+ ST investments$0Estimated total intrinsic
value$2,719.44− All debt$1,480− Preferred stock$100Estimated
intrinsic value of equity$1,139.44The final step is to estimate
the intrinsic common stock price per share, which is the
estimated intrinsic value of equity divided by the number of
shares of common stock: Value of operations$2,719.44+ ST
investments$0Estimated total intrinsic value$2,719.44− All
debt$1,480− Preferred stock$100Estimated intrinsic value of
equity$1,139.44÷ Number of shares50Estimated intrinsic stock
price =$22.79The figure below shows a summary of the
previous calculations.Figure 7-8MicroDrive Inc.'s Intrinsic
Stock Price (Millions, Except for Per Share Data)INPUTS:gL =
5%WACC =10.97%Year =20172018201920202021Projected
FCF =$25$88.0$127.71$206.564$216.892Horizon Value:Value
of operations$2,719+ ST investments$0=$3,815Estimated total
intrinsic value$2,719− All debt$1,480Value of Operations:−
Preferred stock$100Present value of HV$2,266.89Estimated
intrinsic value of equity$1,139+ Present value of FCF$452.55÷
Number of shares50Value of operations =$2,719.44Estimated
intrinsic stock price =$22.79Note: Numbers in the figure are
shown as rounded for clarity in reporting. However unrounded
values are used for all calculations. 7-8 Do Stock Prices Reflect
Long-Term or Short-Term Cash Flows?Managers often claim
that stock prices are "short-term" in nature in the sense that they
reflect what is happening in the near-term and ignore the long-
term. We can use MicroDrive's results to shed light on this
claim.We previously estimated MicroDrive's current value of
operations. We also estimated MicroDrive's horizon value at
Year 5 and calculated its present value. If we divide the present
value of the horizon value, we can estimate how much of
MicrDrive's value is due to cash flows occurring beyond Year 5.
In other words, we can determine how much of MicroDrive's
value is due to long-term cash flows and how much is due to
short-term cash flows.Inputs:Weighted average cost of capital
=10.97%Horizon year =5Horizon value at Year 5 (HV5)
=$3,814.678Value of operations at Year 0 (Vop,0)
=$2,719.439Analysis:Present value of the horizon value
=$2,266.887Value of operations at Year 0
=$2,719.439Results:Percent of current value due to long-term
cash flows (i.e., PV of HV5) =83%Percent of current value due
to short-term cash flows =17%For most stocks, the percentage
of the current price that is due to long-term cash flows is over
80%.7-9 Using the Free Cash Flow Valuation Model to Identify
Value DriversWe can use the free cash flow valuation model we
developed previously for MicroDrive to determine how the
inputs (sales growth, operating profitability, and capital
requirements) affect the value of operations and intrinsic stock
price. It is very easy to do this in Excel by using the Scenario
Manager feature. Following is an explantion of how to use this
feature.The Scenario Manager allows you to specify values for
particular cells and then save those values as a "scenario." If
you later change the values in the cells, perhaps to see the
impact that the change has on an output, the Scenario Manager
allows you to restore the saved scenario without having to re-
input the original values. You can create numerous different
scenarios, and you can even have the Scenario Manager create a
summary that shows the values of the input cells and the values
of the output cells for each scenario that you created.To create a
scenario, go to the Data tab in the menu, look in the Data Tools
section for What-If Analysis, and then select Scenario Manager.
This will open a dialog box that shows seven existing scenarios.
If you select the button for "Add…", you will get another dialog
box asking you to give the scenario a name and to specify the
"Changing cells." The "Changing cells" are the cells with values
that you want the Scenario Manager to save. For example, we
want to save the values for MicroDrive's estimated sales growth
rates, operating profitabiltiy ratio, and capital requirement ratio.
After specifying the "Changing cells", click "Ok" and you will
get a new dialog box asking you to input the values into the
changing cells that you want for this scenario. There will
already be values shown, which are the values currently in those
cells. So if you have already put the values into the cells in the
Excel workbook, you won't have to re-enter them in the dialog
box, you can simply click "Ok" and you will have created a new
scenario.The original dialog box gives you several options,
including adding a scenario, deleting a scenario, and editing a
scenario. It also give you the option to run a "Summary." If you
select the "Summary" button, you get a dialog box asking you to
specify some "Results" cells. For example, we specified the
cells in this worksheet that have the value of operations, the
intrinsic stock price, and the return on invested capital for the
last year in the forecast horizon. After selecting the "Results"
cells, you can click "Ok" and the Scenario Manager will create a
new worksheet named "Scenario Summary". This new sheet
contains the name of each scenario, the values in the "Changing
cells", and the values in the "Results cells. We copied the
information from the "Scenario Summary" into the table below
and then formatted the table to make it a bit more reader-
friendy. Figure 7-9Value Drivers for MicroDrive Inc. (Millions,
Except for Per Share Data)ScenarioAdditional information not
in textbook(1)
Status Quo(2)
Higher Sales Growth (Only)(3)
Higher Operating Profitability (Only)(4)
Better Capital Utilization (Only)(5)
Improve Growth and OP(6)
Improve Growth and CR(7)
Improve Growth, OP, and CR(8)
Status Quo but Lower WACC(9)
Better OP and CRInputsSales growth in 1st
year10%11%10%10%11%11%11%10%10%Sales growth in 2nd
year8%9%8%8%9%9%9%8%8%Sales growth in 3rd
year7%8%7%7%8%8%8%7%7%Long-term sales growth
(gL)5%6%5%5%6%6%6%5%5%Operating profitability
(OP)6%6%7%6%7%6%7%6%7%Capital requirement
(CR)61%61%61%52%61%52%52%61%52%Weighted average
cost
of capital
(WACC)10.97%10.97%10.97%10.97%10.97%10.97%10.97%9.5
0%10.97%ResultsValue of
operations$2,719$2,713$3,682$3,576$3,880$3,751$4,918$3,690
$4,538Intrinsic stock
price$22.79$22.67$42.04$39.91$46.00$43.42$66.76$42.19$59.
16Return on invested
capital
(ROIC)9.84%9.84%11.48%11.54%11.48%11.54%13.46%9.84%
13.46%To better understand why growth doesn't always add
value, we can express the horizon value as:If the numerator in
the fraction in brackes, (1+gL) ROIC − WACC, is negative,
then the value of operations will be less than the total net
operation capital, OpCapT. If ROIC < WACC/(1+WACC), then
growth hurts value. The 2-way data table below show the
difference between the value operations and the amount of
operating capital for different combinations of growth and
ROIC. For input values, we use values similar to those of
MicroDrive's at the horizon.Input Values (Base Case)OpCap
=$4,274gL =5.0%ROIC =9.84%WACC =10.97%Output from
equation above in yellow.Vop =$3,815Vop − OpCap =-$460A
Two-Way Data Table Showing How Combinations of Growth
and ROIC Affect the Value of Operations Minus the Value of
Operating CapitalCombinations of growth and ROIC that have
Vop < OpCap are shown in pink. Notice that for very low values
of ROIC, such as the first row with ROIC = 9.7%, growth
reduces value (you can see this by looking across the row. For
very high values of ROIC, such as the last row with ROIC =
11%, growth adds value. For other combinations, it depends on
the relative values of growth, ROIC, and
WACC.gL−$4600.0%2.5%5.0%7.5%9.5%ROIC9.70%-$495-
$519-$562-$668-$1,0139.80%-$456-$467-$487-$536-
$6959.84%-$442-$448-$460-$488-$5809.90%-$417-$415-$412-
$403-$37710.00%-$378-$363-$337-$271-$5810.10%-$339-
$312-$261-$139$26010.20%-$300-$260-$186-$6$57910.30%-
$261-$208-$111$126$89710.40%-$222-$156-
$36$259$1,21510.50%-$183-$105$39$391$1,53410.60%-$144-
$53$115$524$1,85210.70%-$105-$1$190$656$2,17110.80%-
$66$50$265$788$2,48910.90%-
$27$102$340$921$2,80711.00%$12$154$415$1,053$3,1267-11
Valuing Common Stocks with the Dividend Growth ModelThe
Discounted Dividend ApproachThe value of any financial asset
is the present value of the future cash flows provided by the
asset. When an investor buys a share of stock, he or she
typically expects to receive cash in the form of dividends and
then, eventually, to sell the stock and to receive cash from the
sale. However, the price the first investor receives is dependent
upon the dividends the next investor expects to earn, and so on
for different generations of investors. Thus, the stock's value
ultimately depends on the cash dividends the company is
expected to provide and the discount rate used to find the
present value of those dividends.Here is the basic dividend
valuation equation:P0 =D1+D2+. . . .DN( 1 + rs )( 1 + rs ) 2(
1 + rs ) NThe dividend stream theoretically extends on out
forever, i.e., to N = infinity. Obviously, it would not be
feasible to deal with an infinite stream of dividends, but
fortunately, a relatively simple equation has been developed
that can be used to find the PV of the dividend stream, provided
it is growing at a constant rate.Valuing a Constant Growth
StockIn the constant growth model, we assume that the dividend
and stock will grow forever at a constant growth rate. Naturally,
assuming a constant growth rate for the rest of eternity is a
rather bold assumption. However, considering the implications
of imperfect information, information asymmetry, and general
uncertainty, the assumption of constant growth is often
reasonable. It is reasonable to guess that a given stock will
experience ups and downs throughout its life. By assuming
constant growth, we are trying to find the average of the good
times and the bad times, and we assume that we will see both
scenarios over the firm's life. In addition to a constant growth
rate, we also need the estimated long-term required return for
the stock, and it too must be constant. If these variables are
constant, our price equation for common stock simplifies to the
following expression:P0 =D1( rs – gL )Generally speaking, the
long-run growth rate of a firm is likely to fall between 5% and
8% a year.Example: Value of a Constant Growth StockA firm
just paid a $1.15 dividend and its dividend is expected to grow
at a constant rate of 8%. What is its stock price, assuming it
has a required return of 13.4%?D0 =$1.15gL =8%rs =13.4%P0
=D1=D0 (1 + gL)=$1.2420( rs – gL )( rs – gL )0.0540P0
=$23.00Expected Rate of Return on a Constant Growth
StockUsing the constant growth equation introduced earlier, we
can re-work the equation to solve for rs. In doing so, we are
now solving for an expected return. The expression we are left
is:D1+gLP0This expression tells us that the expected return on
a stock comprises two components. First, it consists of the
expected dividend yield, which is simply the next expected
dividend divided by the current price. The second component
of the expected return is the expected capital gains yield. The
expected capital gains yield is the expected annual price
appreciation of the stock, and is given by gL. This shows us the
dual role of gL in the constant growth rate model. Not only
does g indicate expected dividend growth, but it is also the
expected stock price growth rate.Example: Expected Rate of
Return on a Constant Growth StockYou buy a stock for $23, and
you expect the next annual dividend to be $1.242. Furthermore,
you expect the dividend to grow at a constant rate of 8%. What
is the expected rate of return on the stock, and what is the
dividend yield of the stock?Inputs:P0
$23.00D1$1.242gL8%13.40%Dividend yield =5.40%What is the
expected price of this stock in 1 year?Application of Constant
Growth Model at t=1P1 =D2( rs – gL )D2 =1.34136P1
=$24.84Valuing Nonconstant Growth StocksFor many
companies, it is unreasonable to assume that they grow at a
constant growth rate. Hence, valuation for these companies
proves a little more complicated. The valuation process, in this
case, requires us to estimate the short-run nonconstant growth
rate and predict future dividends. Then, we must estimate a
constant long-term growth rate at which the firm is expected to
grow. Generally, we assume that after a certain point of time,
all firms begin to grow at a rather constant rate. Of course, the
difficulty in this framework is estimating the short-term growth
rate, how long the short-term growth will hold, and the long-
term growth rate.Figure 7-10Illustrative Dividend Growth at
Different RatesData for figure:Growth RatesYearDeclining
ZeroConstantNonconstant1-8%0%8%30%2-8%0%8%20%3-
8%0%8%10%4-8%0%8%8%5-
8%0%8%8%DividendYearDeclining Growth: -8%Zero
GrowthConstant Growth: 8%Long-Term Growth:
8%YearDeclining Growth: -8%Zero GrowthConstant Growth:
8%Long-Term Growth:
8%0$1.15$1.15$1.15$1.1501.15001.15001.15001.15001$1.06$1
.15$1.24$1.5011.05801.15001.24201.49502$0.97$1.15$1.34$1.
7920.97341.15001.34141.79403$0.90$1.15$1.45$1.9730.89551.
15001.44871.97344$0.82$1.15$1.56$2.1340.82391.15001.56462
.13135$0.76$1.15$1.69$2.3050.75791.15001.68972.3018Specifi
cally, we will predict as many future dividends as we can and
discount them back to the present. Then we will treat all
dividends to be received after the convention of constant growth
rate with the Gordon constant growth model described above.
The point in time when the dividend begins to grow constantly
is called the horizon date. When we calculate the constant
growth dividends, we solve for the horizon value (also called a
terminal value or a continuing value) as of the horizon date.
The horizon value can be summarized as:HVT =PT
=DT+1=DT (1 + g)( rs – gL )( rs – gL )This condition holds
true, where T is the horizon date. The horizon value can be
described as the expected value of the stock at the time period
corresponding to the horizon date.A company's stock just paid a
$1.15 dividend, which is expected to grow at 30% the first year,
20% the second year, and 10% the third year. After three years
the dividend is expected to grow constantly at 8% forever. The
stock's required return is 13.4%; what is the price of the stock
today?Figure 7-11Process for Finding the Value of a
Nonconstant Growth StockINPUTS:D0 =$1.15Last dividend the
company paid.rs =13.4%Stockholders' required return.g0,1
=30%Growth rate for Year 1 only.g1,2 =20%Growth rate for
Year 2 only.g2,3 =10%Growth rate for Year 3 only.gL
=8%Constant long-run growth rate for all years after Year
3.ProjectionsYear0123⟶∞Growth
rate30%20%10%8%DividendD0D0(1+g0,1)D1(1+g1,2)D2(1+g1,
2)Dt$1.15$1.495$1.794$1.973↓↓↓D1D2D3─────────────
─────HV3 = (1+rs)1(1+rs)2(1+rs)3↓↓↓↓ D3(1+gL)↓↓↓
─────── ↓↓↓(rs− gL)↓↓↓↓↓↓↓$2.131PVs of
Dividends$1.318⟵
⤶ ↓↓5.400%$1.395⟵
⟵
⟵
⟵
⟵
⤶ ↓↓$1.353⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
⤶ $39.468↓PV of $27.065⟵
⟵
⟵
⟵
⟵
⟵
⟵
⟵
$39.468↓=
──────⟵
⟵
⟵
⟵
= ────── Vop
=$31.13(1+0.134)3(1+rs)3Note: Numbers in the figure are
shown as rounded for clarity in reporting. However unrounded
values are used for all calculations. 7-12 Market Multiple
AnalysisUse the following data in the market multiple approach
to estimate the stock price per share. Forecasted earnings per
share (EPS) =$7.70Average peer price/earnings (P/E) ratio
=12Estimated stock price: $92.407-14 Preferred StockConsider
an issue of preferred stock that pays an $8 dividend and has a
required return of 8%. What is the value of this preferred
stock?Vps =Dps÷rps =$8.00÷8.00% =$100.00Some
preferred stock has a maturity date. Consider a firm whose
preferred stock matures in 50 years, pays a $8 annual dividend,
has a par value of $100, and has a required return of 6%. What
is the price of this preferred stock?Years to Maturity
(N):50Annual Dividend (PMT):$8Par value (FV):$100Required
return, rd (I/YR):6%Vps =$131.52
Harcourt, Inc. items and derived items copyright © 2002 by
Harcourt, Inc.
Declining Growth: -8% 0 1 2 3 4 5
1.1499999999999999 1.0580000000000001
0.97336000000000011 0.89549120000000015
0.82385190400000019 0.75794375168000017 Zero
Growth
Zero Growth
0 1 2 3 4 5 1.1499999999999999
1.1499999999999999 1.1499999999999999
1.1499999999999999 1.1499999999999999
1.1499999999999999 Constant Growth: 8% 0 1
2 3 4 5 1.1499999999999999 1.242
1.3413600000000001 1.4486688000000003
1.5645623040000005 1.6897272883200007 Long-
Term Growth: 8% 0 1 2 3 4 5
1.1499999999999999 1.4949999999999999
1.7939999999999998 1.9734 2.1312720000000001
2.3017737600000001
Sources of Value
Short-term investments = Value of operations = 2 100
Claims on Value
Debt = Preferred stock = Estimated equity value = Total =
28 4 70
Scenario SummaryScenario SummaryCurrent Values:Status
QuoHigher Growth (Only)Higher OP (Only)Better CR
(Only)Improve Growth and OPImprove Growth and CRImprove
Growth, OP, and CRLower WACC (Only)Better OP and
CRCreated by Mike Ehrhardt on 5/22/2014
Modified by Mike Ehrhardt on 5/23/2014Created by Mike
Ehrhardt on 5/22/2014
Modified by Mike Ehrhardt on 5/23/2014Created by Mike
Ehrhardt on 5/22/2014
Modified by Mike Ehrhardt on 5/23/2014Created by Mike
Ehrhardt on 5/22/2014
Modified by Mike Ehrhardt on 5/23/2014Created by Mike
Ehrhardt on 5/22/2014
Modified by Mike Ehrhardt on 5/23/2014Created by Mike
Ehrhardt on 5/22/2014
Modified by Mike Ehrhardt on 5/23/2014Created by Mike
Ehrhardt on 5/22/2014
Modified by Mike Ehrhardt on 5/23/2014Created by Mike
Ehrhardt on 5/23/2014
Modified by Mike Ehrhardt on 5/23/2014Created by Mike
Ehrhardt on 3/21/2015Changing Cells:$A$324Status QuoStatus
QuoHigher Growth (Only)Higher OP (Only)Better CR
(Only)Improve Growth and OPImprove Growth and CRImprove
Growth, OP, and CRLower WACC (Only)Better OP and
CR$F$3278%8%9%8%8%9%9%9%8%8%$G$3277%7%8%7%7
%8%8%8%7%7%$H$3275%5%6%5%5%6%6%6%5%5%$E$327
10%10%11%10%10%11%11%11%10%10%$E$3286%6%6%7%
6%7%6%7%6%7%$E$32961%61%61%61%52%61%52%52%61
%52%$C$28210.97%10.97%10.97%10.97%10.97%10.97%10.97
%10.97%9.50%10.97%Result
Cells:$B$396$2,719.44$2,719.44$2,713.27$3,681.78$3,575.63$
3,879.93$3,751.25$4,917.91$3,689.71$4,537.97$G$460$22.79$
22.79$22.67$42.04$39.91$46.00$43.42$66.76$42.19$59.16$I$3
389.84%9.84%9.84%11.48%11.54%11.48%11.54%13.46%9.84
%13.46%Notes: Current Values column represents values of
changing cells attime Scenario Summary Report was created.
Changing cells for eachscenario are highlighted in gray.
7-4SECTION 7-4SOLUTIONS TO SELF-TEST A company
expects a constant FCF of $240 million per year forever. If the
WACC is 12%, what is the value of operations?Expected
FCF$240WACC12%Vop = $2,000.00A company has a current
value of operations of $800 million. The company has $100
million in short-term investments. If the company has $400
million in debt and has 10 million shares outstanding, what is
the price per share?Vop$800ST investments$100Total
value$900Debt$400Value of equity$500Number of
shares10Price per share$50.00
7-5SECTION 7-5SOLUTIONS TO SELF-TEST A company
expects to have a FCF in 1 year of $300, which is expected to
grow at a constant rate of 3% forever. If the WACC is 11%,
what is the value of operations?Expected FCF1 =$330Expected
gL =3%WACC =11%Vop = $4,125A company's most recent free
cash flow was $270. The company expects to have a FCF in 1
year of $300, which is expected to grow at a constant rate of 3%
forever. If the WACC is 11%, what is the value of
operations?Expected FCF1 =$300Expected gL =3%WACC
=11%Notice that the FCF of $270 at t = 0 is irrelevant to the
value of operations, because it occurred in the past. The value
of operations depends only on the future free cash flows.Vop =
$3,750A company's most recent free cash flow was $600 and is
expected to grow at a constant rate of 4% forever. If the WACC
is 10%, what is the value of operations?FCF0 =$600Expected
gL =4%WACC =10%Vop = $10,400
7-6SECTION 7-6SOLUTIONS TO SELF-TEST A company
expects to have a FCF at Year 10 of $600, which is expected to
grow at a constant rate of 8% thereafter. If the WACC is 8%,
what is the value of operations at Year 10, HV10?Expected
FCF12 =$600Expected gL =4%WACC =8%Vop = $15,600A
company expects a FCF of -$10 million at Year 1 and a FCF of
$20 million at Year 2. FCF is expected to grow at a 5% rate
after Year 2. If the WACC is 10%, what is the horizon value of
operations; i.e., Vop(Year 2)? What is the current value of
operations; i.e., Vop(Year 0)?Long-term growth
rate5%WACC10%Year12FCF1FCF2Expected FCF-
$10.00$20.00Vop(Year 2)$420.00PV of expected FCF$7.44PV
of expected Vop(Year 2)$347.11Vop(Year 0)$354.55
7-7SECTION 7-7SOLUTIONS TO SELF-TEST Cathey
Corporation currently has sales of $1,000, which are expected to
grow by 10% from Year 0 to Year 1 and by 4% from Year 1 to
Year 2. The company currently has and operating profitability
(OP) ratio of 7% and a capital requirement (CR) ratio of 50%
and expects to maintain these ratios at their current levels. The
current level of operating capital is $510. Use these inputs to
forecast free cash flow (FCF) for Years 1 and 2. Hint: You must
first forecast sales, net operating profit after taxes (NOPAT),
and total net operating capital (OpCap) for each year.Sales0
=$1,000g0,1 =10%g1,2 =4%OP = NOPAT/Sales =7%CR =
OpCap/Sales =50%OpCap0 =$510Year0123Growth rate in
sales10%4%4%Sales$1,000$1,100.00$1,144.00$1,189.76NOPA
T$77.00$80.08$83.28OpCap$510$550.00$572.00$594.88Invest
ment in
OpCap$40.00$22.00$22.88FCF$37.00$58.08$60.40Growth in
FCF57.0%4.0%Cathey Corporation has a 12% weighted average
cost of capital. Cathey's free cash flows, estimated in the
previous question, are expected to grow at 4% beginning at
Year 2 and continuing for the foreseeable future. What is the
horizon value (use Year 2 for the horizon)? What is the current
value of operations? Long-term growth
rate4%WACC12%Year12FCF1FCF2Expected
FCF$37.00$58.08HV2 = Vop(Year 2)$755.04PV of expected
FCF$79.34PV of expected HV(Year 2)$601.91Vop(Year
0)$681.25Cathey Corporation has $80 in short-term
investments, $20 in short-term debt, $140 in long-term debt,
$30 in preferred stock, and 10 shares of common stock
outstanding. Use the value of operations from the previous
question to estimate the intrinsic common stock price per
share.Vop =$681.25ST investments =$80.00ST debt
=$20.00Long-term debt =$140.00Preferred stock
=$30.00Number of shares =10Vop$681.25ST
investments$80.00Total value$761.25All debt$160.00Preferred
stock$30.00Value of equity$571.25Number of shares10.00Price
per share$57.13
7-11SECTION 7-11SOLUTIONS TO SELF-TESTIf D1 = $3.00,
P0 = $50, and the expected P at t=1 is equal to $52, what are the
stock’s expected dividend yield, capital gains yield, and total
return for the coming year?D1$3.00P0$50.00Expected
P1$52.00Exp. dividend yield6.0%=B6/B7Exp. capital gains
yield4.0%=(B8-B7)/B7Exp. total return10.0%=C10+C11A stock
is expected to pay a dividend of $2 at the end of the year. The
required rate of return is rs = 12%. What would the stock’s
price be if the growth rate were 4%? D1$2.00gL4%rs12%Stock
price$25.00A stock is expected to pay a dividend of $2 at the
end of the year. The required rate of return is rs = 12%. What
would the stock’s price be if the growth rate were
0%?D1$2.00gL0%rs12%Stock price$16.67If D0 = $4.00, rs =
9%, and g = 5% for a constant growth stock, what are the
stock’s expected dividend yield and capital gains yield for the
coming year?D0$4.00gL5%rs9%Expected D1$4.20Stock
price$105.00Expected dividend yield4.00%Expected capital
gains yield5.00%Alternatively, you know that the capital gains
yield is equal to the growth rate.Expected capital gains yield =
growth rate = 5.00%Because the total return is rs, the dividend
yield is rs minus the capital gains yield:Expected dividend yield
=4.00%Suppose D0 = $5.00 and rs = 10%. The expected growth
rate from Year 0 to Year 1 (g0 to 1) = 20%, the expected growth
rate from Year 1 to Year 2 (g1 to 2) = 10%, and the constant
rate beyond Year 2 is gL = 5%. What are the expected
dividends for Year 1 and Year 2? What is the expected horizon
value price at Year 2? What is the expected price at Time
0?D0$5.00g0 to 120%g1 to
210%gL5%rs10%Year12D1D2Expected
dividends$6.00$6.60Expected HVP,2$138.60PV of expected
dividends$10.91PV of expected HVP,2$114.55Expected price at
Time 0$125.45
7-12SECTION 7-12SOLUTIONS TO SELF-TESTDodd
Corporation is a private company that earned $4.00 per share
for the most recent year. If the average P/E ratio of a group of
comparable public companies is 11, what is an estimate of
Dodd's stock value on a per share basis? Earnings per share
=$4.00Average comparable P/E ratio =11.0Estimated price per
share =$44.00The company in the previous question, Dodd
Corporation, has 100,000 shares of common stock owned by its
founder. Dodd owes $1,300,000 to its bank. Dodd has 11,400
customers. If the average ratio of total entity value to customers
is $500 for a group of comparable public companies, what is
Dodd's estimated total entity value? What is its estimated stock
value on a per share basis?Number of shares =100,000Debt
=$1,300,000Number of customers =11,400Average comparable
ratio of
total entity value to number of customers =$500Estimated
entity value =$5,700,000− Debt$1,300,000Intrinsic equity
value4,400,000÷ Number of shares100,000Estimated price per
share =$44.00
7-14SECTION 7-14SOLUTIONS TO SELF-TEST A preferred
stock has an annual dividend of $5. The required return is 8%.
What is the Vps?Dps$5.00rps8%Vps$62.50
(
)
ú
û
ù
ê
ë
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L
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L
T
T)
Year
Horizon
op(at
g
WACC
WACC
ROIC
g
1
1
OpCap
V
L
TL
TT)Year Horizon op(at
gWACC
WACCROICg1
1OpCapV

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ChapterTool KitChapter 7102715Corporate Valuation and Stock Valu.docx

  • 1. ChapterTool KitChapter 710/27/15Corporate Valuation and Stock Valuation7-4 Valuing Common Stocks—Introducing the Free Cash Flow (FCF) Valuation ModelData for B&B Corporation (Millions)Constant free cash flow (FCF) =$10Weighted average cost of capital (WACC) =10%Short-term investments =$2Debt =$28Preferred stock =$4Number of shares of common stock =5The first step is to estimate the value of operations, which is the present value of all expected free cash flows. Because the FCF's are expected to be constant, this is a perpetuity. The present value of a perpetuity is the cash flow divided by the cost of capital:Value of operations (Vop) =FCF/WACCValue of operations (Vop) =$100.00millionB&B's total value is the sum of value of operations and the short-term investments: Value of operations$100+ ST investments$2Estimated total intrinsic value$102The next step is to estimate the intrinsic value of equity, which is the remaining total value after accounting for the claims of debtholders and preferred stockholders: Value of operations$100+ ST investments$2Estimated total intrinsic value$102− All debt$28− Preferred stock$4Estimated intrinsic value of equity$70The final step is to estimate the intrinsic common stock price per share, which is the estimated intrinsic value of equity divided by the number of shares of common stock: Value of operations$100+ ST investments$2Estimated total intrinsic value$102− All debt$28− Preferred stock$4Estimated intrinsic value of equity$70÷ Number of shares5Estimated intrinsic stock price =$14.00The figure below shows a summary of the previous calculations.Figure 7-2B&B Corporation's Sources of Value and Claims on Value (Millions of Dollars except Per Share Data)Inputs:Valuation AnalysisConstant free cash flow (FCF) =$10Value of operations$100Weighted average cost of capital (WACC) =10%+ ST investments$2Short-term investments =$2Estimated total intrinsic value$102Debt =$28− All debt$28Preferred stock
  • 2. =$4− Preferred stock$4Number of shares of common stock =5Estimated intrinsic value of equity$70÷ Number of shares5Estimated intrinsic stock price$14.00Data for Pie ChartsShort-term investments =$2Value of operations =$100Total =$102Debt =$28Preferred stock =$4Estimated equity value =$70Total =$1027-5 The Constant Growth Model: Valuation when Expected Free Cash Flow Grows at a Constant RateCase 1: The expected free cash flow at t=1 and the expected constant growth rate after t=1 are known.First expected free cash flow (FCF1) =$105Weighted average cost of capital (WACC) =9%Constant growth rate (gL) =5%When free cash flows are expected to grow at a constant rate, the value of operations is:Value of operations (Vop) =FCF1 / [WACC- gL]Value of operations (Vop) =$2,625Case 2: Constant growth is expected to begin immediately.Most recent free cash flow (FCF0) =$200Weighted average cost of capital (WACC) =12%Constant growth rate (gL) =7%When free cash flows are expected to grow at a constant rate, the value of operations is:Value of operations (Vop) =[FCF0(1+gL)]/[WACC-gL]Value of operations (Vop) =$4,2807-6 The Multi-Stage Model: Valuation when Expected Short-Term Free Cash Flow Grows at a Nonconstant RateThurman Corporation's expected free cash flows are shown below.Year01234FCF−$20$80$100$110Growth in FCF25%10%Free cash flows are expected to grow at a 5% rate starting at Year 4 and to continue growing at a 5% rate for the foreseeable future. We know the free cash flow at Year 4 and we know that FCF grows at a constant rate after Year 4. Therefore, we set the horizon date at Year 4.Free cash flow at beginning of the constant growth phase (FCF4) =$110Weighted average cost of capital (WACC) =15%Constant growth rate (gL) =5%HV4 = Vop, at 4 =[FCF4 (1+gL)]/ [WACC-gL]HV4 = Vop, at 4 =$1,155Thurman's time line of expected free cash flows and horizon value is shown below.Year01234FCF−$20$80$100$110Horizon value$1,155Present value of HV4 = $660.375Present value of free cash flows = $171.745Total value of operations at Year 0,
  • 3. Vop, at t=0 =$832.120There is more than one correct way to find the present value of the FCFs and the horizon value. For example, you could find the total cash flows, as shown below, which are equal to the free cash flows except for the last period, when they are equal to the sum of the free cash flow and the horizon value. (It is as though you received the FCF at Year 4 and then "sold" the operations and received cash equal to the horizon value.) You could then find present value of the combined free cash flows and horizon value.Year01234FCF−$20$80$100$110Horizon value$1,155Combined FCF and HV−$20.00$80.00$100$1,265PV of combined FCF and HV = Total value of operations at Year 0, Vop, at t=0 =$832.12Here is a third way to find the present value of the FCFs and the horizon value. The basic idea is to find the value of operations at each date. For the last date, the value of operations is the horizon value. For the previous date, the value of operations is equal to the present value of the sum of the next date's value of operations and FCF. For example, if you sell the operations immediately after receiving the FCF at Year 3, then the purchaser would receive the FCF at Year 4 plus the value of operations at Year 4 (which is the present value of all cash flows beyond Year 4). Year20182019202020212022FCF−$20.00$80.00$100.00$110.00 Horizon value$1,155Vop,t = (FCFt+1 + Vop,t+1)/ (1+WACC)$832.12$976.94$1,043.48$1,100.00$1,155.00Option al Material. You may have noticed that we could have defined the horizon date at Year 3 because we have an estimate of the Year 4 free cash flow, which is expected to grow at a constant rate thereafter. However, we recommend defining the horizon date as the last date in the forecast period even if growth becomes constant at or prior to this date because we have found that this leads to fewer errors. But we illustrate this approach below for the interested reader.Free cash flow at beginning of the constant growth phase (FCF4) =$110Weighted average cost
  • 4. of capital (WACC) =15%Constant growth rate (gL) =5%HV3 = Vop, at 3 =FCF4 / [WACC-gL]HV3 = Vop, at 3 =$1,100Thurman's time line of expected free cash flows and horizon value is shown below.Year0123FCF−$20$80$100Horizon value$1,100Present value of HV4 = $723.268Present value of free cash flows = $108.852Total value of operations at Year 0, Vop, at t=0 =$832.120Following is a summary of the steps used in estimating Thurman Corporation's value of operations.Figure 7- 3Thurman Corporation's Value of Operations (Millions of Dollars)INPUTS:gL = 5%WACC =15%ProjectionsYear01234FCF−$20.00$80.00$100.00$110.00 ⟶⟶ ⟶↴ ↓↓↓↓↓FCF1FCF2FCF3FCF4HV = Vop(t=4)────────────────────────↓(1+WACC)1( 1+WACC)2(1+WACC)3(1+WACC)4 FCF4(1+gL)↓↓↓↓ ───────── ↓↓↓↓ (WACC− gL)↓↓↓↓↓↓↓↓↓$115.500PVs of FCFs−$17.391⟵ ⟵ ⤶ ↓↓↓10.00%$60.491⟵ ⟵ ⟵ ⟵ ⟵ ⤶ ↓↓↓$65.752⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⤶ ↓ $1,155.000$62.893⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⤶ ↓PV of HV$660.375⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ $1,155.000 ⟵ ⟵ ⟵ ⤶ ↓= ────── Vop =$832.12(1+WACC)47-7 Application of the FCF Valuation Model to MicroDriveWe begin with MicroDrive's most recent financial statements and selected additional data.Figure 7-4 MicroDrive’s Most Recent Financial Statements (Millions, Except for Per Share Data)INCOME STATEMENTSBALANCE SHEETS20152016Assets20152016Net sales$ 4,760$ 5,000Cash$ 60$ 50COGS (excl. depr.)3,5603,800ST Investments400Depreciation170200Accounts receivable380500Other operating expenses480500Inventories8201,000EBIT$ 550$ 500Total CA$ 1,300$ 1,550Interest expense100120Net PP&E1,7002,000Pre-tax earnings$ 450$ 380Total assets$ 3,000$ 3,550Taxes (40%)180152NI before pref. div.$ 270$ 228Liabilities and EquityPreferred div.88Accounts payable$ 190$ 200Net income$ 262$ 220Accruals280300Notes
  • 5. payable130280Other DataTotal CL$ 600$ 780Common dividends$48$50Long-term bonds1,0001,200Addition to RE$214$170Total liabilities$ 1,600$ 1,980Tax rate40%40%Preferred stock100100Shares of common stock5050Common stock500500Price per share$40.00$27.00Retained earnings800970Total common equity$ 1,300$ 1,470Weighted average cost of capital (WACC)Total liabs. & equity$ 3,000$ 3,55010.50%10.97%The first step is to calculate the key performance measures that determine free cash flows. Figure 7- 5Key Performance Measures for MicroDrive (Millions of Dollars)MicroDriveIndustry201520162016Calculating Net Operating Profit after Taxes (NOPAT)NOPAT = EBIT(1 − T)$330$300Calculating Net Operating Working Capital (NOWC)Operating current assets$1,260$1,550− Operating current liabilities$470$500NOWC$790$1,050Calculating Total Net Operating Capital (OpCap)NOWC$790$1,050+ Net PP&E$1,700$2,000OpCap$2,490$3,050Investment in operating capital$560Calculating Free Cash Flow (FCF)FCF = NOPAT – Investment in operating capital−$260Calculating Return on Invested Capital (ROIC)ROIC = NOPAT/Total net operating capital13.25%9.84%15.04%Calculating the Operating Profitability Ratio (OP)OP = NOPAT/Sales6.93%6.00%6.92%Calculating the Capital Requirement Ratio (CR)CR = (Total net operating capital)/Sales52.31%61.00%46.00%The next step is to forecast sales, NOPAT, and total net operating capital. We do this by estimating future sales' growth rates, operating profitability ratios, and capital requirement ratios, as shown in Panel A in the Figure below.Yearly sales are forecast by letting the previous year's sales increase by the forecasted sales growth rate. Operating profitability and total net operating capital in a forecasted year are assumed to be proportional to sales in that year.Figure 7-6MicroDrive's Forecast of Operations for the Selected Scenario (Millions of Dollars, Except for Per Share Data)Status QuoIndustryMicroDriveMicroDrivePanel
  • 6. A:ActualActualForecastOperating Ratios20162015201620172018201920202021g = Sales growth rate15%5%10%8%7%5%5%OP = NOPAT/Sales6.92%6.9%6%6%6%6%6%6%CR = OpCap/Sales46.0%52.3%61%61%61%61%61%61%Tax rate40%40%40%40%40%40%40%40%Panel B:ActualForecastOperating Items201620172018201920202021Net sales$5,000$5,500$5,940$6,356$6,674$7,007.270Net operating profit after taxes$300$330$356$381$400$420.436Total net operating capital (OpCap)$3,050$3,355$3,623$3,877$4,071$4,274.434FCF = NOPAT – Investment in OpCap−$260$25$88$128$207$216.892Growth in FCF252%45.1%61.7%5.0%ROIC = NOPAT/OpCap9.84%9.84%9.84%9.84%9.84%9.84%Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations. The next step is to estimate the horizon value and the value of operations, beginning with the horizon value.Free cash flow at beginning of the constant growth phase (FCF2021) =$216.892Weighted average cost of capital (WACC) =10.97%Constant growth rate (gL) =5%HV2021 = Vop, 2021 =[FCF2021 (1+gL)]/ [WACC-gL]HV2021 = Vop, 2021 =$3,814.678MicroDrive's time line of expected free cash flows and horizon value is shown below.Year201620172018201920202021FCF$25.000$88.000$12 7.710$206.564$216.892Horizon value$3,814.678Present value of HV = $2,266.887Present value of free cash flows = $452.552Total value of operations at Year 0, Vop, at t=0 =$2,719.439The figure below shows a summary of these calculations.Figure 7-7MicroDrive Inc.'s Value of Operations (Millions of Dollars)INPUTS:Scenario:Status QuogL = 5%WACC =10.97%ProjectionsYear201620172018201920202021FCF$25.0 00$88.000$127.710$206.564$216.892⟶
  • 7. ↴ ↓↓↓↓↓↓FCF2017FCF2018FCF2019FCF2020FCF2021↓───── ─────────────────────────HV = Vop(2021)(1+WACC)1(1+WACC)2(1+WACC)3(1+WACC)4(1+ WACC)5↓↓↓↓↓↓ FCF2021(1+gL)↓↓↓↓↓ ───────── ↓↓↓↓↓ (WACC− gL)↓↓↓↓↓↓PVs of FCFs$22.529⟵ ⤶ ↓↓↓↓$227.736$71.461⟵ ⟵ ⟵ ⟵ ⟵ ⤶ ↓↓↓0.0597$93. 456⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⤶ ↓↓↓$136.217⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⤶ ↓$3, 814.678$128.889⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⤶ ↓PV of HV$2,266.887⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ $3,814.678 ⟵ ⟵ ⤶ ↓= ────── Vop =$2,719.44(1+WACC)5Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations. Estimating MicroDrive's Intrinsic Stock Price per ShareValue of operations =$2,719.44Weighted average cost of capital (WACC) =10.97%Short-term investments =$0Short-term debt (notes payable) =$280Long-term debt (bonds) =$1,200Preferred stock =$100Number of shares of common stock =50MicroDrive's total value is the sum of value of operations and the short-term investments: Value of operations$2,719.44+ ST investments$0Estimated total intrinsic value$2,719.44The next step is to estimate the intrinsic value of equity, which is the remaining total value after accounting for the claims of debtholders and preferred stockholders: Value of operations$2,719+ ST investments$0Estimated total intrinsic value$2,719.44− All debt$1,480− Preferred stock$100Estimated intrinsic value of equity$1,139.44The final step is to estimate the intrinsic common stock price per share, which is the estimated intrinsic value of equity divided by the number of shares of common stock: Value of operations$2,719.44+ ST investments$0Estimated total intrinsic value$2,719.44− All debt$1,480− Preferred stock$100Estimated intrinsic value of equity$1,139.44÷ Number of shares50Estimated intrinsic stock price =$22.79The figure below shows a summary of the previous calculations.Figure 7-8MicroDrive Inc.'s Intrinsic Stock Price (Millions, Except for Per Share Data)INPUTS:gL = 5%WACC =10.97%Year =20172018201920202021Projected
  • 8. FCF =$25$88.0$127.71$206.564$216.892Horizon Value:Value of operations$2,719+ ST investments$0=$3,815Estimated total intrinsic value$2,719− All debt$1,480Value of Operations:− Preferred stock$100Present value of HV$2,266.89Estimated intrinsic value of equity$1,139+ Present value of FCF$452.55÷ Number of shares50Value of operations =$2,719.44Estimated intrinsic stock price =$22.79Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations. 7-8 Do Stock Prices Reflect Long-Term or Short-Term Cash Flows?Managers often claim that stock prices are "short-term" in nature in the sense that they reflect what is happening in the near-term and ignore the long- term. We can use MicroDrive's results to shed light on this claim.We previously estimated MicroDrive's current value of operations. We also estimated MicroDrive's horizon value at Year 5 and calculated its present value. If we divide the present value of the horizon value, we can estimate how much of MicrDrive's value is due to cash flows occurring beyond Year 5. In other words, we can determine how much of MicroDrive's value is due to long-term cash flows and how much is due to short-term cash flows.Inputs:Weighted average cost of capital =10.97%Horizon year =5Horizon value at Year 5 (HV5) =$3,814.678Value of operations at Year 0 (Vop,0) =$2,719.439Analysis:Present value of the horizon value =$2,266.887Value of operations at Year 0 =$2,719.439Results:Percent of current value due to long-term cash flows (i.e., PV of HV5) =83%Percent of current value due to short-term cash flows =17%For most stocks, the percentage of the current price that is due to long-term cash flows is over 80%.7-9 Using the Free Cash Flow Valuation Model to Identify Value DriversWe can use the free cash flow valuation model we developed previously for MicroDrive to determine how the inputs (sales growth, operating profitability, and capital requirements) affect the value of operations and intrinsic stock price. It is very easy to do this in Excel by using the Scenario Manager feature. Following is an explantion of how to use this
  • 9. feature.The Scenario Manager allows you to specify values for particular cells and then save those values as a "scenario." If you later change the values in the cells, perhaps to see the impact that the change has on an output, the Scenario Manager allows you to restore the saved scenario without having to re- input the original values. You can create numerous different scenarios, and you can even have the Scenario Manager create a summary that shows the values of the input cells and the values of the output cells for each scenario that you created.To create a scenario, go to the Data tab in the menu, look in the Data Tools section for What-If Analysis, and then select Scenario Manager. This will open a dialog box that shows seven existing scenarios. If you select the button for "Add…", you will get another dialog box asking you to give the scenario a name and to specify the "Changing cells." The "Changing cells" are the cells with values that you want the Scenario Manager to save. For example, we want to save the values for MicroDrive's estimated sales growth rates, operating profitabiltiy ratio, and capital requirement ratio. After specifying the "Changing cells", click "Ok" and you will get a new dialog box asking you to input the values into the changing cells that you want for this scenario. There will already be values shown, which are the values currently in those cells. So if you have already put the values into the cells in the Excel workbook, you won't have to re-enter them in the dialog box, you can simply click "Ok" and you will have created a new scenario.The original dialog box gives you several options, including adding a scenario, deleting a scenario, and editing a scenario. It also give you the option to run a "Summary." If you select the "Summary" button, you get a dialog box asking you to specify some "Results" cells. For example, we specified the cells in this worksheet that have the value of operations, the intrinsic stock price, and the return on invested capital for the last year in the forecast horizon. After selecting the "Results" cells, you can click "Ok" and the Scenario Manager will create a new worksheet named "Scenario Summary". This new sheet contains the name of each scenario, the values in the "Changing
  • 10. cells", and the values in the "Results cells. We copied the information from the "Scenario Summary" into the table below and then formatted the table to make it a bit more reader- friendy. Figure 7-9Value Drivers for MicroDrive Inc. (Millions, Except for Per Share Data)ScenarioAdditional information not in textbook(1) Status Quo(2) Higher Sales Growth (Only)(3) Higher Operating Profitability (Only)(4) Better Capital Utilization (Only)(5) Improve Growth and OP(6) Improve Growth and CR(7) Improve Growth, OP, and CR(8) Status Quo but Lower WACC(9) Better OP and CRInputsSales growth in 1st year10%11%10%10%11%11%11%10%10%Sales growth in 2nd year8%9%8%8%9%9%9%8%8%Sales growth in 3rd year7%8%7%7%8%8%8%7%7%Long-term sales growth (gL)5%6%5%5%6%6%6%5%5%Operating profitability (OP)6%6%7%6%7%6%7%6%7%Capital requirement (CR)61%61%61%52%61%52%52%61%52%Weighted average cost of capital (WACC)10.97%10.97%10.97%10.97%10.97%10.97%10.97%9.5 0%10.97%ResultsValue of operations$2,719$2,713$3,682$3,576$3,880$3,751$4,918$3,690 $4,538Intrinsic stock price$22.79$22.67$42.04$39.91$46.00$43.42$66.76$42.19$59. 16Return on invested capital (ROIC)9.84%9.84%11.48%11.54%11.48%11.54%13.46%9.84% 13.46%To better understand why growth doesn't always add value, we can express the horizon value as:If the numerator in the fraction in brackes, (1+gL) ROIC − WACC, is negative, then the value of operations will be less than the total net operation capital, OpCapT. If ROIC < WACC/(1+WACC), then
  • 11. growth hurts value. The 2-way data table below show the difference between the value operations and the amount of operating capital for different combinations of growth and ROIC. For input values, we use values similar to those of MicroDrive's at the horizon.Input Values (Base Case)OpCap =$4,274gL =5.0%ROIC =9.84%WACC =10.97%Output from equation above in yellow.Vop =$3,815Vop − OpCap =-$460A Two-Way Data Table Showing How Combinations of Growth and ROIC Affect the Value of Operations Minus the Value of Operating CapitalCombinations of growth and ROIC that have Vop < OpCap are shown in pink. Notice that for very low values of ROIC, such as the first row with ROIC = 9.7%, growth reduces value (you can see this by looking across the row. For very high values of ROIC, such as the last row with ROIC = 11%, growth adds value. For other combinations, it depends on the relative values of growth, ROIC, and WACC.gL−$4600.0%2.5%5.0%7.5%9.5%ROIC9.70%-$495- $519-$562-$668-$1,0139.80%-$456-$467-$487-$536- $6959.84%-$442-$448-$460-$488-$5809.90%-$417-$415-$412- $403-$37710.00%-$378-$363-$337-$271-$5810.10%-$339- $312-$261-$139$26010.20%-$300-$260-$186-$6$57910.30%- $261-$208-$111$126$89710.40%-$222-$156- $36$259$1,21510.50%-$183-$105$39$391$1,53410.60%-$144- $53$115$524$1,85210.70%-$105-$1$190$656$2,17110.80%- $66$50$265$788$2,48910.90%- $27$102$340$921$2,80711.00%$12$154$415$1,053$3,1267-11 Valuing Common Stocks with the Dividend Growth ModelThe Discounted Dividend ApproachThe value of any financial asset is the present value of the future cash flows provided by the asset. When an investor buys a share of stock, he or she typically expects to receive cash in the form of dividends and then, eventually, to sell the stock and to receive cash from the sale. However, the price the first investor receives is dependent upon the dividends the next investor expects to earn, and so on for different generations of investors. Thus, the stock's value ultimately depends on the cash dividends the company is
  • 12. expected to provide and the discount rate used to find the present value of those dividends.Here is the basic dividend valuation equation:P0 =D1+D2+. . . .DN( 1 + rs )( 1 + rs ) 2( 1 + rs ) NThe dividend stream theoretically extends on out forever, i.e., to N = infinity. Obviously, it would not be feasible to deal with an infinite stream of dividends, but fortunately, a relatively simple equation has been developed that can be used to find the PV of the dividend stream, provided it is growing at a constant rate.Valuing a Constant Growth StockIn the constant growth model, we assume that the dividend and stock will grow forever at a constant growth rate. Naturally, assuming a constant growth rate for the rest of eternity is a rather bold assumption. However, considering the implications of imperfect information, information asymmetry, and general uncertainty, the assumption of constant growth is often reasonable. It is reasonable to guess that a given stock will experience ups and downs throughout its life. By assuming constant growth, we are trying to find the average of the good times and the bad times, and we assume that we will see both scenarios over the firm's life. In addition to a constant growth rate, we also need the estimated long-term required return for the stock, and it too must be constant. If these variables are constant, our price equation for common stock simplifies to the following expression:P0 =D1( rs – gL )Generally speaking, the long-run growth rate of a firm is likely to fall between 5% and 8% a year.Example: Value of a Constant Growth StockA firm just paid a $1.15 dividend and its dividend is expected to grow at a constant rate of 8%. What is its stock price, assuming it has a required return of 13.4%?D0 =$1.15gL =8%rs =13.4%P0 =D1=D0 (1 + gL)=$1.2420( rs – gL )( rs – gL )0.0540P0 =$23.00Expected Rate of Return on a Constant Growth StockUsing the constant growth equation introduced earlier, we can re-work the equation to solve for rs. In doing so, we are now solving for an expected return. The expression we are left is:D1+gLP0This expression tells us that the expected return on a stock comprises two components. First, it consists of the
  • 13. expected dividend yield, which is simply the next expected dividend divided by the current price. The second component of the expected return is the expected capital gains yield. The expected capital gains yield is the expected annual price appreciation of the stock, and is given by gL. This shows us the dual role of gL in the constant growth rate model. Not only does g indicate expected dividend growth, but it is also the expected stock price growth rate.Example: Expected Rate of Return on a Constant Growth StockYou buy a stock for $23, and you expect the next annual dividend to be $1.242. Furthermore, you expect the dividend to grow at a constant rate of 8%. What is the expected rate of return on the stock, and what is the dividend yield of the stock?Inputs:P0 $23.00D1$1.242gL8%13.40%Dividend yield =5.40%What is the expected price of this stock in 1 year?Application of Constant Growth Model at t=1P1 =D2( rs – gL )D2 =1.34136P1 =$24.84Valuing Nonconstant Growth StocksFor many companies, it is unreasonable to assume that they grow at a constant growth rate. Hence, valuation for these companies proves a little more complicated. The valuation process, in this case, requires us to estimate the short-run nonconstant growth rate and predict future dividends. Then, we must estimate a constant long-term growth rate at which the firm is expected to grow. Generally, we assume that after a certain point of time, all firms begin to grow at a rather constant rate. Of course, the difficulty in this framework is estimating the short-term growth rate, how long the short-term growth will hold, and the long- term growth rate.Figure 7-10Illustrative Dividend Growth at Different RatesData for figure:Growth RatesYearDeclining ZeroConstantNonconstant1-8%0%8%30%2-8%0%8%20%3- 8%0%8%10%4-8%0%8%8%5- 8%0%8%8%DividendYearDeclining Growth: -8%Zero GrowthConstant Growth: 8%Long-Term Growth: 8%YearDeclining Growth: -8%Zero GrowthConstant Growth: 8%Long-Term Growth: 8%0$1.15$1.15$1.15$1.1501.15001.15001.15001.15001$1.06$1
  • 14. .15$1.24$1.5011.05801.15001.24201.49502$0.97$1.15$1.34$1. 7920.97341.15001.34141.79403$0.90$1.15$1.45$1.9730.89551. 15001.44871.97344$0.82$1.15$1.56$2.1340.82391.15001.56462 .13135$0.76$1.15$1.69$2.3050.75791.15001.68972.3018Specifi cally, we will predict as many future dividends as we can and discount them back to the present. Then we will treat all dividends to be received after the convention of constant growth rate with the Gordon constant growth model described above. The point in time when the dividend begins to grow constantly is called the horizon date. When we calculate the constant growth dividends, we solve for the horizon value (also called a terminal value or a continuing value) as of the horizon date. The horizon value can be summarized as:HVT =PT =DT+1=DT (1 + g)( rs – gL )( rs – gL )This condition holds true, where T is the horizon date. The horizon value can be described as the expected value of the stock at the time period corresponding to the horizon date.A company's stock just paid a $1.15 dividend, which is expected to grow at 30% the first year, 20% the second year, and 10% the third year. After three years the dividend is expected to grow constantly at 8% forever. The stock's required return is 13.4%; what is the price of the stock today?Figure 7-11Process for Finding the Value of a Nonconstant Growth StockINPUTS:D0 =$1.15Last dividend the company paid.rs =13.4%Stockholders' required return.g0,1 =30%Growth rate for Year 1 only.g1,2 =20%Growth rate for Year 2 only.g2,3 =10%Growth rate for Year 3 only.gL =8%Constant long-run growth rate for all years after Year 3.ProjectionsYear0123⟶∞Growth rate30%20%10%8%DividendD0D0(1+g0,1)D1(1+g1,2)D2(1+g1, 2)Dt$1.15$1.495$1.794$1.973↓↓↓D1D2D3───────────── ─────HV3 = (1+rs)1(1+rs)2(1+rs)3↓↓↓↓ D3(1+gL)↓↓↓ ─────── ↓↓↓(rs− gL)↓↓↓↓↓↓↓$2.131PVs of Dividends$1.318⟵ ⤶ ↓↓5.400%$1.395⟵ ⟵ ⟵ ⟵ ⟵ ⤶ ↓↓$1.353⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⤶ $39.468↓PV of $27.065⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ ⟵ $39.468↓= ──────⟵ ⟵ ⟵ ⟵ = ────── Vop =$31.13(1+0.134)3(1+rs)3Note: Numbers in the figure are
  • 15. shown as rounded for clarity in reporting. However unrounded values are used for all calculations. 7-12 Market Multiple AnalysisUse the following data in the market multiple approach to estimate the stock price per share. Forecasted earnings per share (EPS) =$7.70Average peer price/earnings (P/E) ratio =12Estimated stock price: $92.407-14 Preferred StockConsider an issue of preferred stock that pays an $8 dividend and has a required return of 8%. What is the value of this preferred stock?Vps =Dps÷rps =$8.00÷8.00% =$100.00Some preferred stock has a maturity date. Consider a firm whose preferred stock matures in 50 years, pays a $8 annual dividend, has a par value of $100, and has a required return of 6%. What is the price of this preferred stock?Years to Maturity (N):50Annual Dividend (PMT):$8Par value (FV):$100Required return, rd (I/YR):6%Vps =$131.52 Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc. Declining Growth: -8% 0 1 2 3 4 5 1.1499999999999999 1.0580000000000001 0.97336000000000011 0.89549120000000015 0.82385190400000019 0.75794375168000017 Zero Growth Zero Growth 0 1 2 3 4 5 1.1499999999999999 1.1499999999999999 1.1499999999999999 1.1499999999999999 1.1499999999999999 1.1499999999999999 Constant Growth: 8% 0 1 2 3 4 5 1.1499999999999999 1.242 1.3413600000000001 1.4486688000000003 1.5645623040000005 1.6897272883200007 Long- Term Growth: 8% 0 1 2 3 4 5 1.1499999999999999 1.4949999999999999 1.7939999999999998 1.9734 2.1312720000000001 2.3017737600000001 Sources of Value
  • 16. Short-term investments = Value of operations = 2 100 Claims on Value Debt = Preferred stock = Estimated equity value = Total = 28 4 70 Scenario SummaryScenario SummaryCurrent Values:Status QuoHigher Growth (Only)Higher OP (Only)Better CR (Only)Improve Growth and OPImprove Growth and CRImprove Growth, OP, and CRLower WACC (Only)Better OP and CRCreated by Mike Ehrhardt on 5/22/2014 Modified by Mike Ehrhardt on 5/23/2014Created by Mike Ehrhardt on 5/22/2014 Modified by Mike Ehrhardt on 5/23/2014Created by Mike Ehrhardt on 5/22/2014 Modified by Mike Ehrhardt on 5/23/2014Created by Mike Ehrhardt on 5/22/2014 Modified by Mike Ehrhardt on 5/23/2014Created by Mike Ehrhardt on 5/22/2014 Modified by Mike Ehrhardt on 5/23/2014Created by Mike Ehrhardt on 5/22/2014 Modified by Mike Ehrhardt on 5/23/2014Created by Mike Ehrhardt on 5/22/2014 Modified by Mike Ehrhardt on 5/23/2014Created by Mike Ehrhardt on 5/23/2014 Modified by Mike Ehrhardt on 5/23/2014Created by Mike Ehrhardt on 3/21/2015Changing Cells:$A$324Status QuoStatus QuoHigher Growth (Only)Higher OP (Only)Better CR (Only)Improve Growth and OPImprove Growth and CRImprove Growth, OP, and CRLower WACC (Only)Better OP and CR$F$3278%8%9%8%8%9%9%9%8%8%$G$3277%7%8%7%7 %8%8%8%7%7%$H$3275%5%6%5%5%6%6%6%5%5%$E$327 10%10%11%10%10%11%11%11%10%10%$E$3286%6%6%7% 6%7%6%7%6%7%$E$32961%61%61%61%52%61%52%52%61 %52%$C$28210.97%10.97%10.97%10.97%10.97%10.97%10.97 %10.97%9.50%10.97%Result
  • 17. Cells:$B$396$2,719.44$2,719.44$2,713.27$3,681.78$3,575.63$ 3,879.93$3,751.25$4,917.91$3,689.71$4,537.97$G$460$22.79$ 22.79$22.67$42.04$39.91$46.00$43.42$66.76$42.19$59.16$I$3 389.84%9.84%9.84%11.48%11.54%11.48%11.54%13.46%9.84 %13.46%Notes: Current Values column represents values of changing cells attime Scenario Summary Report was created. Changing cells for eachscenario are highlighted in gray. 7-4SECTION 7-4SOLUTIONS TO SELF-TEST A company expects a constant FCF of $240 million per year forever. If the WACC is 12%, what is the value of operations?Expected FCF$240WACC12%Vop = $2,000.00A company has a current value of operations of $800 million. The company has $100 million in short-term investments. If the company has $400 million in debt and has 10 million shares outstanding, what is the price per share?Vop$800ST investments$100Total value$900Debt$400Value of equity$500Number of shares10Price per share$50.00 7-5SECTION 7-5SOLUTIONS TO SELF-TEST A company expects to have a FCF in 1 year of $300, which is expected to grow at a constant rate of 3% forever. If the WACC is 11%, what is the value of operations?Expected FCF1 =$330Expected gL =3%WACC =11%Vop = $4,125A company's most recent free cash flow was $270. The company expects to have a FCF in 1 year of $300, which is expected to grow at a constant rate of 3% forever. If the WACC is 11%, what is the value of operations?Expected FCF1 =$300Expected gL =3%WACC =11%Notice that the FCF of $270 at t = 0 is irrelevant to the value of operations, because it occurred in the past. The value of operations depends only on the future free cash flows.Vop = $3,750A company's most recent free cash flow was $600 and is expected to grow at a constant rate of 4% forever. If the WACC is 10%, what is the value of operations?FCF0 =$600Expected gL =4%WACC =10%Vop = $10,400 7-6SECTION 7-6SOLUTIONS TO SELF-TEST A company expects to have a FCF at Year 10 of $600, which is expected to grow at a constant rate of 8% thereafter. If the WACC is 8%,
  • 18. what is the value of operations at Year 10, HV10?Expected FCF12 =$600Expected gL =4%WACC =8%Vop = $15,600A company expects a FCF of -$10 million at Year 1 and a FCF of $20 million at Year 2. FCF is expected to grow at a 5% rate after Year 2. If the WACC is 10%, what is the horizon value of operations; i.e., Vop(Year 2)? What is the current value of operations; i.e., Vop(Year 0)?Long-term growth rate5%WACC10%Year12FCF1FCF2Expected FCF- $10.00$20.00Vop(Year 2)$420.00PV of expected FCF$7.44PV of expected Vop(Year 2)$347.11Vop(Year 0)$354.55 7-7SECTION 7-7SOLUTIONS TO SELF-TEST Cathey Corporation currently has sales of $1,000, which are expected to grow by 10% from Year 0 to Year 1 and by 4% from Year 1 to Year 2. The company currently has and operating profitability (OP) ratio of 7% and a capital requirement (CR) ratio of 50% and expects to maintain these ratios at their current levels. The current level of operating capital is $510. Use these inputs to forecast free cash flow (FCF) for Years 1 and 2. Hint: You must first forecast sales, net operating profit after taxes (NOPAT), and total net operating capital (OpCap) for each year.Sales0 =$1,000g0,1 =10%g1,2 =4%OP = NOPAT/Sales =7%CR = OpCap/Sales =50%OpCap0 =$510Year0123Growth rate in sales10%4%4%Sales$1,000$1,100.00$1,144.00$1,189.76NOPA T$77.00$80.08$83.28OpCap$510$550.00$572.00$594.88Invest ment in OpCap$40.00$22.00$22.88FCF$37.00$58.08$60.40Growth in FCF57.0%4.0%Cathey Corporation has a 12% weighted average cost of capital. Cathey's free cash flows, estimated in the previous question, are expected to grow at 4% beginning at Year 2 and continuing for the foreseeable future. What is the horizon value (use Year 2 for the horizon)? What is the current value of operations? Long-term growth rate4%WACC12%Year12FCF1FCF2Expected FCF$37.00$58.08HV2 = Vop(Year 2)$755.04PV of expected FCF$79.34PV of expected HV(Year 2)$601.91Vop(Year 0)$681.25Cathey Corporation has $80 in short-term
  • 19. investments, $20 in short-term debt, $140 in long-term debt, $30 in preferred stock, and 10 shares of common stock outstanding. Use the value of operations from the previous question to estimate the intrinsic common stock price per share.Vop =$681.25ST investments =$80.00ST debt =$20.00Long-term debt =$140.00Preferred stock =$30.00Number of shares =10Vop$681.25ST investments$80.00Total value$761.25All debt$160.00Preferred stock$30.00Value of equity$571.25Number of shares10.00Price per share$57.13 7-11SECTION 7-11SOLUTIONS TO SELF-TESTIf D1 = $3.00, P0 = $50, and the expected P at t=1 is equal to $52, what are the stock’s expected dividend yield, capital gains yield, and total return for the coming year?D1$3.00P0$50.00Expected P1$52.00Exp. dividend yield6.0%=B6/B7Exp. capital gains yield4.0%=(B8-B7)/B7Exp. total return10.0%=C10+C11A stock is expected to pay a dividend of $2 at the end of the year. The required rate of return is rs = 12%. What would the stock’s price be if the growth rate were 4%? D1$2.00gL4%rs12%Stock price$25.00A stock is expected to pay a dividend of $2 at the end of the year. The required rate of return is rs = 12%. What would the stock’s price be if the growth rate were 0%?D1$2.00gL0%rs12%Stock price$16.67If D0 = $4.00, rs = 9%, and g = 5% for a constant growth stock, what are the stock’s expected dividend yield and capital gains yield for the coming year?D0$4.00gL5%rs9%Expected D1$4.20Stock price$105.00Expected dividend yield4.00%Expected capital gains yield5.00%Alternatively, you know that the capital gains yield is equal to the growth rate.Expected capital gains yield = growth rate = 5.00%Because the total return is rs, the dividend yield is rs minus the capital gains yield:Expected dividend yield =4.00%Suppose D0 = $5.00 and rs = 10%. The expected growth rate from Year 0 to Year 1 (g0 to 1) = 20%, the expected growth rate from Year 1 to Year 2 (g1 to 2) = 10%, and the constant rate beyond Year 2 is gL = 5%. What are the expected dividends for Year 1 and Year 2? What is the expected horizon
  • 20. value price at Year 2? What is the expected price at Time 0?D0$5.00g0 to 120%g1 to 210%gL5%rs10%Year12D1D2Expected dividends$6.00$6.60Expected HVP,2$138.60PV of expected dividends$10.91PV of expected HVP,2$114.55Expected price at Time 0$125.45 7-12SECTION 7-12SOLUTIONS TO SELF-TESTDodd Corporation is a private company that earned $4.00 per share for the most recent year. If the average P/E ratio of a group of comparable public companies is 11, what is an estimate of Dodd's stock value on a per share basis? Earnings per share =$4.00Average comparable P/E ratio =11.0Estimated price per share =$44.00The company in the previous question, Dodd Corporation, has 100,000 shares of common stock owned by its founder. Dodd owes $1,300,000 to its bank. Dodd has 11,400 customers. If the average ratio of total entity value to customers is $500 for a group of comparable public companies, what is Dodd's estimated total entity value? What is its estimated stock value on a per share basis?Number of shares =100,000Debt =$1,300,000Number of customers =11,400Average comparable ratio of total entity value to number of customers =$500Estimated entity value =$5,700,000− Debt$1,300,000Intrinsic equity value4,400,000÷ Number of shares100,000Estimated price per share =$44.00 7-14SECTION 7-14SOLUTIONS TO SELF-TEST A preferred stock has an annual dividend of $5. The required return is 8%. What is the Vps?Dps$5.00rps8%Vps$62.50 ( ) ú û ù ê ë é