How to calculate long term constant growth in fcf

Mini Case
1/6/15
Chapter 8 Mini Case
Situation
Your employer, a mid-sized human resources management company, is considering expansion into related fields, including the acquisition of Temp Force Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporary heavy workloads. Your employer is also considering the purchase of a Biggerstaff & McDonald (B&M), a privately held company owned by two friends, each with 5 million shares of stock. B&M currently has free cash flow of $24 million, which is expected to grow at a constant rate of 5%. B&M’s financial statements report marketable securities of $100 million, debt of $200 million, and preferred stock of $50 million. B&M’s weighted average cost of capital (WACC) is 11%. Answer the following questions.
a. Describe briefly the legal rights and privileges of common stockholders.
Features of Common Stock
1. Common Stock represents ownership. 2. Ownership implies control. 3. Stockholders elect directors. 4. Directors hire management who attempt to maximize stock price.
Classified Stock
Classified Stock carries special provisions. For example, shares could be classified as founders' shares which come with voting rights but dividend restrictions.
b. What is free cash flow (FCF)? What is the weighted average cost of capital? What is the free cash flow valuation model?
c. Use a pie chart to illustrate the sources that comprise a hypothetical company’s total value. Using another pie chart, show the claims on a company’s value. How is equity a residual claim?
Data for charts
Column1
10
Mkt. Sec. 1
Claims on Value
Pref. Stk. 1
Debt 3
7
d. Suppose the free cash flow at Time 1 is expected to grow at a constant rate of gL forever. If gL < WACC, what is a formula for the present value of expected free cash flows when discounted at the WACC? If the most recent free cash flow is expected to grow at a constant rate of gL forever (and gL < WACC), what is a formula for the present value of expected free cash flows when discounted at the WACC?
If constant growth begins at Time 1:
If constant growth begins at Time 0:
e. Use B&M’s data and the free cash flow valuation model to answer the following questions.
INPUT DATA SECTION: Data used for valuation (in millions)
Free cash flow $24.0
WACC 11%
Growth 5%
Short-term investments $100.0
Debt $200.0
Preferred stock $50.0
Number of shares of stock 10.0
(1) What is its estimated value of operations?
Vop = FCF1 = FCF0 (1+gL)
(WACC-gL) (WACC-gL)
Vop = $25.2
0.06
Vop = $420.00
(2) What is its estimated total corporate value?
Value of Operation $420.0
Plus Value of Non-operating Assets $100.0
Total Corporate Value $520.0
(3) What is its estimated intrinsic value of equity?
Debt holders have the first claim on corporate value. Preferred stockholders have the next claim and the remaining is left to common stockholders.
Total Corporate Value $520.0
Minus Value of Debt $200.0
Minus Value of Preferred Stock $50.0
Intrinsic Value of Equity $270.0
(4) What is its estimated intrinsic stock price per share?
Intrinsic Value of Equity $270.0
Divided by number of shares 10.0
Intrinsic price per share $27.00
Estimating the Value of R&R’s Stock Price (Millions, Except for Per Share Data)
INPUTS:
Value of operations = $420.00
Value of nonoperating assets = $100.00
All debt = $200.00
Preferred stock = $50.00
Number of shares of common stock = 10.00
ESTIMATING PRICE PER SHARE
Value of operations $420.00
+ Value of nonoperating assets 100.00
Total estimated value of firm $520.00
− Debt 200.00
− Preferred stock 50.00
Estimated value of equity $270.00
÷ Number of shares 10.00
Estimated stock price per share = $27.00
f. You have just learned that B&M has undertaken a major expansion that will change its expected free cash flows to −$10 million in 1 year, $20 million in 2 years, and $35 million in 3 years. After 3 years, free cash flow will grow at a rate of 5%. No new debt or preferred stock were added, the investment was financed by equity from the owners. Assume the WACC is unchanged at 11% and it that there are still has 10 million shares of stock outstanding.
(1.) What is its horizon value (i.e., its value of operations at year three)? What is its current value of operations (i.e., at time zero)?
Explicit forecast:
Year 0 1 2 3
FCF FCF1 FCF2 FCF3
Constant growth from Year 3 and afterwards:
Year 0 1 2 3 4 5 … t
FCF FCF1 FCF2 FCF3 FCF3(1+gL) FCF4(1+gL) FCFt(1+gL)
Explicit forecast ends at Year 3, so make the horizon date Year 3, too. (Note: it is possible to make the horizon date Year 2 because FCF3 is known and grows at a constant rate, but it is easy to make mistakes if horizon year is not set equal to end of explicit forecast.)
HV3 = Vop,3 = PV of FCF4 and beyond discounted back to Year 3
Year 0 1 2 3 4 5 … t
FCF FCF3(1+gL) FCF4(1+gL) FCFt(1+gL)
HV3 ←↵ ←↵ ←↵
Because free cash flows are constant from Year 4 and beyond, we can apply the constant growth model at Year 3:
The general horizon value formula is:
R&R's explicit forecast:
Year 0 1 2 3
FCF −$10.00 $20.00 $35.00
After Year 3, gL = 5%
WACC = 11%
R&R's horizon value:
HV3 = Vop,3 = FCF0 (1+gL)
(WACC-gL)
HV3 = Vop,3 = $36.750
6%
HV3 = Vop,3 = $612.50
After estimating the horizon value, you can estimate the current value of operations by following these steps: (1) Find the present value of the FCFs from the explicit forecast, discounted back to Time 0 at the WACC; (2) find the present value of the horizon value, discounted back to Time 0 at the WACC; and (3) sum the PV of the FCFs and the PV of the horizon value. This sum is the present value of all future FCF from Time 0 to infinity, discounted back to Time 0. Therefore, this sum is the current value of operations, Vop,0.
Year 0 1 2 3 4 5 … t
FCF FCF1 FCF2 FCF3
PV of FCF in explicit forecast ←↵ ←↵ ←↵
FCF3(1+gL) FCF4(1+gL) FCFt(1+gL)
HV3 ←↵ ←↵ ←↵
PV of HV is the PV of FCF beyond the explicit forecast ←↵ ←↵ ←↵
B&M's Value of Operations (Millions of Dollars)
INPUTS:
gL = 5.00%
WACC = 11.00% Projections
Year 0 1 2 3 4
FCF −$10.00 $20.00 $35.00
↓ ↓ ↓
FCF1 FCF2 FCF3
────── ────── ──────
(1+WACC)1 (1+WACC)2 (1+WACC)3
HV = Vop,3
FCF3(1+gL)
PVs of FCFs −$9.009 ─────────
$16.232 (WACC− gL)
$25.592
PV of HV $447.855 $612.50 $36.75
= ────── = ────
Vop = $480.67 (1+WACC)3 6.00%
(2.) What is its value of equity on a price per share basis?
Estimating the Value of B&M’s Stock Price (Millions, Except for Per Share Data)
INPUTS:
Value of operations = $480.67
Value of nonoperating assets = $100.00
All debt = $200.00
Preferred stock = $50.00
Number of shares of common stock = 10.00
ESTIMATING PRICE PER SHARE
Value of operations $480.67
+ Value of nonoperating assets 100.00
Total estimated value of firm $580.67
− Debt 200.00
− Preferred stock 50.00
Estimated value of equity $330.67
÷ Number of shares 10.00
Estimated stock price per share = $33.07
g. If B&M undertakes the expansion, what percent of B&M’s value of operations at Year 0 is due to cash flows from Years 4 and beyond? Hint: use the horizon value at t = 3 to help answer this question.
INPUTS:
Vop,0 = $480.67
HV3 = $612.50
First, calculate the present value of the horizon value. Then divide the Year 0 value of operations by the present value of the horizon value. This will show what percent of value is due to cash flows occurring 4 or more years in the future.
PV of HV3 = HV3 / (1+WACC)3
PV of HV3 = $447.85
Percent of value due to cash flows beyond Year 3 PV of HV3
=
Vop,0
Percent of value due to cash flows beyond Year 3
= 93%
h. Based on your answer to the previous question, what are two reasons why managers often emphasize short-term earnings?
i. Your employer also is considering the acquistion of Hatfield Medical Supplies. You have gathered the following data regarding Hatfield, with all dollars reported in millions: (1) most recent sales of $2,000; (2) most recent total net operating capital, OpCap = $1,120; (3) most recent operating profitability ratio, OP = NOPAT/Sales = 4.5%; and (4) most recent capital requirement ratio, CR = OpCap/Sales = 56%. You estimate that the growth rate in sales from Year 0 to Year 1 will be 10%, from Year 1 to Year 2 will be 8%, from Year 2 to Year 3 will be 5%, and from Year 3 to Year 4 will be 5%. You also estimate that the long-term growth rate beyond Year 4 will be 5%. Assume the operating profitability and capital requirement ratios will not change. Use this information to forecast Hatfield's sales, net operating profit after taxes (NOPAT), OpCap, free cash flow, and return on invested capital (ROIC) for Years 1 through 4. Also estimate the annual growth in free cash flow for Years 2 through 4. The weighted average cost of capital (WACC) is 9%. How does the ROIC in Year 4 compare with the WACC?
No Change Actual Forecast
Year 0 1 2 3 4
Inputs
WACC 9.0%
Sales $2,000
OpCap $1,120
Sales growth rate 10% 8% 5% 5%
NOPAT/Sales 4.5% 4.5% 4.5% 4.5% 4.5%
OpCAP/Sales 56.0% 56.0% 56.0% 56.0% 56.0%
Forecast
Sales $2,000 $2,200 $2,376 $2,495 $2,620
NOPAT $99 $107 $112 $117.879
OpCap $1,120 $1,232 $1,331 $1,397.088 $1,466.942
FCF −$13.00 $8.360 $45.738 $48.025
Growth in FCF -164% 447.1% 5.0%
ROIC 8.0% 8.0% 8.0% 8.0%
j. What is the horizon value at Year 4? What is the value of operations at Year 4? Which is larger, and what can explain the difference? What is the value of operations at Year 0? How does the value of operations compare with the current total net operating capital?
Horizon Value:
= $1,260.65
Value of Operations:
Present value of HV $893.08
+ Present value of FCF $64.450
Value of operations ≈ $958
The value of operations is less than the total net operating capital because the ROIC is too low when compared to the WACC. ROIC must be greater than WACC/(1+gL) before the horizon value exceeds the total net operating capital.
ROIC needed to make HV greater than Vop at horizon: ROIC = WACC/(1+gL)
ROIC at horizon = 8.04% < 8.57% = WACC/(1+gL)
Horizon value ≈ $1,261 < $1,467 = OpCap at horizon
Current value of operations ≈ $958 < $1,120 = OpCap at horizon
k. What are value drivers? What happens to the ROIC and current value of operations if expected growth increases by 1 percentage point relative to the original growth rates (including the long-term growth rate)? What can explain this? Hint: Use Scenario Manager.
Value drivers are the inputs to the free cash flow valuation model that managers are able to influence: sales growth rates, operating profitability, capital requirements, and the cost of capital.
Using the Scenario Manager, the new ROIC and value of operations are:
Scenario No Change Improve Growth
g0,1 10% 11%
g1,2 8% 9%
g2,3 5% 6%
g3,4 5% 6%
gL 5% 6%
OP 4.5% 4.5%
CR 56.0% 56.0%
ROIC 8.0% 8.0%
Current value of operations $958 $933
WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%
Growth hurts value because the ROIC is too low. Growth will only help value if ROIC>WACC/(1+WACC).
l. Assume growth rates are at their original levels. What happens to the ROIC and current value of operations if the operating profitability ratio increases to 5.5%? Now assume growth rates and operating profitability ratios are at their original levels. What happens to the ROIC and current value of operations if the capital requirement ratio decreases to 51%? Assume growth rates are at their original levels. What is the impact of simultaneous improvements in operating profitability and capital requirements? What is the impact of simultaneous improvements in the growth rates, operating profitability, and capital requirements? Hint: Use Scenario Manager.
Using the Scenario Manager and improving operating profitability, the new ROIC and value of operations are:
Scenario No Change Improve OP
g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
g3,4 5% 5%
gL 5% 5%
OP 4.5% 5.5%
CR 56.0% 56.0%
ROIC 8.0% 9.8%
Current value of operations $958 $1,523
WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%
Using the Scenario Manager and improving capital requirements, the new ROIC and value of operations are:
Scenario No Change Improve CR
g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
g3,4 5% 5%
gL 5% 5%
OP 4.5% 4.5%
CR 56.0% 51.0%
ROIC 8.0% 8.8%
Current value of operations $958 $1,191
WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%
Using the Scenario Manager and improving operating profitability and capital requirements, the new ROIC and value of operations are:
Scenario No Change Improve OP and CR
g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
g3,4 5% 5%
gL 5% 5%
OP 4.5% 5.5%
CR 56.0% 51.0%
ROIC 8.0% 10.8%
Current value of operations $958 $1,756
WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%
Using the Scenario Manager and improving growth rates, operating profitability, and capital requirements, the new ROIC and value of operations are:
Scenario No Change Improve All
g0,1 10% 11%
g1,2 8% 9%
g2,3 5% 6%
g3,4 5% 6%
gL 5% 6%
OP 4.5% 5.5%
CR 56.0% 51.0%
ROIC 8.0% 10.8%
Current value of operations $958 $2,008
WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%
m. What insight does the free cash flow valuation model give provide us about possible reasons for market volatility? Hint: Look at the value of operations for the combinations of ROIC and gL in the previous questions.
ROIC
gL 8.0% 8.8% 9.8% 10.8%
5% $958 $1,191 $1,523 $1,756
6% $933 $2,008
Notice that small changes in ROIC and growth cause large changes in value.
b. (1.) Write out a formula that can be used to value any dividend-paying stock, regardless of its dividend pattern.
The value of any financial asset is equal to the present value of 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. Moreover, the price any 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:
D1 + D2 + . . . . DN
( 1 + rs ) ( 1 + rs ) 2 ( 1 + rs ) N
The dividend stream theoretically extends on out forever, i.e., n = infinity. Obviously, it would not be feasible to deal with an infinite stream of dividends, but fortunately, an equation has been developed that can be used to find the PV of the dividend stream, provided it is growing at a constant rate.
Naturally, trying to estimate an infinite series of dividends and interest rates forever would be a tremendously difficult task. Now, we are charged with the purpose of finding a valuation model that is easier to predict and construct. That simplification comes in the form of valuing stocks on the premise that they have a constant growth rate.
(2.) What is a constant growth stock? How are constant growth stocks valued?