Why two analysts using the same model get different values
Values differ mainly because analysts disagree on revenue growth, profitability and the terminal value. Setting price equal to value shows the long-run growth the market assumes. Revenue growth without matching investment overstates value, financing should not create much value, and disagreement itself helps markets price stocks.
Before this: Discounted Cash Flow and Growth Models, Financial Statement Forecasting
On the exam
- Explain why value estimates from the same modeling approach may differ based on analyst assumptions regarding revenue, profitability, investment, and financing
Explain why value estimates from the same modeling approach may differ based on assumptions about revenue, profitability, investment and financing. Expect: the long-run growth rate implied by a price in a two-stage free cash flow to equity (FCFE) model, the direction of a value change when revenue, margins, investment or debt assumptions change, and which assumption should not drive large differences.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
Why do analysts disagree?
Some stocks are hard to value : well-informed analysts disagree widely about intrinsic value. Take Sorvik Batteries, a fictional maker trading at 60 euros (EUR). Fourteen analysts cover it and their targets run from EUR 38 to EUR 110. The lowest is about 65% below the highest (38 ÷ 110 = 0.345).
The three most important sources of different targets are views of revenue growth over the forecast horizon, views of how profitability will change, and estimates of the terminal value , the value of all the cash flows beyond the forecast horizon. Investment and financing assumptions matter too, but financing should not drive large gaps (see the financing section below).
- Revenue growth Memorize over the forecast horizon
- Profitability Memorize margin changes
- Terminal value Memorize long-run growth and the horizon
- Investment Use it must match the growth
- Financing Use it should not create much value
The same goes for multiples. Fair multiples depend on fundamentals such as expected growth, so a bullish and a bearish analyst need not apply the same multiple to the same stock (see relative valuation).
What growth does the price imply?
Use it
Instead of estimating value, assume the price is right () and solve the model for the one assumption left unknown, usually the long-run growth rate . Then ask whether that growth is believable. The model is the two-stage free cash flow to equity (FCFE) model from the two-stage model lesson: explicit cash flows for years, then a long-run growth rate.
The inputs are the FCFE for each year of the horizon and for the first year after it, the horizon , the cost of equity and the long-run growth rate . is the market value of equity, or the price per share if FCFE is per share. The module on the capital asset pricing model and factor models covers how analysts estimate , so here it is given.
Solving for gives the implied growth rate.
Read it from the inside out. The bracket is the part of the price that the forecast years do not explain. Compounded years, it is the value the market implies at the end of the horizon. divided by that value is the forward FCFE yield at the end of the horizon. So the implied long-run growth rate is the cost of equity minus that yield.
Exam questions run this both ways: the growth a price implies, or the value a growth rate gives.
An equity market value is 9,000.00 million and the cost of equity is 10.00%. An analyst forecasts free cash flow to equity (FCFE) of 150.00, 260.00 and 380.00 million over three years and 450.00 million in the year after. The long-run growth rate implied by the market value is closest to:
10.00% − 450.00 ÷ (1.331 × (9,000.00 − 636.74)) = 5.96%
Long-run growth rate, g_l5.96%
- CF2NDCLR WORK
- 0ENTER↓150ENTER↓↓260ENTER↓↓380ENTER
- NPV10ENTER↓CPTSTO2636.74, present value of years 1 to 3
- 2NDQUIT
- 1.1y^x3=STO11.331
- 9000−RCL2=×RCL1=11,131.50, the implied value at the end of year 3
- 1/x×450=0.0404, the forward yield
- +|-+0.1=0.0596, so 5.96%
CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute · STO store · QUIT leave the worksheet · y^x power · RCL recall a stored number · 1/x reciprocal · +|- change sign
- fCLEAR REG
- 0gCF0150gCFj260gCFj380gCFj
- 10ifNPV636.74, present value of years 1 to 3
- CHS9000+8,363.26
- 1.1ENTER3y^x×11,131.50, the implied value at the end of year 3
- 1/x450×0.0404, the forward yield
- CHS0.1+0.0596, so 5.96%
f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value · CHS change sign · ENTER enter (on the HP, puts the number on the stack) · y^x power · 1/x reciprocal
If an analyst believes two companies have the same prospects, the one whose price implies lower long-run growth is the better value: similar growth at a lower price. The cost of equity matters too. At = 11%, Analyst A’s implied growth rises to 7.07%, because a higher discount rate needs more growth to justify the same price.
Where do the cash flows come from?
Every FCFE forecast bundles assumptions about revenue, profitability, investment and financing. Three relations from earlier modules make them visible. In the last one, ROE is return on equity.
The equity reinvestment rate is the share of net income that stays in the business after borrowing is counted, and long-run FCFE growth is that share earning the return on equity.
A company expects net income of 540.00, net investment of 150.00 and net debt issued of 60.00, and a return on equity (ROE) of 30.00% on what it reinvests. Its long-run growth rate of free cash flow to equity (FCFE) is closest to:
(150.00 − 60.00) ÷ 540.00 × 0.3 = 5.00%
Long-run FCFE growth, g5.00%
- 150−60=÷540=×0.3=0.05, so 5.00%
- 150ENTER60−540÷0.3×0.05
ENTER enter (on the HP, puts the number on the stack)
How do revenue and profitability move value?
Memorize
A forecast with more revenue than the market expects tends to raise value, but only if costs do not rise faster. All changes below are relative to market expectations, and investment and financing are assumed to move in step with the business.
| Net margin up | Net margin down | Net margin unchanged | |
|---|---|---|---|
| Revenue up | value rises more than revenue | value rises less than revenue, and may fall | value rises as much as revenue |
| Revenue down | value falls less than revenue, and may rise | value falls more than revenue | value falls as much as revenue |
| Revenue unchanged | value rises (margin gain) | value falls (margin loss) | no change |
Halden’s base case uses EUR millions, a cost of equity of 10% and long-run growth of 5% applied to year-4 FCFE.
| Year | Revenue | Net margin | Net income | Net investment | Net debt issued | FCFE |
|---|---|---|---|---|---|---|
| 1 | 3,000 | 12% | 360 | 400 | 190 | 150 |
| 2 | 3,600 | 12% | 432 | 300 | 128 | 260 |
| 3 | 4,200 | 12% | 504 | 220 | 96 | 380 |
| 4 | 4,500 | 12% | 540 | 150 | 60 | 450 |
The value is 636.74 + (450 ÷ 0.05) ÷ 1.331 = 636.74 + 9,000 ÷ 1.331 = 636.74 + 6,761.83 = 7,398.57. Against the market value of 9,000, this analyst sees the shares as about 22% overvalued (9,000 ÷ 7,398.57 − 1 = 21.6%). That fits the price implying 5.96% growth rather than 5%.
Exam tip Higher revenue with lower margins can raise or lower value. It depends on the size of the two changes.
How does investment move value?
Memorize
Net investment is what lets revenue grow, and it often foreshadows future revenue, profit and cash flow. So be wary of a model that grows revenue and income without matching investment: the extra cash flow would not arrive without the spending.
Three runs on Halden, each with revenue +8% and the margin unchanged at 12%:
| Run | Change | FCFE years 1-4 | Value | Change in value |
|---|---|---|---|---|
| Revenue only | revenue +8%; investment and debt unchanged | 178.80, 294.56, 420.32, 493.20 | 8,132.75 | +9.92% (more than revenue: growth for free, a warning sign) |
| Revenue and investment | revenue and net investment +8%; debt unchanged | 146.80, 270.56, 402.72, 481.20 | 7,890.28 | +6.65% (less than revenue) |
| Everything in step | revenue, net investment and net debt issued +8% | 162.00, 280.80, 410.40, 486.00 | 7,990.46 | +8.00% (FCFE scales by exactly 8%) |
The first run beats 8% because net income rises 8% while the fixed reinvestment is subtracted, so FCFE rises faster than net income. That only holds while FCFE is below net income.
Investment growth against income growth tells you what the forecast assumes about long-run returns.
| Assumption | Free cash flow | Long-run implication |
|---|---|---|
| Investment grows faster than income | falls | higher reinvestment rate, lower return on capital |
| Investment grows as fast as income | no pressure either way | consistent with stable long-run growth |
| Investment grows slower than income | rises | lower reinvestment rate, higher return on capital |
Say what return on capital your forecast assumes, because it decides whether growth adds value (see return on invested capital).
Can financing assumptions create value?
The form of financing can nudge value up or down, but companies create value mainly through their operations. So two careful analysts should not end up far apart because of financing assumptions, and a model should not quietly create value from them.
The mechanics are simple. In an FCFE model, net debt issued adds to FCFE. An analyst who assumes the company repays debt gets lower FCFE and a lower equity value. One who assumes heavy borrowing gets higher near-term FCFE. Ask whether the borrowing is sustainable and whether the forecast includes its cost (see the Modigliani-Miller propositions).
Now try both halves of this lesson yourself. The first tab finds the growth a price implies. The second changes one Halden assumption at a time.
Try this 0 of 3
- Switch to Analyst B
- Make Analyst B's implied growth higher than A's
- Raise rₑ to 11% with Analyst A
Halden Grid (fictional), EUR millions. Free cash flow to equity (FCFE) for each forecast year and the year after; present values (PV) at the cost of equity.
To justify EUR 9,000m, FCFE must grow 5.96% a year after year 3, forever. Ask whether that is believable: if the companies' prospects match, the one whose price implies lower growth is the better value.
Show working
PV of forecast years = 150.00 ÷ 1.1 + 260.00 ÷ 1.1² + 380.00 ÷ 1.1³ = 136.36 + 214.88 + 285.50 = 636.74
Value implied at the horizon = (Pₜ − PV) × (1 + rₑ)3 = (9,000 − 636.74) × 1.331 = 8,363.26 × 1.331 = 11,131.50
Forward FCFE yield = FCFE in year 4 ÷ that value = 450.00 ÷ 11,131.50 = 4.04%; gₗ = rₑ − yield = 10.00% − 4.04% = 5.96%
The TI BA II Plus works in chain mode (left to right), so compute (1 + rₑ)n first and store it; typed after a product, [y^x] would raise the whole product to the power.
- CF2NDCLR WORK
- 0ENTER↓150ENTER↓↓260ENTER↓↓380ENTER
- NPV10ENTER↓CPTSTO2636.74
- 2NDQUIT
- 1.1y^x3=STO11.331
- 9000−RCL2=×RCL1=11,131.50
- 1/x×450=0.0404
- +|-+0.1=0.0596, so 5.96%
CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute · STO store · QUIT leave the worksheet · y^x power · RCL recall a stored number · 1/x reciprocal · +|- change sign
- fCLEAR REG
- 0gCF0150gCFj260gCFj380gCFj
- 10ifNPV636.74
- CHS9000+8,363.26
- 1.1ENTER3y^x×11,131.50
- 1/x450×0.0404
- CHS0.1+0.0596
f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value · CHS change sign · ENTER enter (on the HP, puts the number on the stack) · y^x power · 1/x reciprocal
Is disagreement a problem?
No. A common beginner’s belief is that reports built on the same history should converge on one consensus price. In fact different views widen the range of expectations, which drives price discovery and keeps markets efficient. This divergence of opinion is healthy, and contrarian views, which run against the consensus (the activist short sellers of the previous lesson are the extreme case), challenge the status quo.
Take a bullish and a bearish analyst covering Kestrel Air. For next year the bear forecasts 0.90 times the bull’s revenue but only 0.72 times the bull’s earnings before interest, taxes, depreciation and amortization (EBITDA). For example, if the bull expects revenue of 1,000 at a 25% EBITDA margin (250) and the bear 900 at a 20% margin (180), then 180 ÷ 250 = 0.72. Pessimism about near-term revenue and, above all, profitability drives the gap in their targets.
Where an analyst sits can shape the view too. A global analyst may see the stock as a way into a country’s market, while a local analyst watches regional competition that outsiders miss.
Memorize this
MemorizeRevenue and margin against value
| Margin up | Margin down | Margin flat | |
|---|---|---|---|
| Revenue up | value up more | value up less, maybe down | value up equally |
| Revenue down | value down less, maybe up | value down more | value down equally |
| Revenue flat | up | down | none |
Memory hook Same direction = amplify; opposite directions = it depends on the size.
Know it cold Three main sources of different targets: revenue growth, profitability, terminal value. Financing should not create much value.
MemorizeInvestment, growth and the price
| Item | Remember |
|---|---|
| Investment faster than income | free cash flow down; reinvestment up; return on capital down |
| Investment slower than income | free cash flow up; reinvestment down; return on capital up |
| FCFE | net income − net investment + net debt issued |
| Long-run growth | (net investment − net debt issued) ÷ net income × return on equity |
| Implied | − forward FCFE yield at the horizon |
Memory hook No growth without investment: revenue up with investment flat is too good to be true.
Know it cold Same prospects, lower implied growth in the price = better value.
- Revenue growth Memorize over the forecast horizon
- Profitability Memorize margin changes
- Terminal value Memorize long-run growth and the horizon
- Investment Use it must match the growth
- Financing Use it should not create much value
Quick example
Free cash flow to equity (FCFE) of 150, 260 and 380 over three years, 450 in year 4, cost of equity 10% and long-run growth 5%. 636.74 + (450 ÷ 0.05) ÷ 1.331 = 636.74 + 6,761.83 = 7,398.57.
- CF2NDCLR WORK
- 0ENTER↓150ENTER↓↓260ENTER↓↓380ENTER
- NPV10ENTER↓CPTSTO2 636.74
- 2NDQUIT
- 1.1y^x3=STO1 1.331
- 450÷0.05÷RCL1+RCL2= 7,398.57
CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute · STO store · QUIT leave the worksheet · y^x power · RCL recall a stored number
- fCLEAR REG
- 0gCF0150gCFj260gCFj380gCFj
- 10ifNPV 636.74
- 450ENTER0.05÷1.1ENTER3y^x÷+ 7,398.57
f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value · ENTER enter (on the HP, puts the number on the stack) · y^x power
Quick example
Market value 2,000, cost of equity 9%, FCFE of 60 and 80 in years 1 and 2, 95 in year 3. (2,000 − 122.38) × 1.09² = 2,230.80; yield 95 ÷ 2,230.80 = 4.26%; g_l = 9% − 4.26% = 4.74%.
- CF2NDCLR WORK
- 0ENTER↓60ENTER↓↓80ENTER
- NPV9ENTER↓CPTSTO2 122.38
- 2NDQUIT
- 1.09y^x2=STO1 1.1881
- 2000−RCL2=×RCL1= 2,230.80
- 1/x×95= 0.0426
- +|-+0.09= 0.0474
CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute · STO store · QUIT leave the worksheet · y^x power · RCL recall a stored number · 1/x reciprocal · +|- change sign
- fCLEAR REG
- 0gCF060gCFj80gCFj
- 9ifNPV 122.38
- CHS2000+ 1,877.62
- 1.09ENTER2y^x× 2,230.80
- 1/x95× 0.0426
- CHS0.09+ 0.0474
f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value · CHS change sign · ENTER enter (on the HP, puts the number on the stack) · y^x power · 1/x reciprocal
Quick example
Net income 540, net investment 150, net debt issued 60. 540 − 150 + 60 = 450.
- 540−150+60= 450
- 540ENTER150−60+ 450
ENTER enter (on the HP, puts the number on the stack)
Quick example
Net income 540, net investment 150, net debt issued 60. (150 − 60) ÷ 540 = 16.67%, the same as 1 − 450 ÷ 540.
- 150−60=÷540= 0.1667
- 150ENTER60−540÷ 0.1667
ENTER enter (on the HP, puts the number on the stack)
Quick example
Net income 200, net investment 130, net debt issued 30, return on equity (ROE) 14%. Reinvestment rate (130 − 30) ÷ 200 = 50%, and 50% × 14% = 7.0%.
- 130−30=÷200=×0.14= 0.07
- 130ENTER30−200÷0.14× 0.07
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
Implied growth
Market value 3,500; cost of equity 9%; FCFE 80, 110, 140, then 160.
(3,500 − 274.08) × 1.09³ = 4,177.65; 9% − 160 ÷ 4,177.65 = 5.17%. Traps: 4.04% (bracket not compounded), 5.47% (forecast-year present values ignored).
-
Revenue and margin
Revenue up, margin down: what happens to value?
It depends on the size of the two; value may fall. The trap is "always rises".
-
Revenue and investment
Revenue and net investment both +10%, debt unchanged.
Value rises less than 10%. The trap is exactly 10%.
-
Which assumption should not cause big gaps?
Revenue, margins, terminal value or financing?
Financing. The trap is terminal value.
Exam traps
- Dividing next year's FCFE by the bracket without compounding it n years.
- Forgetting to subtract the present value of the forecast-year FCFE from the price.
- Assuming a longer forecast horizon always lowers implied growth. It does only if the extra years grow faster than the long-run rate.
- Raising revenue without raising investment, then trusting the higher value.
- Reading the revenue and margin grid as "more revenue always means more value".
- Letting financing assumptions create value. Deleveraging lowers an FCFE value and borrowing raises it mechanically.
Checkpoint
3 exam-style questions. About 90 seconds each.
1A company's equity has a market value of 4,800 million pounds sterling (GBP). An analyst forecasts free cash flow to equity (FCFE) of GBP 120 million, GBP 170 million and GBP 230 million for the next three years and GBP 260 million for the year after, and uses a cost of equity of 11%. The long-run FCFE growth rate implied by the market value is closest to:
2An analyst's free cash flow to equity (FCFE) model values a company at 500 million euros (EUR). In every forecast year, FCFE is below net income. The analyst raises forecast revenue by 5% in every year and changes nothing else: the net margin, net investment, net debt issued, cost of equity and long-run growth rate stay the same. The new value is most likely:
3A stock is described as hard to value. This most likely means that:
Key takeaways
- Different targets come mostly from different revenue growth, profitability and terminal value assumptions.
- Setting price equal to value in a two-stage FCFE model reveals the long-run growth the market assumes: implied growth = cost of equity − forward FCFE yield at the horizon.
- FCFE = net income − net investment + net debt issued; long-run growth = equity reinvestment rate × return on equity.
- Revenue growth without matching investment overstates value; financing should not create much value.
- Disagreement is healthy: it drives price discovery.
Quick example
Free cash flow to equity (FCFE) of 150, 260 and 380 over three years, 450 in year 4, cost of equity 10% and long-run growth 5%. 636.74 + (450 ÷ 0.05) ÷ 1.331 = 636.74 + 6,761.83 = 7,398.57.
- CF2NDCLR WORK
- 0ENTER↓150ENTER↓↓260ENTER↓↓380ENTER
- NPV10ENTER↓CPTSTO2 636.74
- 2NDQUIT
- 1.1y^x3=STO1 1.331
- 450÷0.05÷RCL1+RCL2= 7,398.57
CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute · STO store · QUIT leave the worksheet · y^x power · RCL recall a stored number
- fCLEAR REG
- 0gCF0150gCFj260gCFj380gCFj
- 10ifNPV 636.74
- 450ENTER0.05÷1.1ENTER3y^x÷+ 7,398.57
f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value · ENTER enter (on the HP, puts the number on the stack) · y^x power
Quick example
Market value 2,000, cost of equity 9%, FCFE of 60 and 80 in years 1 and 2, 95 in year 3. (2,000 − 122.38) × 1.09² = 2,230.80; yield 95 ÷ 2,230.80 = 4.26%; g_l = 9% − 4.26% = 4.74%.
- CF2NDCLR WORK
- 0ENTER↓60ENTER↓↓80ENTER
- NPV9ENTER↓CPTSTO2 122.38
- 2NDQUIT
- 1.09y^x2=STO1 1.1881
- 2000−RCL2=×RCL1= 2,230.80
- 1/x×95= 0.0426
- +|-+0.09= 0.0474
CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute · STO store · QUIT leave the worksheet · y^x power · RCL recall a stored number · 1/x reciprocal · +|- change sign
- fCLEAR REG
- 0gCF060gCFj80gCFj
- 9ifNPV 122.38
- CHS2000+ 1,877.62
- 1.09ENTER2y^x× 2,230.80
- 1/x95× 0.0426
- CHS0.09+ 0.0474
f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value · CHS change sign · ENTER enter (on the HP, puts the number on the stack) · y^x power · 1/x reciprocal
Quick example
Net income 540, net investment 150, net debt issued 60. 540 − 150 + 60 = 450.
- 540−150+60= 450
- 540ENTER150−60+ 450
ENTER enter (on the HP, puts the number on the stack)
Quick example
Net income 540, net investment 150, net debt issued 60. (150 − 60) ÷ 540 = 16.67%, the same as 1 − 450 ÷ 540.
- 150−60=÷540= 0.1667
- 150ENTER60−540÷ 0.1667
ENTER enter (on the HP, puts the number on the stack)
Quick example
Net income 200, net investment 130, net debt issued 30, return on equity (ROE) 14%. Reinvestment rate (130 − 30) ÷ 200 = 50%, and 50% × 14% = 7.0%.
- 130−30=÷200=×0.14= 0.07
- 130ENTER30−200÷0.14× 0.07
ENTER enter (on the HP, puts the number on the stack)
Questions about this lesson?
Where this comes back
- The CAPM, the Market Model and Factor Models Equities
- Scenario analysis with probability weights Financial Statement Forecasting
Questions candidates ask
Why do analysts' price targets for the same stock differ so much?
Mostly because they forecast different revenue growth, different profit margins and different terminal values. Investment and financing assumptions add to the gap. Stocks where informed analysts disagree widely are called hard to value.
How do you find the growth rate implied by a stock price?
Set the price equal to the value in a two-stage FCFE model, subtract the present value of the forecast years, compound the rest to the end of the horizon and divide next year's FCFE by it. The implied growth is the cost of equity minus that yield.
Does higher revenue always mean a higher valuation?
No. If margins fall enough, value can drop. And if revenue grows without the investment it needs, the higher value is not credible.
Can financing assumptions change an FCFE valuation?
Mechanically yes: borrowing adds to FCFE and repaying debt subtracts. But value comes mainly from operations, so analysts should not let financing assumptions create large value differences.
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