Why two analysts using the same model get different values

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).

Different values, same model

• 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 ($P_t = IV_t$) and solve the model for the one assumption left unknown, usually the long-run growth rate $g_l$. 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 $n$ years, then a long-run growth rate.

$$P_t = IV_t = \sum_{i=1}^{n} \dfrac{\text{FCFE}_{t+i}}{(1 + r_e)^i} + \dfrac{\text{FCFE}_{t+n+1} / (r_e - g_l)}{(1 + r_e)^n}$$

The inputs are the FCFE for each year of the horizon and for the first year after it, the horizon $n$, the cost of equity $r_e$ and the long-run growth rate $g_l$. $P_t$ 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 $r_e$, so here it is given.

Solving for $g_l$ gives the implied growth rate.

$$g_l = r_e - \dfrac{\text{FCFE}_{t+n+1}}{(1 + r_e)^n \left[ P_t - \sum_{i=1}^{n} \dfrac{\text{FCFE}_{t+i}}{(1 + r_e)^i} \right]}$$

Read it from the inside out. The bracket is the part of the price that the forecast years do not explain. Compounded $n$ years, it is the value the market implies at the end of the horizon. $\text{FCFE}_{t+n+1}$ 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.

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 $r_e$ = 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.

$$\text{FCFE} = \text{Net income} - \text{Net investment} + \text{Net debt issued}$$

$$\text{Equity reinvestment rate} = \dfrac{\text{Net investment} - \text{Net debt issued}}{\text{Net income}} = 1 - \dfrac{\text{FCFE}}{\text{Net income}}$$

$$\text{Long-run FCFE growth} = \text{Equity reinvestment rate} \times \text{ROE}$$

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.

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.

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.