Business Planning and Evaluation · Chapter 2 · 2.2 · trainer

How much do we know about tomorrow?

The bank will ask about the growth rate, the supplier about the order, the board about the risk. Can you answer with figures?

Rolandas Rakštys · Lecturer · Vytautas Magnus University, Agriculture Academy · Faculty of Bioeconomy Development, Department of Business and Rural Development · [email protected] · ORCID 0000-0003-0299-9930

Chapter 2 “The business planning and evaluation process”, section 2.2 · English translation of v1.0.11 (2026-10-15) · trainer v1.0.2 · 6 parts · ≈ 50 min

Rakštys, R. (2026). Chapter 2. The business planning and evaluation process (English translation of v1.0.11, 2026-10-15). Verslo planavimas ir vertinimas [Business planning and evaluation]. Vytautas Magnus University, Agriculture Academy. https://rakstys.eu/studijos/verslo-planavimas-ir-vertinimas/en/skyriai/ch02/ · CC BY-NC-ND 4.0

Section 2.2 · analytical models and formulas

Choose a formula

Formula (2.1) · CAGR

1 / 7 · Situation

How fast has the company grown?

CAGR compound annual growth rateV₀ initial valueVₙ final valuen number of periods

The manager of a food processing company is preparing a loan application. The growth rate will become the principal assumption of the application, so the bank will ask about it first.

5002020

8202025

Loan application

Revenue in 2025EUR 820 thousand

Growth assumption_____ % a year

Revenue, EUR thousand – the company’s annual reports; a teaching example, the figures match the scale of an average Lithuanian processing company.

Formula (2.1) · CAGR

2 / 7 · Method

Which indicator makes it possible to compare growth across different periods on a single standard?

CAGR compound annual growth rate

Formula (2.1) · CAGR

3 / 7 · Data

Select the cards needed for formula (2.1)

V₀ initial valueVₙ final valuen number of periodsGDP gross domestic product

Formula (2.1) · CAGR

4 / 7 · Calculation

Calculate the compound annual growth rate

CAGR compound annual growth rateV₀ initial valueVₙ final valuen number of periods

CAGR = (V_nV₀)^1/n − 1 = (820500)^1/5 − 1 = 1.64^0.2 − 1 = CAGR in per cent %

Formula (2.1) · CAGR

5 / 7 · Conclusion

Which sentence can go in the application?

CAGR compound annual growth rate

Formula (2.1) · CAGR

6 / 7 · Why

Why is CAGR (10.4 %) lower than 64 % / 5 = 12.8 %?

CAGR compound annual growth rateV₀ initial value

Formula (2.1) · CAGR

7 / 7 · Limitation

What does CAGR not see?

CAGR compound annual growth rate

Change the revenue of the intermediate years, EUR thousand:

2021 2022 2023 2024

CAGR10.4 %

average of the annual changes

Try it in the calculator (2.1) ↗

Formula (2.2) · SMA

1 / 6 · Situation

How much should be ordered for May?

SMA simple moving averagek window size – the number of periods in the averageF forecast

The purchasing manager of a trading company has to place the May order with a supplier by the end of the month: too large an order will tie up cash in inventory, too small an order will leave the shelves empty.

January42

February38

March45

April41

May?

Sales, EUR thousand – the company’s sales records; a teaching example.

Formula (2.2) · SMA

2 / 6 · Method

When is the moving average suitable?

SMA simple moving average

Formula (2.2) · SMA

3 / 6 · Data

Which months go into the May forecast when k = 3?

SMA simple moving averagek window size

Formula (2.2) · SMA

4 / 6 · Calculation

Calculate the forecast for May

SMA simple moving averageF forecastk window size

F_May = SMA_Apr = 1kΣ Y_i = 38 + 45 + 413 = Forecast for May, EUR thousand EUR thousand

Formula (2.2) · SMA

5 / 6 · Conclusion

What does EUR 41.3 thousand mean?

SMA simple moving average

Formula (2.2) · SMA

6 / 6 · Limitation

How does the window size change the forecast?

SMA simple moving averagek window size

Choose k:

Try it in the calculator (2.2) ↗

Formula (2.3) · Smoothing

1 / 8 · Situation

Can the forecast respond faster?

α smoothing parameterexponential smoothing greater weight to the latest dataF forecastY actual value

The same purchasing manager notices that the moving average is slow to respond to change and wants a forecast that gives more weight to the most recent month.

April forecast43

actual April sales41

May forecast?

EUR thousand – the same sales records; a teaching example.

Formula (2.3) · Smoothing

2 / 8 · Data

Select the cards needed for formula (2.3)

α smoothing parameterF forecastY actual valueSMA simple moving average

Formula (2.3) · Smoothing

3 / 8 · Calculation

Calculate the forecast for May

α smoothing parameterF forecastY actual value

F₅ = α · Y₄ + (1 − α) · F₄ = 0.2 × 41 + 0.8 × 43 = Forecast for May, EUR thousand EUR thousand

Formula (2.3) · Smoothing

4 / 8 · Conclusion

The actual figure was 41, yet the forecast fell only from 43 to 42.6. Why?

α smoothing parameter

Formula (2.3) · Smoothing

5 / 8 · What if

How does α change the forecast?

α smoothing parameterF forecast

α = 0.2

to the new actual figure (41)20 %

to the old forecast (43)80 %

MAY FORECAST42.6

Forecast accuracy · MAE

6 / 8 · Accuracy

Which method should be relied on next quarter?

MAE mean absolute errorY actual figureF forecast

The methods give a figure, but none of them says whether it can be trusted. Accuracy is measured like this: the method is applied to historical data already available, and you see how far it deviated from them.

Month	1	2	3	4
Forecast F	41.0	42.3	41.7	43.0
Actual Y	38	45	41	44

Moving average forecasts and actual figures, EUR thousand – the same sales records.

Forecast accuracy · MAE

7 / 8 · Calculation

Calculate the mean absolute error

MAE mean absolute errorY actual figureF forecast

MAE = 1nΣ |Y_t − F_t| = |38 − 41.0| + |45 − 42.3| + |41 − 41.7| + |44 − 43.0|4 = MAE, EUR thousand

Forecast accuracy · MAE

8 / 8 · Conclusion

The forecast misses by EUR 1.85 thousand on average. What does that mean for the decision?

MAE mean absolute error

Formula (2.4) · Regression

1 / 7 · Situation

What can be expected in return for the marketing budget?

linear regression Ŷ = a + bXOLS ordinary least squaresa interceptb regression coefficient (slope)

The marketing manager is asking for additional funds in next year’s budget and has to justify what the company can expect in return.

Year	X – budget	Y – revenue
1	10	285
2	20	320
3	30	350
4	40	380
5	50	405

EUR thousand – the company’s management accounts; a teaching example.

Formula (2.4) · Regression

2 / 7 · Calculation

Calculate the regression coefficient b

OLS ordinary least squaresb regression coefficient (slope)n number of observations

n = 5ΣX = 150ΣY = 1 740ΣXY = 55 200ΣX² = 5 500

b = nΣXY − ΣXΣYnΣX² − (ΣX)² = 276 000 − 261 00027 500 − 22 500 = b

Formula (2.4) · Regression

3 / 7 · Calculation

Which calculation of the intercept a is correct?

a interceptb regression coefficient (slope)X̄, Ȳ means: 30 and 348

Formula (2.4) · Regression

4 / 7 · Calculation

What revenue can be expected with a budget of EUR 45 thousand?

Ŷ forecast valuea interceptb regression coefficient (slope)

Ŷ = a + bX = 258 + 3.0 × 45 = Ŷ, EUR thousand EUR thousand

Formula (2.4) · Regression

5 / 7 · Conclusion

What can the manager tell the board?

b regression coefficient (slope)a intercept

Forecast accuracy · R²

6 / 7 · Why

R² ≈ 0.997. Does this prove that marketing causes revenue growth?

R² coefficient of determination

R² = 1 − Σ(Y − Ŷ)² = 30Σ(Y − Ȳ)² = 9 030 ≈ 0.997 calculated from this example’s data, as in the chapter; the 0.82 mentioned in the chapter is an example of a more usual value, not the result of this example

Formula (2.4) · Regression

7 / 7 · Limitation

How far can the line be extended?

Ŷ forecast value

Budget X = EUR 45 thousand

Ŷ = EUR 393 thousand

within the observed data

R² ≈ 0.997 is suspiciously good: the teaching data are neatly arranged. In reality such a close fit is a warning, not a triumph – regression shows correlation, not causation.

Try it in the calculator (2.4) ↗

Formulas (2.5)–(2.6) · Scenarios

1 / 7 · Situation

How much revenue will the new product bring?

E(V) weighted expected valueσ standard deviationp probability of a scenarioV value under a scenario

The board is deciding whether to start producing a new product and asks not for a single figure but for a range with probabilities.

Scenario	Probability p	Revenue V, EUR thousand
Optimistic	0.25	600
Base	0.50	400
Pessimistic	0.25	200

Estimates by the sales team and production; a teaching example.

Formulas (2.5)–(2.6) · Scenarios

2 / 7 · Calculation

Calculate the weighted expected value

E(V) weighted expected valuep probabilityV value

E(V) = Σ p_i · V_i = 0.25 × 600 + 0.50 × 400 + 0.25 × 200 = E(V), EUR thousand EUR thousand

Formulas (2.5)–(2.6) · Scenarios

3 / 7 · Calculation

Calculate the standard deviation

σ standard deviationE(V) weighted expected value

σ = √Σ p_i(V_i − E(V))² = √(0.25 × 200² + 0.50 × 0² + 0.25 × 200²) = σ, EUR thousand EUR thousand

Formulas (2.5)–(2.6) · Scenarios

4 / 7 · Assessment

How large is the dispersion of this project?

CV coefficient of variationσ standard deviation

Indicative thresholds of the textbook’s Excel model: up to 15 % – relatively low dispersion, 15–30 % – moderate, above 30 % – high. This is a didactic convention, not a universal norm.

Formulas (2.5)–(2.6) · Scenarios

5 / 7 · Why

Why did the expected value coincide with the base scenario?

E(V) weighted expected value

Formulas (2.5)–(2.6) · Scenarios

6 / 7 · Conclusion

Why is the expected value alone not enough for the board?

E(V) weighted expected valueσ standard deviationCV coefficient of variation

Formulas (2.5)–(2.6) · Scenarios

7 / 7 · Limitation

What happens when the probabilities are asymmetric?

E(V) expected valueσ standard deviationCV coefficient of variation

Optimistic (600): p = 0.25 Pessimistic (200): p = 0.25

Base (400): p = 0.50 (the remainder up to 1)

E(V)400

σ141

CV35 %

high dispersion

Try it in the calculator (2.5) ↗

Formula (2.7) · Elasticity

1 / 7 · Situation

How far does the value of the project depend on price?

ε elasticity coefficientNPV net present value

Before negotiations with a buyer, the finance director has to know how far the value of the project depends on price: if the dependence is strong, a discount will cost more than it appears to.

base scenarioEUR 10 per unitNPV EUR 500 thousand

price −10 %EUR 9 per unitNPV EUR 325 thousand

The model of the same project; a teaching example.

Formula (2.7) · Elasticity

2 / 7 · Data

Select the cards needed for formula (2.7)

ε elasticity coefficientNPV net present value

Formula (2.7) · Elasticity

3 / 7 · Calculation

Calculate the elasticity of NPV with respect to price

ε elasticity coefficientNPV net present value

ε = ΔY / YΔX / X = (325 − 500) / 500(9 − 10) / 10 = ε

Formula (2.7) · Elasticity

4 / 7 · Conclusion

What does ε = 3.5 mean?

ε elasticity coefficientNPV net present value

Formula (2.7) · Elasticity

5 / 7 · Conclusion

What is such an assumption called, and what should be done with it?

load-bearing assumption the assumption on which value depends most

Formula (2.7) · Elasticity

6 / 7 · Why

Why will the discount cost more than it appears to?

ε elasticity coefficientNPV net present value

Formula (2.7) · Elasticity

7 / 7 · Limitation

Why can one not go further than these two points?

ε elasticity coefficientNPV net present value

Choose the price:

Elasticity is a local measure: ε = 3.5 was measured between these two points and does not hold for the whole range of prices. The chapter gives no NPV for other prices, so they are not shown here.

NPV, EUR THOUSAND500

Change in NPV: 0 %

Try it in the calculator (2.7) ↗

The end

Where this material comes from

Figures and concepts are taken from the numerical examples in section 2.2 of Chapter 2, from section 2.5 (the Excel model) and from the textbook’s glossary (CAGR, moving average, exponential smoothing, mean absolute error, coefficient of determination, coefficient of variation, elasticity, load-bearing assumption).

Rakštys, R. (2026). Chapter 2. The business planning and evaluation process (English translation of v1.0.11, 2026-10-15). Verslo planavimas ir vertinimas [Business planning and evaluation]. Vytautas Magnus University, Agriculture Academy. https://rakstys.eu/studijos/verslo-planavimas-ir-vertinimas/en/skyriai/ch02/ · CC BY-NC-ND 4.0

These slides are based on the textbook Verslo planavimas ir vertinimas [Business Planning and Evaluation]. The text was translated, structured and visually laid out with the help of artificial intelligence tools (Claude), following the protocol for working with AI and the verification procedures set by the author.

How much do we know about tomorrow?

Choose a formula

How fast has the company grown?

Which indicator makes it possible to compare growth across different periods on a single standard?

Select the cards needed for formula (2.1)

Calculate the compound annual growth rate

Which sentence can go in the application?

Why is CAGR (10.4 %) lower than 64 % / 5 = 12.8 %?

What does CAGR not see?

How much should be ordered for May?

When is the moving average suitable?

Which months go into the May forecast when k = 3?

Calculate the forecast for May

What does EUR 41.3 thousand mean?

How does the window size change the forecast?

Can the forecast respond faster?

Select the cards needed for formula (2.3)

Calculate the forecast for May

The actual figure was 41, yet the forecast fell only from 43 to 42.6. Why?

How does α change the forecast?

Which method should be relied on next quarter?

Calculate the mean absolute error

The forecast misses by EUR 1.85 thousand on average. What does that mean for the decision?

What can be expected in return for the marketing budget?

Calculate the regression coefficient b

Which calculation of the intercept a is correct?

What revenue can be expected with a budget of EUR 45 thousand?

What can the manager tell the board?

R² ≈ 0.997. Does this prove that marketing causes revenue growth?

How far can the line be extended?

How much revenue will the new product bring?

Calculate the weighted expected value

Calculate the standard deviation

How large is the dispersion of this project?

Why did the expected value coincide with the base scenario?

Why is the expected value alone not enough for the board?

What happens when the probabilities are asymmetric?

How far does the value of the project depend on price?

Select the cards needed for formula (2.7)

Calculate the elasticity of NPV with respect to price

What does ε = 3.5 mean?

What is such an assumption called, and what should be done with it?

Why will the discount cost more than it appears to?

Why can one not go further than these two points?

Where this material comes from

Trainer storyboard