Business Planning and Evaluation · Chapter 1 · 1.2 · trainer

Calculate like a valuer

Choose the method and the data, calculate, draw a conclusion – and see where the formula has its limits.

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 1 “Foundations of Business Value”, section 1.2 · English translation of v0.16.5 (2026-10-15) · trainer v1.0.2 · 6 parts · ≈ 53 min

Rakštys, R. (2026). Chapter 1. Foundations of Business Value (English translation of v0.16.5, 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/ch01/ · CC BY-NC-ND 4.0

Section 1.2 · analytical models and formulas

Choose a formula

Formula (1.1) · DCF

1 / 6 · Situation

What are these five years of cash flows worth today?

DCF discounted cash flow modelFCF free cash flowWACC weighted average cost of capitalTV terminal valuePV present value

Year	1	2	3	4	5
FCF_t, EUR thousand	100	110	121	133	146

WACC = 10 %

Formula (1.1) · DCF

2 / 6 · Method

How do you calculate what these cash flows are worth today?

FCF free cash flowWACC weighted average cost of capital

Formula (1.1) · DCF

3 / 6 · Data

Select the cards needed for the first term of formula (1.1)

FCF free cash flowWACC weighted average cost of capitalTV terminal valueg long-term growth raten length of the forecast period

Formula (1.1) · DCF

4 / 6 · Calculation

Calculate the term for year 4

FCF free cash flowWACC weighted average cost of capitalTV terminal value

Σ5t=1FCF_t(1 + WACC)^t+ TV_n(1 + WACC)ⁿ

t = 1

1001.10

90.9

t = 2

1101.21

90.9

t = 3

1211.331

90.9

t = 4

1331.4641

your answer

t = 5

1461.6105

90.7

= EUR 454.2 thousandthe value today of five years of cash flows

Formula (1.1) · DCF

5 / 6 · Conclusion

What does EUR 454.2 thousand mean?

TV terminal valuePV present value

CLEARANCE SALE −71.8 %

Formula (1.1) · DCF

6 / 6 · Limitation

How does the discount rate change the value?

WACC weighted average cost of capital

Choose WACC:

8 %9 %10 %11 %12 %

Try it in the calculator (1.1) ↗

Formula (1.2) · Terminal value

1 / 7 · Situation

What is the period after five years worth?

TV terminal valueFCF free cash flowWACC weighted average cost of capitalPV present valueDCF discounted cash flow model

1

2

3

4

5

6 · 7 · 8 · …

EUR 454.2 thousand – already valued (1.1)TV = ?

Formula (1.2) · Terminal value

2 / 7 · Method

How do you calculate TV?

TV terminal valueFCF free cash flowWACC weighted average cost of capitalg long-term growth rate

Formula (1.2) · Terminal value

3 / 7 · Data

What is needed to calculate TV₅?

TV terminal valueFCF free cash flowWACC weighted average cost of capitalPV present valueg long-term growth raten length of the forecast period

Formula (1.2) · Terminal value

4 / 7 · Calculation

Calculate TV₅

TV terminal valueFCF free cash flowWACC weighted average cost of capitalg long-term growth rate

TV₅ = FCF₅ × (1 + g)WACC − g = 146 × 1.02 = 148.920.10 − 0.02 = 0.08 = Terminal value, EUR thousand

Formula (1.2) · Terminal value

5 / 7 · To today

How do you get the value of the company today (V₀)?

V₀ value of the company todayPV present valueTV terminal value

You have the PV of five years of cash flows (454.2) and TV (1 861.5).

Formula (1.2) · Terminal value

6 / 7 · Conclusion

TV makes up 71.8 % of the value of the company. What does that mean?

TV terminal valueDCF discounted cash flow model

Formula (1.2) · Terminal value

7 / 7 · Limitation

What happens when growth approaches the rate?

TV terminal valueWACC weighted average cost of capitalg long-term growth rateV₀ value of the company today

WACC = 10 %. Choose the growth rate g:

↑ beyond the screenThe formula does not hold

TV₅: 1 861.5
V₀: 1 610.1
TV share of value: 71.8 %

Try it in the calculator (1.2) ↗

Formula (1.3) · EVA

1 / 7 · Situation

Does the company create value?

EVA economic value addedNOPAT net operating profit after taxIC invested capitalWACC weighted average cost of capitalFCF free cash flow

NOPAT = EUR 200 thousand

Formula (1.3) · EVA

2 / 7 · Method

How do you calculate EVA?

EVA economic value addedNOPAT net operating profit after taxIC invested capitalWACC weighted average cost of capital

Formula (1.3) · EVA

3 / 7 · Data

What is needed to calculate EVA?

EVA economic value addedNOPAT net operating profit after taxIC invested capitalWACC weighted average cost of capitalFCF free cash flowg long-term growth rate

Formula (1.3) · EVA

4 / 7 · Calculation

Calculate EVA, EUR thousand

EVA economic value addedNOPAT net operating profit after taxIC invested capitalWACC weighted average cost of capital

EVA = NOPAT − (IC × WACC) = 200 − (1 500 × 0.10) = Economic value added, EUR thousand

Formula (1.3) · EVA

5 / 7 · Conclusion

EVA is EUR 50 thousand. What does that mean?

EVA economic value addedNOPAT net operating profit after tax

Formula (1.3) · EVA

6 / 7 · Another case

And if NOPAT were EUR 120 thousand?

NOPAT net operating profit after taxEVA economic value added

NOPAT is EUR 120 thousand; everything else is unchanged. Which statement is correct?

Formula (1.3) · EVA

7 / 7 · Limitation

Creating or destroying – what does it depend on?

NOPAT net operating profit after taxIC invested capitalWACC weighted average cost of capitalEVA economic value added

NOPAT: EUR 200 thousand WACC: 10 %

IC: 1 500
IC × WACC: 150
EVA: 50

creates value

EVA compares NOPAT with the cost of capital, so the answer also depends on which WACC is applied.

Try it in the calculator (1.3) ↗

Formula (1.4) · WACC

1 / 6 · Situation

What does the company’s capital cost?

WACC weighted average cost of capitalDCF discounted cash flow modelNOPAT net operating profit after tax

Capital – EUR 1 000 thousand

Equity E · 60060 % · cost r_e = 12 %

Debt D · 40040 % · cost r_d = 5 %

Corporate income tax rate T_c = 17 %

Formula (1.4) · WACC

2 / 6 · Method

How do you calculate WACC?

WACC weighted average cost of capital

Formula (1.4) · WACC

3 / 6 · Data

What is needed to calculate WACC?

WACC weighted average cost of capitalNOPAT net operating profit after taxg long-term growth rate

Formula (1.4) · WACC

4 / 6 · Calculation

Calculate the debt term, %

WACC weighted average cost of capital

WACC = EE + D × r_e + DE + D × r_d × (1 − T_c)

equity term

6001 000 × 12 %

= 7.2 %

debt term

4001 000 × 5 % × (1 − 0.17)

= Debt term, per cent %

WACC = 7.2 + 1.66 = 8.86 ≈ 8.9 %weighted average cost of capital

Formula (1.4) · WACC

5 / 6 · Conclusion

WACC is 8.9 %. What does that mean?

WACC weighted average cost of capitalDCF discounted cash flow model

Formula (1.4) · WACC

6 / 6 · Limitation

How much does the cost of equity matter?

WACC weighted average cost of capital

Cost of equity r_e: 12 %

Equity term: 7.2 %
Debt term: 1.66 %

WACC8.9 %

WACC is a discount rate, and small changes in the discount rate can generate large changes in valuation. You saw how the rate changes value at the end of part (1.1). More on sensitivity: section 1.1.5 ↗

Try it in the calculator (1.4) ↗

Formulas (1.5)–(1.8)

1 / 8 · Situation

Is value a single number?

Xₜ state vector of business valueΩ structural functionVₜ · Eₜ · Dₜ value, expectations, decisions

1 610 EUR thousand · DCF

CFₜᵉexpected cash flows

Aₜtangible assets

Iₜintangible capital

Kₜcapital structure

Sₜstrategic position

Bₜbehavioural / perceptual state

Rₜrisk parameters

Formula (1.5) · vector

2 / 8 · Vector

Select the dimensions of the vector Xₜ

Xₜ state vector of business value

Formula (1.5) · vector

3 / 8 · Instruments

Which dimensions of the vector does DCF value?

Xₜ state vector of business valueDCF discounted cash flow model

Formula (1.6) · dynamics

4 / 8 · Dynamics

What does the equation X_t+1 = G(X_t, a_t, ε_t+1) show?

aₜ managerial actionsεₜ₊₁ exogenous shocksG transition function

Formula (1.7) · composition

5 / 8 · Composition

What does Ω mean in formula (1.7)?

Ω structural functionΦₜ institutional and informational context

Formula (1.8) · loop

6 / 8 · Loop

How does the loop V_t ↔ E_t ↔ D_t move?

Vₜ valueEₜ expectationsDₜ decisions

Formulas (1.5)–(1.8)

7 / 8 · Why?

Why can formulas (1.5)–(1.8) not be calculated in the way DCF can?

Xₜ state vector of business valueΩ structural function

Formulas (1.5)–(1.8)

8 / 8 · Limitation

See how value moves

εₜ₊₁ exogenous shocksaₜ managerial actionsXₜ state vector

CFₜᵉ

Aₜ

Iₜ

Kₜ

Sₜ

Bₜ

Rₜ

Since all the models depend on assumptions, sensitivity analysis is indispensable: a valuation result is presented as a range with its assumptions, not as a single “exact” figure.

More: section 1.1.2 ↗

Sensitivity analysis

1 / 7 · Situation

What is the company worth – exactly 1 610?

WACC weighted average cost of capitalg long-term growth rateDCF discounted cash flow model

1 610EUR thousand±?

WACC = 10 %

g = 2 %

Sensitivity analysis

2 / 7 · Table

Click the cells and compare them with the base case

WACC weighted average cost of capitalg long-term growth rate

WACC 8 %WACC 9 %WACC 10 %WACC 11 %WACC 12 %g = 1 %g = 2 %g = 3 %

Values in EUR thousand; the table from section 1.2 of the chapter (FCF EUR 100–146 thousand). The frame marks the base case.

Base case: WACC 10 %, g 2 % – EUR 1 610 thousand.

Sensitivity analysis

3 / 7 · Direction

In which cell of the table is value highest?

WACC weighted average cost of capitalg long-term growth rate

Sensitivity analysis

4 / 7 · Asymmetry

When WACC falls by 1 percentage point, value rises by 14.9 %; when it rises, value falls by only 11.6 %. Why?

WACC weighted average cost of capitalg long-term growth rate

Sensitivity analysis

5 / 7 · Calculation

How many times greater is the highest value in the table than the lowest?

WACC weighted average cost of capitalg long-term growth rate

2 5271 191 = Ratio

1 1912 527EUR thousand · more than a twofold difference

Sensitivity analysis

6 / 7 · Conclusion

How should the valuation result be presented?

WACC weighted average cost of capitalg long-term growth rate

Sensitivity analysis

7 / 7 · Why?

Why does the chapter call the DCF result not so much an “answer” as a “sensitivity range”?

WACC weighted average cost of capitalg long-term growth rate

APA 7

References

Phelan, S. E. (1997). Exposing the Illusion of Confidence in Financial Analysis. Management Decision, 35(2), 163–168. https://doi.org/10.1108/00251749710160322

Figures and concepts are taken from the numerical examples in section 1.2 of Chapter 1, from section 1.1.2 and from the textbook’s glossary (PV, discount rate, FCF, EVA, NOPAT, WACC, exogenous and endogenous, reflexivity).

Rakštys, R. (2026). Chapter 1. Foundations of Business Value (English translation of v0.16.5, 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/ch01/ · 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.

Calculate like a valuer

Choose a formula

What are these five years of cash flows worth today?

How do you calculate what these cash flows are worth today?

Select the cards needed for the first term of formula (1.1)

Calculate the term for year 4

What does EUR 454.2 thousand mean?

How does the discount rate change the value?

What is the period after five years worth?

How do you calculate TV?

What is needed to calculate TV₅?

Calculate TV₅

How do you get the value of the company today (V₀)?

TV makes up 71.8 % of the value of the company. What does that mean?

What happens when growth approaches the rate?

Does the company create value?

How do you calculate EVA?

What is needed to calculate EVA?

Calculate EVA, EUR thousand

EVA is EUR 50 thousand. What does that mean?

And if NOPAT were EUR 120 thousand?

Creating or destroying – what does it depend on?

What does the company’s capital cost?

How do you calculate WACC?

What is needed to calculate WACC?

Calculate the debt term, %

WACC is 8.9 %. What does that mean?

How much does the cost of equity matter?

Is value a single number?

Select the dimensions of the vector Xₜ

Which dimensions of the vector does DCF value?

What does the equation Xt+1 = G(Xt, at, εt+1) show?

What does Ω mean in formula (1.7)?

How does the loop Vt ↔ Et ↔ Dt move?

Why can formulas (1.5)–(1.8) not be calculated in the way DCF can?

See how value moves

What is the company worth – exactly 1 610?

Click the cells and compare them with the base case

In which cell of the table is value highest?

When WACC falls by 1 percentage point, value rises by 14.9 %; when it rises, value falls by only 11.6 %. Why?

How many times greater is the highest value in the table than the lowest?

How should the valuation result be presented?

Why does the chapter call the DCF result not so much an “answer” as a “sensitivity range”?

References

Trainer storyboard

What does the equation X_t+1 = G(X_t, a_t, ε_t+1) show?

How does the loop V_t ↔ E_t ↔ D_t move?