Z = 1, 2x₁ + 1, 4x₂ + 3, 3x₃ + 0, 6x₄ + 1, 0x₅

$$x_{1} = \frac{aktywa\ biezace - pasywa\ biezace}{aktywa\ ogolem} = \frac{kapital\ pracujacy}{aktywa\ ogolem}$$

$$x_{2} = \frac{\text{skumulowany\ zysk\ zatrzyman}y}{aktywa\ ogolem}$$

$$x_{3} = \frac{zysk\ przed\ opodatkowaniem\ i\ zaplaceniem\ odsetek}{aktywa\ ogolem}\backslash n$$

$$x_{5} = \ \frac{sprzedaz}{aktywa\ ogolem}$$

$$NPV = \ \sum_{t = 0}^{n}\frac{\text{NCF}_{t}}{\left( 1 + r \right)^{t}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }NPV = \sum_{t = 1}^{n}{\frac{\text{CF}_{t}}{{(1 + r)}^{t}} - PV\ }$$

$LtV = \frac{\text{kredyty}}{calosc\ inwestycji}$ $D_{N} = r \times \sum_{i = 1}^{n}{\text{gap}_{i} \times \frac{W_{i}}{12}}$

D_N = P_o − K_o

D_N = r_srA × A − r_srP × P

D_N = r_srA × A − r_srP × P

Zał: r_srA = r_b = r_srP

D_N = r_b × A − r_b × P

D_N = r_b(A−P) → GAP (luka)

WRZS= $\frac{a_{i}(p_{l})}{r}$

L₀ = A₁ + A₂ + … + A_n − P₁ − P₂ − … − P_k

D₀₌A₁ × a₁₀ + A₂ × a₂₀ + … + A_n × a_n0 − P₁ × p₁₀ − P₂ × p₂₀ − … − P_m × p_m0

D₁₌A₁ × a₁₁ + A₂ × a₂₁ + … + A_n × a_n1 − P₁ × p₁₁ − P₂ × p₂₁ − … − P_m × p_m1

D_N = A₁ * a₁₁ + A₂ * a₂₁ + … + A_n * a_n1 − P₁ * p₁₁ − P₂ * p₂₁ − … − P_m * p_m1 − (A₁*a₁₀+A₂*a₂₀+…+A_n*a_n0−P₁*p₁₀−P₂*p₂₀−…−P_m*p_m0)

D_N = A₁(a₁₁−a₁₀) + A₂(a₂₁−a₂₀) + … + A_n(a_n1−a_n0) − P₁(p₁₁−p₁₀) − P₂(p₂₁−p₂₀) − … − P_k(p_m1−p_m0)

D_N = A₁ * a₁ + A₂ * a₂ + … + A_n * a_n − P₁ * p₁ − P₂ * p₂ − … − P_m * p_m

D_N = r * GAP,

$${D}_{N} = A_{1}*{a}_{1}*\frac{r}{r} + A_{2}*{a}_{2}*\frac{r}{r} + \ldots + A_{n}*{a}_{n}*\frac{r}{r} - P_{1}*{p}_{1}*\frac{r}{r} - P_{2}*{p}_{2}*\frac{r}{r} - \ldots - P_{m}*{p}_{m}*\frac{r}{r}$$

$${D}_{N} = r*\left( A_{1}*\frac{{a}_{1}}{r} + A_{2}*\frac{{a}_{2}}{r} + \ldots + A_{n}*\frac{{a}_{n}}{r} - P_{1}*\frac{{p}_{1}}{r} - P_{2}*\frac{{p}_{2}}{r} - \ldots - P_{n}*\frac{{p}_{m}}{r} \right) = r*\text{GAP}_{s}$$

$${D}_{N} = r*\left( \sum_{i = 1}^{n}{A_{i}*\text{WRZS}_{i} - \sum_{k = 1}^{m}\text{WRZS}_{k}} \right) = r*\text{GAP}_{s}$$

$${\text{WRZS}^{A} = \sum_{}^{}{\text{WRZS}_{i}^{A}*w_{i}^{A}}\backslash n}{\text{WRZS}^{P} = \sum_{}^{}{\text{WRZS}_{k}^{P}*w_{k}^{P}}}$$

$$r_{b} = \frac{r_{a}*q_{a} - r_{p}*q_{p}}{q_{a} - q_{b}}$$

$D = \frac{\sum_{t = 1}^{n*m}{\frac{C_{t}}{\left( 1 + \frac{\text{YTM}}{m} \right)^{t}}*t}}{\sum_{t = 1}^{n*m}\frac{C_{t}}{\left( 1 + \frac{\text{YTM}}{m} \right)^{t}}} = \ \frac{\sum_{t = 1}^{n*m}{\frac{C_{t}}{\left( 1 + \frac{\text{YTM}}{m} \right)^{t}}*t}}{\text{PV}}$ $D = \frac{D_{0}}{m}$

$$MD = \ \frac{D}{1 + \text{YTM}_{0}}$$

$$\frac{PV}{\text{PV}_{0}} = - D \times \frac{YTM}{1 + \text{YTM}_{0}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\frac{PV}{\text{PV}_{0}} = - MD \times YTM\ \backslash n$$

$$D_{p} = \sum_{i = 1}^{n}{D_{i} \times w_{i}}$$

$$IR = \frac{\sum_{t = 1}^{n}\frac{C_{t}\left( t - h \right)^{2}}{\left( 1 + YTM \right)^{t}}}{I_{o}}$$

$$RV = \frac{\text{NII}_{t1}}{{(1 + YTM)}^{1}} + \frac{\text{NII}_{t2}}{{(1 + YTM)}^{2}} + \ldots + \frac{\text{NII}_{\text{tn}}}{{(1 + YTM)}^{n}}$$

$$RV = \frac{\text{NII}}{{(1 + YTM)}^{1}} + \frac{\text{NII}}{{(1 + YTM)}^{2}} + \ldots + \frac{\text{NII}}{{(1 + YTM)}^{n}}$$

$$RV = NII\left( \frac{1}{{(1 + YTM)}^{1}} + \frac{1}{{(1 + YTM)}^{2}} + \ldots + \frac{1}{{(1 + YTM)}^{n}} \right)$$

RV = NII * S_n

$S_{n} = \frac{a_{1}}{1 - q}$ $S_{n} = \frac{\frac{1}{1 + YTM}}{1 - \frac{1}{1 + YTM}}\text{\ \ \ \ }S_{n} = \frac{\frac{1}{1 + YTM}}{\frac{1 + YTM - 1}{1 + YTM}}\text{\ \ \ }S_{n} = \frac{1}{\text{YTM}}$

$$RV = S_{n} = \frac{\text{NII}_{t1}}{1 - q}$$

$$RV = \frac{\text{NII}}{\text{YTM}}$$

$${MV = - DG\frac{YTM}{1 + \text{YTM}_{0}}\text{PV}\left( A_{t0} \right)\backslash n}{\text{MV}_{t1} = \text{MV}_{t0} + MV\backslash n}{DG = D_{A} - \frac{PV(Z_{t0})}{PV(A_{t0})}D_{z}}$$

lub

VaR = (kσ-µ)W₀

$$W_{w} = \frac{F_{w}}{CWK*12,5}$$

$$W_{w} = \frac{F_{w}}{\sum_{}^{}{A_{i} \times w_{i}}}$$

$$ROA = \frac{\text{zysk\ netto}}{\text{aktywa}}$$

$EM = \frac{\text{aktywa\ }}{kapital\ wlasny}$

$$NEM = \frac{\text{zysk\ netto}}{przychody\ ogolem}$$

ROE = ROA x EM

ROA = AU x NM

ROE = AU x NM x EM

EVA =  (ROIC  −  WACC) x K

EVA  =  NOPAT  −  c x TC

$$RORAC = \frac{E(Y)}{\text{VaR}}$$

$$RAROC = \frac{E\left( Y \right) - k\sigma e}{\text{VaR}}$$