Kikokoto cha Altman Z-Score kwa Tathmini ya Hatari

Altman Z-Score Hesabu

Utangulizi

Altman Z-Score ni mfano wa kifedha ulioanzishwa na Edward I. Altman mwaka 1968 kutabiri uwezekano wa kampuni kufilisika ndani ya miaka miwili. Inachanganya uwiano wa kifedha muhimu tano kwa kutumia jumla yenye uzito ili kutathmini afya ya kifedha ya kampuni. Z-Score inatumiwa sana na wawekezaji, wakopeshaji, na wachambuzi wa kifedha kutathmini hatari ya mkopo.

Fomula

Altman Z-Score inahesabiwa kwa kutumia fomula ifuatayo:

Z = 1.2X_1 + 1.4X_2 + 3.3X_3 + 0.6X_4 + 1.0X_5

Ambapo:

$X_1 = \frac{\text{Kazi ya Kifedha}}{\text{Mali Zote}}$
$X_2 = \frac{\text{Faida Iliyoshikiliwa}}{\text{Mali Zote}}$
$X_3 = \frac{\text{Faida Kabla ya Riba na Kodi (EBIT)}}{\text{Mali Zote}}$
$X_4 = \frac{\text{Thamani ya Soko ya Hisa}}{\text{Madeni Yote}}$
$X_5 = \frac{\text{Mauzo}}{\text{Mali Zote}}$

Maelezo ya Vigezo

Kazi ya Kifedha (WC): Mali za sasa zisizokuwa na madeni ya sasa. Inaonyesha likuiditi ya kifedha ya muda mfupi.
Faida Iliyoshikiliwa (RE): Faida iliyokusanywa ambayo imewekezwa tena katika kampuni. Inaonyesha faida ya muda mrefu.
EBIT: Faida kabla ya riba na kodi. Inaonyesha ufanisi wa uendeshaji.
Thamani ya Soko ya Hisa (MVE): Idadi ya hisa zilizo katika soko mara kwa mara na bei ya sasa ya hisa. Inaonyesha imani ya wanahisa.
Madeni Yote (TL): Jumla ya madeni ya sasa na ya muda mrefu.
Mauzo: Jumla ya mapato kutoka kwa bidhaa au huduma zilizouzwa.
Mali Zote (TA): Jumla ya mali za sasa na zisizokuwa za sasa.

Hesabu

Mwongozo wa Hatua kwa Hatua

Hesabu Uwiano wa Kifedha:
- $X_1 = \frac{\text{WC}}{\text{TA}}$
- $X_2 = \frac{\text{RE}}{\text{TA}}$
- $X_3 = \frac{\text{EBIT}}{\text{TA}}$
- $X_4 = \frac{\text{MVE}}{\text{TL}}$
- $X_5 = \frac{\text{Mauzo}}{\text{TA}}$
Tumia Uzito kwa Kila Uwiano:
- Weka uzito kwa kila uwiano wa $X$ kwa kutumia koeficienti zinazofaa.
Jumlisha Uwiano Zilizopimwa:
- $Z = 1.2X_1 + 1.4X_2 + 3.3X_3 + 0.6X_4 + 1.0X_5$

Mfano wa Nambari

Kiwango cha fedha cha kampuni ni kama ifuatavyo (kwa USD milioni):

Kazi ya Kifedha (WC): $50 milioni
Faida Iliyoshikiliwa (RE): $200 milioni
EBIT: $100 milioni
Thamani ya Soko ya Hisa (MVE): $500 milioni
Madeni Yote (TL): $400 milioni
Mauzo: $600 milioni
Mali Zote (TA): $800 milioni

Kuhesabu Uwiano:

$X_1 = \frac{50}{800} = 0.0625$
$X_2 = \frac{200}{800} = 0.25$
$X_3 = \frac{100}{800} = 0.125$
$X_4 = \frac{500}{400} = 1.25$
$X_5 = \frac{600}{800} = 0.75$

Kuhesabu Z-Score:

\begin{align*} Z &= 1.2(0.0625) + 1.4(0.25) + 3.3(0.125) + 0.6(1.25) + 1.0(0.75) \\ &= 0.075 + 0.35 + 0.4125 + 0.75 + 0.75 \\ &= 2.3375 \end{align*}

Tafsiri

Z-Score > 2.99: Eneo Salama – Uwezekano mdogo wa kufilisika.
1.81 < Z-Score < 2.99: Eneo la Kijivu – Hatari isiyo wazi; tahadhari inahitajika.
Z-Score < 1.81: Eneo la Dhiki – Uwezekano mkubwa wa kufilisika.

Matokeo: Z-Score ya 2.34 inaweka kampuni katika Eneo la Kijivu, ikionyesha uwezekano wa kutokuwa na utulivu kifedha.

Mambo ya Kando na Mipaka

Thamani Mbaya: Thamani mbaya za neti, faida iliyoshikiliwa, au kazi ya kifedha zinaweza kupunguza sana Z-Score.
Matumizi: Mfano wa asili unafaa zaidi kwa kampuni za umma za viwanda.
Tofauti za Sekta: Kampuni zisizo za viwanda, za kibinafsi, na za masoko yanayoibuka zinaweza kuhitaji mifano iliyorekebishwa (mfano, Z'-Score, Z''-Score).
Masharti ya Kiuchumi: Sababu za kiuchumi za makundi hazizingatiwi katika mfano.

Matumizi

Maombi

Utambuzi wa Kufilisika: Ugunduzi wa mapema wa dhiki ya kifedha.
Analizi ya Mkopo: Kusaidia wakopeshaji kutathmini hatari za mkopo.
Maamuzi ya Uwekezaji: Kuongoza wawekezaji kuelekea kampuni zenye afya ya kifedha.
Mkakati wa Kampuni: Kusaidia usimamizi kutathmini afya ya kifedha na kufanya marekebisho ya kimkakati.

Mbadala

Mifano ya Z'-Score na Z''-Score

Z'-Score: Imebadilishwa kwa kampuni za kibinafsi za viwanda.
Z''-Score: Imebadilishwa zaidi kwa kampuni zisizo za viwanda na za masoko yanayoibuka.

Mifano Mingine

Ohlson O-Score: Mfano wa regression wa logistic unaotabiri hatari ya kufilisika.
Zmijewski Score: Mbadala wa mfano wa probit unaozingatia dhiki ya kifedha.

Wakati wa Kutumia Mbadala:

Kwa kampuni zinazotoka nje ya sekta ya viwanda.
Wakati wa kutathmini kampuni za kibinafsi au zisizo za umma.
Katika muktadha tofauti wa kiuchumi au maeneo ya kijiografia.

Historia

Edward Altman alianzisha mfano wa Z-Score mwaka 1968 katikati ya kuongezeka kwa kufilisika kwa kampuni. Akitumia uchambuzi wa tofauti nyingi (MDA), Altman alichambua kampuni 66 ili kubaini uwiano wa kifedha muhimu unaotabiri kufilisika. Mfano huu umerekebishwa tangu wakati huo na unabaki kuwa chombo cha msingi katika tathmini ya hatari ya mkopo.

Maelezo ya Ziada

Athari za Manipulation ya Kifedha

Kampuni zinaweza kujihusisha na mbinu za uhasibu ambazo zinapandisha kwa muda uwiano wa kifedha.
Ni muhimu kuzingatia mambo ya ubora pamoja na alama za kiasi.

Uunganisho na Vipimo Vingine

Changanya Z-Score na uchambuzi mwingine (mfano, uchambuzi wa mtiririko wa fedha, mwenendo wa soko).
Tumia kama sehemu ya mchakato wa kina wa utafiti.

Mifano ya Kanuni

Excel

1' Excel VBA Function for Altman Z-Score Calculation
2Function AltmanZScore(wc As Double, re As Double, ebit As Double, mve As Double, tl As Double, sales As Double, ta As Double) As Double
3    Dim X1 As Double, X2 As Double, X3 As Double, X4 As Double, X5 As Double
4    
5    X1 = wc / ta
6    X2 = re / ta
7    X3 = ebit / ta
8    X4 = mve / tl
9    X5 = sales / ta
10    
11    AltmanZScore = 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5
12End Function
13
14' Usage in a cell:
15' =AltmanZScore(A1, B1, C1, D1, E1, F1, G1)
16' Where A1 to G1 contain the respective input values
17

Python

1## Altman Z-Score Calculation in Python
2def calculate_z_score(wc, re, ebit, mve, tl, sales, ta):
3    X1 = wc / ta
4    X2 = re / ta
5    X3 = ebit / ta
6    X4 = mve / tl
7    X5 = sales / ta
8    z_score = 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5
9    return z_score
10
11## Example usage:
12wc = 50
13re = 200
14ebit = 100
15mve = 500
16tl = 400
17sales = 600
18ta = 800
19
20z = calculate_z_score(wc, re, ebit, mve, tl, sales, ta)
21print(f"Altman Z-Score: {z:.2f}")
22

JavaScript

1// JavaScript Altman Z-Score Calculation
2function calculateZScore(wc, re, ebit, mve, tl, sales, ta) {
3  const X1 = wc / ta;
4  const X2 = re / ta;
5  const X3 = ebit / ta;
6  const X4 = mve / tl;
7  const X5 = sales / ta;
8  const zScore = 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5;
9  return zScore;
10}
11
12// Example usage:
13const zScore = calculateZScore(50, 200, 100, 500, 400, 600, 800);
14console.log(`Altman Z-Score: ${zScore.toFixed(2)}`);
15

Java

1// Java Altman Z-Score Calculation
2public class AltmanZScore {
3    public static double calculateZScore(double wc, double re, double ebit, double mve, double tl, double sales, double ta) {
4        double X1 = wc / ta;
5        double X2 = re / ta;
6        double X3 = ebit / ta;
7        double X4 = mve / tl;
8        double X5 = sales / ta;
9        return 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5;
10    }
11
12    public static void main(String[] args) {
13        double zScore = calculateZScore(50, 200, 100, 500, 400, 600, 800);
14        System.out.printf("Altman Z-Score: %.2f%n", zScore);
15    }
16}
17

R

1## R Altman Z-Score Calculation
2calculate_z_score <- function(wc, re, ebit, mve, tl, sales, ta) {
3  X1 <- wc / ta
4  X2 <- re / ta
5  X3 <- ebit / ta
6  X4 <- mve / tl
7  X5 <- sales / ta
8  z_score <- 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5
9  return(z_score)
10}
11
12## Example usage:
13z_score <- calculate_z_score(50, 200, 100, 500, 400, 600, 800)
14cat("Altman Z-Score:", round(z_score, 2))
15

MATLAB

1% MATLAB Altman Z-Score Calculation
2function z_score = calculate_z_score(wc, re, ebit, mve, tl, sales, ta)
3    X1 = wc / ta;
4    X2 = re / ta;
5    X3 = ebit / ta;
6    X4 = mve / tl;
7    X5 = sales / ta;
8    z_score = 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5;
9end
10
11% Example usage:
12z_score = calculate_z_score(50, 200, 100, 500, 400, 600, 800);
13fprintf('Altman Z-Score: %.2f\n', z_score);
14

C++

1// C++ Altman Z-Score Calculation
2#include <iostream>
3
4double calculateZScore(double wc, double re, double ebit, double mve, double tl, double sales, double ta) {
5    double X1 = wc / ta;
6    double X2 = re / ta;
7    double X3 = ebit / ta;
8    double X4 = mve / tl;
9    double X5 = sales / ta;
10    return 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5;
11}
12
13int main() {
14    double zScore = calculateZScore(50, 200, 100, 500, 400, 600, 800);
15    std::cout << "Altman Z-Score: " << zScore << std::endl;
16    return 0;
17}
18

C#

1// C# Altman Z-Score Calculation
2using System;
3
4class Program
5{
6    static double CalculateZScore(double wc, double re, double ebit, double mve, double tl, double sales, double ta)
7    {
8        double X1 = wc / ta;
9        double X2 = re / ta;
10        double X3 = ebit / ta;
11        double X4 = mve / tl;
12        double X5 = sales / ta;
13        return 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5;
14    }
15
16    static void Main()
17    {
18        double zScore = CalculateZScore(50, 200, 100, 500, 400, 600, 800);
19        Console.WriteLine($"Altman Z-Score: {zScore:F2}");
20    }
21}
22

Go

1// Go Altman Z-Score Calculation
2package main
3
4import (
5    "fmt"
6)
7
8func calculateZScore(wc, re, ebit, mve, tl, sales, ta float64) float64 {
9    X1 := wc / ta
10    X2 := re / ta
11    X3 := ebit / ta
12    X4 := mve / tl
13    X5 := sales / ta
14    return 1.2*X1 + 1.4*X2 + 3.3*X3 + 0.6*X4 + X5
15}
16
17func main() {
18    zScore := calculateZScore(50, 200, 100, 500, 400, 600, 800)
19    fmt.Printf("Altman Z-Score: %.2f\n", zScore)
20}
21

Swift

1// Swift Altman Z-Score Calculation
2func calculateZScore(wc: Double, re: Double, ebit: Double, mve: Double, tl: Double, sales: Double, ta: Double) -> Double {
3    let X1 = wc / ta
4    let X2 = re / ta
5    let X3 = ebit / ta
6    let X4 = mve / tl
7    let X5 = sales / ta
8    return 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + X5
9}
10
11// Example usage:
12let zScore = calculateZScore(wc: 50, re: 200, ebit: 100, mve: 500, tl: 400, sales: 600, ta: 800)
13print(String(format: "Altman Z-Score: %.2f", zScore))
14

Marejeo

Altman, E. I. (1968). Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. The Journal of Finance, 23(4), 589–609.
Altman Z-Score. Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Altman_Z-score
Investopedia - Altman Z-Score. Retrieved from https://www.investopedia.com/terms/a/altman.asp