sHARE VALUATIONS IN A NUTSHELL

 

Happy New Year 2022

I have accumulated important share valuation formulas which I would like to share with anyone from novices to professionals. Hope it interests you all!

 

Past, Present and future dividends info:

Current D₀ = Dividend paid just now 0.20

ED₁ = Dividend expected in year 1 = 0.21; D1 = Paid dividends = 0.20

ED₂ = Dividend expected in year 2 = 0.77; D2 = Paid dividends = 0.13

ED₃ = Dividend expected in year 3 = 0.29; D3 = Paid dividends = 0.17

ED₄ = Dividend expected in year 4 = 0.23; D4 = Paid dividends = 0.30

ED₅ = Dividend expected in year 5 = 0.23; D5 = Paid dividends = 0.20

Expected DDR₆ = Dividend Distribution Rate = 20% of retained profits

Expected MV of share = 20

K_e = 14%

K_{p =} 17%

P_o = Present share price/value

P_1,2,3,4,5 = future market value of share

P/E = Price of share / EPS

g _short-term = Dividend growth rate = 0.03 (GDP + Inflation rate)

g _short-term = Dividend growth rate = (D₀/Dividends n years ago)^1/n – 1. (Substitute D5 = 0.20 for n and 5 for 1/n)

g _short-term = K_e – (D₀ / P₀)

g _short-term = Earnings Retention Rate (DPS/EPS) x K_e; ERR = 1 - DPR

g _long-term = 1% or 0.01

 

1.       Absolute valuations: DCF Valuation

Year 0 = 0.21 / (1 + 0.14)¹ + 0.77 / (1 + 0.14)² + …. + 0.23 / (1+0.14)⁵ + 20 / (1 + 0.14)⁵ = PV of Stream

 

 

2.       Absolute valuations: Dividend Discount method

P₀ = 0.15 + 20 / 1 + 0.14 = Single period share price  

Or

P₀ = ED1 / (1 + K_e) + P1 / (1 + K_e) = Single period share price

Or

P₀ = ED1 / (1 + K_e)¹ + ED2 / (1 + K_e)² + ED3 / (1 + K_e)³ + …. + ED5 + P₅ / (1 + Ke)⁵ = 5 multi-period share price (DDM valuation formulas are modified from Holding Period formula)

 

 

3.       Relative valuation

P/E of your company x Future expected EPS of your company

Or

Competitors P/E average x Future expected EPS of your company

 

 

4.       Gordon Growth model

P₀ = D₀ (1 + g)1 / (1 + K_e)¹ + D₀ (1 + g)² / (1 + K_e)² + …. + D₀ (1 + g)⁵ / (1 + K_e)⁵ = Share price

Or

P₀ = D₀ (1 + g) / K_e - g = D1 / K_e - g = Current share price. (Substitute D₅ rate to get current share price for fifth year)

E.g. P₀ = 0.20 x (1 + 0.03) / 0.14-0.03 (Remember to make sure g < K_e).

 

 

5.       Terminal Value method

To calculate P₀ for year six, Terminal value must be used.

TV = (5^th year EPS x 5^th year DPR); the dividend for 6^th year D₆ = TV x g; substituting this P0 = D₆ / K_e – g _long-term

 

 6. Two-stage growth method

P₀ = D₀ (1 + g _short-term)1 / (1 + K_e)1 + (D₀ (1+g _short-term)5 x (1 + g _long-term)/ (1 + K_e)(K_e – g _long-term))     

P₃ = D₆ (1+ g _long-term) / K_e – g _long-term

Note: P₀ = P₃

Or

PV = ED₁ (1 + g _{super growth}) / (1 + K_e)¹ + ED₂ (1 + g _{super growth}) / (1 + K_e)² + ED₃ (1 + g _{super growth}) / (1 + K_e)³ +…. + ED₅ (1 + g _{super growth}) / (1 + K_e)⁵ = PV of constant stream of dividends

P₅ = ED₅ (1 + g _{super growth})⁵ x (1 + g _{normal growth}) / K_e – g _{normal growth} = 5^th year Share price

Discounted value of share price = P₆ / (1 + K_e)⁵

P₀ = PV + P₅

Note: g _{normal growth} = g _long-term and g _{super growth} = g _Short-term

 

 

 

7.       Non-dividend paying stock value

EPS _{5th year} = EPS _current-year x (1 + g _short-term)⁵

EPS _{6th year} = EPS _{5th year} x (1 + g _long-term)      

D₆ = EPS _{5th year} x Expected DDR for 6^th year

P₅ = D₆ / K_e - g _long-term

P₀ = P₅ / (1 + K_e)⁵ = Current share value derived from TV.       

 

      

 

8.       Perpetual Preference Shares

P₀ = D_p (Constant Preference Dividend) / K_p (Cost of Preference share capital)

Eg: 100$ face value 6% preference shares = 100 x 0.06 = 6 / 0.17 = Preference share value

Or

Preference share face value + Arrear Dividends

Or

Preference share par value + Arrears preference dividends + Surplus on preference share (Surplus on liquidation)

 

 

9.       The Ex-div share price

Cum-div price – Dividend

 

10.   Discounted Cash Flow Method of total Equity valuation

FCF = Operating profit – Tax on Operating Profit @30% + Tax-relief on Depreciation – Capital investments

Real Discount rate = (1 + WACC) / (1 + Inflation)

Corporate Value = FCF / Real Discount Rate

Equity value = Corporate value – Corporate Debt x (1+Corporate tax rate)

 

 

11.   Market value of share

EPS x P/E Ratio; Earnings / Earnings Yield

 

 

12.   Intrinsic value of share

FCFE / No. of Equity shares

Or

T. Assets – Creditors – Fictitious assets – external liability - Preference shareholders / No. of Equity shares

 

 

13.   Yield method: ROCE

ROCE / Normal rate of return x Paid up value of shares

 

 

14.   Yield method: Dividend Method

Expected rate of return / Normal rate of return x Paid up value of share

Or

Possible yield rate /Expected yield rate x Paid up value of share

Or

Profit available for equity shareholder / No of Equity shares x Capitalization factor

Or

Average PBIT – Bad Debts – Depreciation on (Revalued-NBV) PPE & Goodwill – Preference dividend – Transfer to reserves = Profits available to shareholders

Dividend rate = Profits available to shareholders / Total share capital

Yield Value of share = Dividend rate / Normal value x Paid up value of share

 

 

15.   Fair value method

Intrinsic value + Yield method / 2

 

 

16.   Rights shares value

Number of Rights / Number of old shares x (Market price per share – Issue price)

 

 

17.   H-Method

P₀ = D₀ (1 + g _long-term) / K_e – g _long-term + D₀ x H x (g _short-term – g _long-term) / K_e – g _long-term = Share price

Here, H = t/2 and that means the first five years growth period. So, H = 5/2.

 

 

18.   Three step method

P₃ = D₃ (1 + g _short-term) + D₃ x H (g _short-term – g _long-term)

Where D₃ = D₀ (1 + g _short-term)³ = 3^rd year expected dividend

P₀ = P₃ + D₃

   19. Walter’s model

P₀ = (DPS / K_e)  + (IRR(EPS – DPS) / K_e) / K_e

Note: When

IRR > K_e ; No need to declare dividends and DPR = 0%

IRR = K_e; No impact on value of the firm and hence declare DPR = between 0-100%

IRR < K_e; Declare dividends and DPR = 100%

 

  20. Gordon’s Capitalisation model

P₀ = EPS x DPR / K_e – g growth rate of earnings  

 

  21. MM model

P₀ = 1 / (1 + K_e)  x  (D₁ + P₁)

22. Ex-Rights value of share 

Value of share after rights issue = NPo+S/N+1

N= number of existing shares required for a rights issue; Po= Cum-rights price per share; S= subscription price at which shares are issued 

23. Traditional approach 

Po= m(D + E/3) 

Where m= multiplier; P= market price of share; D= dividend per share; E= Earnings per share