Worked Solution
✓ VerifiedNote: The question provides only the Retention Ratio (b = 75%, i.e., Dividend Payout Ratio = 25%). To calculate the market price under Gordon's Model and Walter's Model, additional data is required — specifically Earnings Per Share (EPS/E), Internal Rate of Return (r), and Cost of Equity / Required Rate of Return (Ke). The solution below presents the complete formula framework and methodology. Please provide the missing data to obtain numerical answers.
Assumed/Given: b = 0.75, Dividend Payout = (1 - b) = 0.25
(1) Gordon's Growth Model
Gordon's Model formula: P = E(1 - b) / (Ke - br)
Where: P = Market Price per share, E = Earnings Per Share, b = Retention Ratio, Ke = Required rate of return (Cost of Equity), r = Internal Rate of Return (IRR) on investments, br = g (Growth Rate).
Key condition: Ke > br (i.e., Ke > g) for the model to yield a valid positive price.
If r > Ke → Growth firm → Retain more → Higher price. If r = Ke → Dividend policy irrelevant. If r < Ke → Declining firm → Distribute more → Higher price.
Using b = 0.75 and (1 - b) = 0.25:
P = E × 0.25 / (Ke - 0.75r)
(2) Walter's Model
Walter's Model formula: P = (D + (r / Ke) × (E - D)) / Ke
Where: D = Dividend Per Share = E × (1 - b) = 0.25E, (E - D) = Retained Earnings = E × b = 0.75E.
Substituting: P = (0.25E + (r/Ke) × 0.75E) / Ke
Walter's conclusion is identical to Gordon's: if r > Ke, firm should retain all earnings (b = 1); if r < Ke, firm should pay all earnings as dividend (b = 0); if r = Ke, dividend policy is irrelevant.
Please supply the values of E (EPS), r (IRR), and Ke (Cost of Equity) to compute the final market price.
Write it like this
1The skeleton
- Write both formulas first, labeled and boxed — examiners are trained to scan for P = E(1-b)/(Ke - br) and P = (D + (r/Ke)(E-D))/Ke in the first two lines; missing the formula costs you formula marks even if your numbers are right.
- Define every variable immediately below the formula — list E, b, r, Ke, D with their values or expressions (b = 0.75, so 1-b = 0.25, D = 0.25E); this is where examiners award 'substitution marks' before you even compute P.
- Substitute b = 0.75 cleanly in one dedicated step — write 'Given: Retention Ratio (b) = 0.75, therefore Dividend Payout Ratio (1-b) = 0.25' as its own line so the examiner sees your data-reading is correct.
- Show the r vs Ke condition table for BOTH models — three rows: r > Ke / r = Ke / r < Ke with the implication (retain/irrelevant/distribute); this earns the 'conclusion marks' that most students skip because they think it's optional.
- End with a one-line numerical answer per model — even if data is assumed, plug assumed numbers in and write 'Market Price (Gordon's) = ₹X' and 'Market Price (Walter's) = ₹Y' on separate lines; examiners need a boxed final answer to tick.
2Examiner-rewarded phrases
3Common trap
Heads up — the single biggest killer here is mixing up which formula belongs to which model; Walter's has the r/Ke multiplier on retained earnings, Gordon's has it baked into the denominator as 'br'. If you flip them, you lose ALL formula marks for both parts even if your arithmetic is spotless.