A firm has an expected dividend payout ratio of 60%, and an expected dividend growth rate of 5% per year. What is the firm's Price/Earnings ratio if the appropriate discount rate is 8% per year?
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A. B. C. D.A
Value = 0.60/(0.08-0.05) = 20.
To determine the firm's Price/Earnings (P/E) ratio, we need to calculate the present value of future dividends and divide it by the present value of future earnings.
Given:
First, let's calculate the expected dividend for the next year (D₁). We can use the dividend payout ratio to find it:
D₁ = Expected dividend payout ratio × Expected earnings = 0.60 × E₀
Next, we need to calculate the expected dividend for the year after next (D₂) by applying the dividend growth rate to D₁:
D₂ = D₁ × (1 + Dividend growth rate) = D₁ × (1 + 0.05) = D₁ × 1.05
Using the constant growth dividend discount model, we can calculate the present value of the expected dividends (PVD) using the discount rate:
PVD = D₁ / (1 + Discount rate) + D₂ / (1 + Discount rate)² + D₃ / (1 + Discount rate)³ + ...
The present value of future dividends is an infinite series because dividends are expected to continue growing indefinitely. To simplify the calculation, we can use the Gordon growth model to calculate the present value of future dividends beyond the third year:
PVD = D₃ / (Discount rate - Dividend growth rate)
We can substitute the expressions for D₁ and D₂ into the present value formula:
PVD = D₁ / (1 + Discount rate) + D₂ / (1 + Discount rate)² + (D₁ × 1.05) / (Discount rate - 0.05)
Now, let's calculate the present value of future dividends:
PVD = 0.60 × E₀ / (1 + 0.08) + (0.60 × E₀ × 1.05) / (1 + 0.08)² + (0.60 × E₀ × 1.05) / (0.08 - 0.05)
Next, we need to calculate the present value of future earnings (PVE) using the discount rate:
PVE = E₀ / (1 + Discount rate) + E₁ / (1 + Discount rate)² + E₂ / (1 + Discount rate)³ + ...
Since earnings are expected to grow at the same rate as dividends (5% per year), we can use the same expression for PVE as for PVD:
PVE = E₀ / (1 + Discount rate) + (E₀ × 1.05) / (1 + Discount rate)² + (E₀ × 1.05) / (0.08 - 0.05)
Finally, we can calculate the Price/Earnings (P/E) ratio by dividing the present value of future dividends (PVD) by the present value of future earnings (PVE):
P/E ratio = PVD / PVE
P/E ratio = (0.60 × E₀ / (1 + 0.08) + (0.60 × E₀ × 1.05) / (1 + 0.08)² + (0.60 × E₀ × 1.05) / (0.08 - 0.05)) / (E₀ / (1 + 0.08) + (E₀ × 1.05) / (1 + 0.08)² + (E₀ × 1.05) / (0.08 - 0.05))
Simplifying the expression:
P/E ratio = (0.60 / (