Calculate The VA

Calculate The Va

Calculate the PV of the dividends paid during the supernatural growth period; find the PV of Turbo's stock price at the end of Year 3; and sum the components to determine the stock's current value. Additionally, compute P1^ and P2^, and analyze dividend yields and capital gains yields for Years 1-3 to understand total returns.

Sample Paper For Above instruction

Valuation of Stock Using Dividend Discount Model and Growth Assumptions

The valuation of stocks is an essential aspect of investment analysis, relying heavily on the present value (PV) of expected future dividends and stock prices. In this paper, I will demonstrate the process of calculating the current value of a stock using projected dividends during a period of supernatural (supernormal) growth, as well as the terminal stock price at the end of the growth period. Additionally, I will compute the one-year and two-year forward prices (P1^ and P2^), analyze dividend yields, and capital gains yields for Years 1 through 3.

Calculation of Dividends During the Supernormal Growth Period

Initially, we calculate the dividends over the years of supernatural growth. Using the provided growth rates, we find:

- D1 = $1.15 × 1.15 = $1.3225

- D2 = $1.3225 × 1.15 = $1.5209 (rounded to $1.52)

- D3 = $1.52 × 1.13 ≈ $1.7176 (rounded to $1.72)

- D4 = $1.72 × 1.06 ≈ $1.8212 (rounded to $1.82)

Next, discount these dividends to their PVs using the appropriate discount rate (rs). Assuming a discount rate of 12%, the PV of each dividend is:

- PV of D1 = $1.3225 / (1.12)^1 ≈ $1.181

- PV of D2 = $1.52 / (1.12)^2 ≈ $1.211

- PV of D3 = $1.72 / (1.12)^3 ≈ $1.224

- PV of D4 = $1.82 / (1.12)^4 ≈ $1.228

The total PV of dividends during the supernormal growth period is the sum:

PV of Dividends ≈ $1.181 + $1.211 + $1.224 + $1.228 ≈ $4.844

Calculating the Terminal Stock Price at the End of Year 3

The stock's price at Year 3, P3^, is based on the Gordon Growth Model, assuming the perpetual growth rate after Year 3 is g = 6%. The formula is:

P3^ = D4 × (1 + g) / (rs - g)

Substituting the known values:

P3^ = $1.82 × (1 + 0.06) / (0.12 - 0.06) = $1.82 × 1.06 / 0.06 ≈ $1.931 / 0.06 ≈ $32.18

The PV of P3^ discounted back to today is:

PV of P3^ = $32.18 / (1.12)^3 ≈ $32.18 / 1.4049 ≈ $22.91

Calculating the Current Stock Price (P0)

The total value of the stock today involves summing the PV of dividends during the supernormal growth period and the PV of the stock price at Year 3:

P0 = PV of Dividends + PV of P3^ ≈ $4.844 + $22.91 ≈ $27.75

Calculations of P1^ and P2^

The one-year forward price, P1^, is:

P1^ = D2 × (1 + g) / (rs - g) ≈ $1.52 × 1.06 / 0.06 ≈ $1.611 / 0.06 ≈ $26.85

Similarly, the two-year forward price, P2^, is:

P2^ = D3 × (1 + g) / (rs - g) ≈ $1.72 × 1.06 / 0.06 ≈ $1.823 / 0.06 ≈ $30.38

Dividend Yields and Capital Gains for Years 1-3

- Year 1:

Dividend Yield = D1 / P0 ≈ $1.3225 / $27.75 ≈ 4.77%

Capital Gains Yield = (P1^ - P0) / P0 ≈ ($26.85 - $27.75) / $27.75 ≈ -3.24%

Total Return ≈ 4.77% - 3.24% ≈ 1.53%

- Year 2:

Dividend Yield = D2 / P1^ ≈ $1.52 / $26.85 ≈ 5.66%

Capital Gains Yield = (P2^ - P1^) / P1^ ≈ ($30.38 - $26.85) / $26.85 ≈ 13.09%

Total Return ≈ 5.66% + 13.09% ≈ 18.75%

- Year 3:

Dividend Yield = D3 / P2^ ≈ $1.72 / $30.38 ≈ 5.66%

Capital Gains Yield = (P3^ - P2^) / P2^ ≈ ($32.18 - $30.38) / $30.38 ≈ 5.83%

Total Return ≈ 5.66% + 5.83% ≈ 11.49%

Implications for Investors and Financial Management

The calculations highlight that in periods of supernormal growth, high dividend yields and substantial capital gains can be expected, which significantly contribute to total returns. Investors must consider such growth-phase valuations carefully, recognizing the impact of assumptions related to growth rates and discount rates. Financial managers should examine these parameters in relation to the company's future prospects, market conditions, and risk factors, ensuring realistic valuations that guide investment and dividend policy decisions.

In conclusion, systematic valuation models incorporating discounted dividends and terminal price estimations provide valuable insights for investment decision-making. Accurate assumptions and sensitivity analyses are critical to reflecting the true value and the associated risks, ultimately supporting more informed financial strategies.

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