Suppose That A Firm's Recent Earnings Per Share And D 322399

Suppose That A Firms Recent Earnings Per Share And Dividend Per Share

Suppose that a firm’s recent earnings per share (EPS) and dividend per share (DPS) are $2.80 and $1.90, respectively. Both are expected to grow at an annual rate of 11%. However, the firm’s current price-to-earnings (P/E) ratio of 20 seems high given this growth rate. The P/E ratio is projected to decline to 16 over five years. The task is to compute the dividends over the next five years, the stock price in five years, and the present value of these cash flows using a 13% discount rate.

Paper For Above instruction

The valuation of a firm's stock involves understanding its dividend growth, future earnings, and anticipated stock prices. In this scenario, given the recent earnings per share (EPS) and dividend per share (DPS), along with growth expectations and a declining P/E ratio, an integrated valuation approach can be undertaken to estimate future dividends, stock price, and present value.

Calculation of Future Dividends

The current dividend per share (DPS) is $1.90, and it is expected to grow annually at 11%. The future dividends for the next five years can be calculated using the compound growth formula:

D_t = D_0 × (1 + g)^t

where D_0 is the current dividend, g is the growth rate, and t is the year.

- Year 1: $1.90 × (1 + 0.11)^1 = $1.90 × 1.11 = $2.109

- Year 2: $1.90 × (1 + 0.11)^2 = $1.90 × 1.2321 = $2.341

- Year 3: $1.90 × (1 + 0.11)^3 = $1.90 × 1.3676 = $2.592

- Year 4: $1.90 × (1 + 0.11)^4 = $1.90 × 1.5196 = $2.889

- Year 5: $1.90 × (1 + 0.11)^5 = $1.90 × 1.6873 = $3.188

Calculation of Stock Price in Five Years

The stock price in five years (P_5) can be estimated based on the expected P/E ratio at that time and the projected earnings. First, forecast the earnings per share (EPS) in five years:

E_5 = EPS_0 × (1 + g)^5 = $2.80 × 1.6873 = $4.722

The expected P/E ratio in five years is 16, so:

P_5 = P/E_5 × E_5 = 16 × $4.722 = $75.552

Present Value of Future Cash Flows

To determine the fair value of the stock today, discount the future dividends and the estimated stock price in five years at the given discount rate of 13%. The present value (PV) of each dividend is:

PV_D_t = D_t / (1 + r)^t

where r is the discount rate.

The present value of the stock price in five years also needs to be discounted back to the present:

PV_P_5 = P_5 / (1 + r)^5

Calculations:

- PV of Year 1 dividend: $2.109 / 1.13^1 = $1.867

- PV of Year 2 dividend: $2.341 / 1.13^2 = $1.835

- PV of Year 3 dividend: $2.592 / 1.13^3 = $1.804

- PV of Year 4 dividend: $2.889 / 1.13^4 = $1.774

- PV of Year 5 dividend: $3.188 / 1.13^5 = $1.744

- PV of stock price in Year 5: $75.552 / 1.13^5 = $50.883

Adding these present values:

Total PV = $1.867 + $1.835 + $1.804 + $1.774 + $1.744 + $50.883 = $58.693

Conclusion

The estimated present value of the stock, considering the projected dividends and future stock price, is approximately $58.69. This valuation reflects the expected growth in dividends and earnings, as well as the decline in the P/E ratio over five years, providing an insightful estimate of the company's intrinsic value based on current assumptions.

References

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