Question

P/E Model and Cash Flow Valuation (LG8-5, LG8-7) Suppose that a firm’s recent earnings per share and dividend per share are $2.60 and $1.60, respectively. Both are expected to grow at 10 percent. However, the firm’s current P/E ratio of 25 seems high for this growth rate. The P/E ratio is expected to fall to 21 within five years. Compute the dividends over the next five years. Compute the value of this stock in five years.

Answer 1

The dividends for the next five years, given a 10% growth rate, are calculated for each year, resulting in a final year dividend of $2.57. The value of the stock in five years, using the projected P/E ratio of 21 and the grown EPS, is $88.62 per share. Present discounted value is a key concept in stock valuation, based on which future cash flows are discounted to estimate a stock's present value.

Step-by-step explanation:

To compute the dividends over the next five years when both earnings per share (EPS) and dividend per share (DPS) are expected to grow at a rate of 10 percent, we need to apply the constant growth model to the current dividend. We begin with the current DPS of $1.60 and increase it by 10% annually. Therefore, the dividends for the next five years will be:

• Year 1: $1.60 * (1 + 0.10) = $1.76
• Year 2: $1.76 * (1 + 0.10) = $1.94
• Year 3: $1.94 * (1 + 0.10) = $2.13
• Year 4: $2.13 * (1 + 0.10) = $2.34
• Year 5: $2.34 * (1 + 0.10) = $2.57

To calculate the value of the stock in five years, we use the P/E ratio expected in five years along with the projected EPS at that time. The EPS in five years can be calculated using the initial EPS of $2.60 growing at 10 percent for five years, which gives us:

Earnings After 5 Years = $2.60 * (1 + 0.10)^5 = $4.22.

Now, using the expected P/E ratio of 21, the value of the stock after five years is:

Value of Stock = Future EPS * Future P/E = $4.22 * 21 = $88.62.

This implies that based on the given growth and P/E adjustment, the stock is projected to be valued at $88.62 per share in five years.

The present discounted value (PDV) is crucial for stock valuation. It represents the current worth of expected future cash flows, given a certain discount rate. In this scenario, we would need to discount the expected dividends and future stock price to their present values and sum them to estimate the present value of the stock. The provided PV calculation seems off since the large figure mentioned ($256,500 per share) is not aligned with typical stock prices, and unless confirmed, it may be an error or related to a different context.