Question

Management has recently announced that expected dividends for the next three years will be as follows: Year 1 2 3 Dividend $3.00 2.25 1.50 The firm’s assets will then be liquidated and the proceeds invested in the preferred stock of other firms so that the company will be able to pay an annual dividend of $1.25 indefinitely. If your required return on investments in common stock is 10 per-cent, what is the maximum you should pay for this stock

Answer 1

To calculate the maximum price to pay for the stock, add the present value of the expected dividends for the first three years to the present value of the perpetual dividends that start in year four, discounted back to present values.

Step-by-step explanation:

The question at hand relates to the valuation of a company's stock based on expected dividends and the present value of those dividends. To determine the maximum price one should pay for the stock, you must calculate the present value of the future dividend payments plus the present value of the perpetuity that the company will provide after the third year.

The formula for the present value (PV) of a dividend in a specific year is:

PV = Dividend / (1 + r)n

Where:
r = required rate of return (10%)
n = number of years in the future the dividend will be received

For the given dividends:

• Year 1: PV = $3 / (1 + 0.10)1
• Year 2: PV = $2.25 / (1 + 0.10)2
• Year 3: PV = $1.50 / (1 + 0.10)3

Additionally, the value of the perpetuity starting in year 4 can be calculated using the perpetuity formula:

PV = Dividend / r

Since the perpetuity is starting in year 4,

PV = $1.25 / 0.10

To find the present value of this perpetuity at year 3, it needs to be discounted back to its present value:

PVperpetuity at Year 3= ($1.25 / 0.10) / (1 + 0.10)3

The sum of all these present values will give the maximum price one should pay for the stock today.