Question

You want to invest in the equity of gateway inc. which has just announced a dividend of $7 per share on its common stock. gateway also announced that it expects to increase the dividend at a 9% annual rate for the first two years and at a 5% rate for the next two years, and then grow the dividend at a 3% rate thereafter. your required rate of return on the stock is 16%. calculate the value of stock of gateway inc. as of today.

Answer 1

Using the dividend discount model with varying growth rates for dividends, the total present value of the expected dividends and terminal value of Gateway Inc. stock is calculated to be approximately $59.19.

Step-by-step explanation:

The value of Gateway Inc:

Stock can be calculated using the dividend discount model (DDM), which consists of present value calculations for expected future dividends, growing at varying rates over different time periods, offset by the investor's required rate of return. First, calculate the present value of dividends for the first four years, which have different growth rates:

1. Year 1: $7.00 * (1 + 0.09) / (1 + 0.16) = $6.6379
2. Year 2: $7.00 * (1 + 0.09)^2 / (1 + 0.16)^2 = $6.2972
3. Year 3: $7.63 * (1 + 0.05) / (1 + 0.16)^3 = $5.5451
4. Year 4: $8.01 * (1 + 0.05)^2 / (1 + 0.16)^4 = $5.0832
5. Then, calculate the present value of the stock at the end of year 4, when the growth rate stabilizes at 3%: Terminal value at the end of Year 4 = Dividend at Year 5 / (Required rate of return - Constant growth rate)
   Terminal value at the end of Year 4 = $8.41 * (1 + 0.03) / (0.16 - 0.03) = $63.1043
   Present value of terminal value = $63.1043 / (1 + 0.16)^4 = $35.6256
6. Sum all the present values:
   Total value of stock = $6.6379 + $6.2972 + $5.5451 + $5.0832 + $35.6256 = $59.1890