Final answer:
To estimate Alpha Corp's true value, the question requires using a two-stage dividend discount model (DDM) factoring in different dividend growth rates for the initial high-growth phase and the subsequent constant growth phase, given the last dividend and the required rate of return.
Step-by-step explanation:
The student is asking how to estimate the true value of Alpha Corp given a changing dividend growth scenario and a required rate of return. To perform this valuation, we use a two-stage dividend discount model (DDM). Calculating the present value of dividends during the high-growth phase (first five years) and the subsequent lower, constant growth phase from year six onward helps us determine the company's estimated true value. The last known dividend (D0) is $4, growth rate for the first 5 years is 30%, stable growth rate from year 6 onwards is 8%, and the required rate of return is 11.4%.
The calculation is a two-part process. For the first 5 years, we calculate the dividends by growing $4 by 30% each year and discounting each of those dividends back to the present using the formula D1 / (1+r)^1 + D2 / (1+r)^2 + ... + D5 / (1+r)^5. For the second stage, we need to find the value at the end of year 5 of all dividends expected from year 6 onwards. This is done using the formula P5 = D6 / (r - g), where D6 is the expected dividend in year 6 (which is the year 5 dividend grown by 8%), r is the required rate of return, and g is the constant growth rate from year 6 onwards. We then discount this price back to present value. Adding the two present values together, we get the estimated true value of Alpha Corp.
This calculation requires an understanding of financial theories, notably the dividend discount model, and skills in algebra and calculator use. The student is likely in a finance program in college where such valuation techniques are taught.