Question

A company has been growing at a rate of 30.0% per year in recent years. This same nonconstant growth rate is expected to last for another 5 years. If D0 = $2.33, rs = 14.0%, and gL (long-term constant growth after year 5) = 4.0%, then what is this company's stock worth today (P0)?

Answer 1

To calculate the stock's worth today (P0), we can use the dividend discount model (DDM). Firstly, we need to calculate the present value (PV) of the dividends expected to be received during the 5-year nonconstant growth phase. After that, we calculate the PV for the perpetual growth phase and sum the two PVs to find P0.

Step-by-step explanation:

To calculate the stock's worth today (P0), we can use the dividend discount model (DDM).

Since the company's growth rate is nonconstant in the first 5 years, we need to calculate the present value (PV) of the dividends expected to be received during that period. We can use the formula: PV = D1/(1+rs) + D2/(1+rs)² + ... + D5/(1+rs)⁵, where D1, D2, ..., D5 represent the expected dividends for each year and rs is the required rate of return or discount rate.

After the 5 years, the company's constant growth rate starts, and we can use the formula to calculate the PV for the perpetual growth phase: PV = D6/(rs - gL), where D6 is the dividend expected at year 6 and gL is the long-term constant growth rate.

Finally, we can sum the PVs of the first 5 years and the perpetual growth phase to find the stock's worth today (P0).