Question

The current (t=0) dividend of ABC Corp is $1.00 per share. Dividends are expected to grow at 20% from t=0 to t=1, and t=1 to t=2 (today is t=0). Starting at year 2 (t=2), dividends are expected to grow at 5% indefinitely. Assume the required rate of return for the equity of ABC is 10%.

a) Calculate the intrinsic value today (t=0) of a share of ABC.
b) Calculate the intrinsic value of a share of ABC next year (i.e., at t=1).
c) Suppose you buy the stock at the price you calculated in part (a). Calculate the expected holding period return from t=0 to t=1 assuming that next year's (i.e., t = 1) price is equal to its intrinsic value.
d) Should your answer to part (c) be equal to 10%? Explain.

Answer 1

The intrinsic value of ABC Corp's stock at t=0 is approximately $24.89 per share, assuming a perpetual growth rate of dividends and the required rate of return. At t=1, this value is approximately $26.18 per share. The expected holding period return from t=0 to t=1 based on these values aligns with the required rate of return, which is 10%.

Step-by-step explanation:

To calculate the intrinsic value of a share of ABC Corp at t=0, we would use the Dividend Discount Model (DDM). This involves calculating the present value of expected future dividends. Given the growth rates and dividends information provided:

• The dividend at t=1 will be $1.00 × (1 + 20%) = $1.20.
• The dividend at t=2 will be $1.20 × (1 + 20%) = $1.44.
• Starting at t=2, the dividend will grow at a perpetual rate of 5%. So the value at t=2 is calculated using the formula for a perpetuity: Dividend at t=2 / (required rate of return - perpetual growth rate), which is $1.44 / (10% - 5%) = $28.80.

To find the present value, we discount these dividends back to today:

• PV of Dividend at t=1: $1.20 / (1+10%) = $1.09 (approximately)
• PV of Dividend at t=2 including all future dividends: $28.80 / (1+10%)^2 = $23.80 (approximately)

Adding these up gives us the intrinsic value at t=0: $1.09 + $23.80 = $24.89 (approximately).

For t=1, we simply need to calculate the PV of the $28.80 expected at t=2, since this already accounts for all future dividends: $28.80 / (1+10%) = $26.18 (approximately).

The expected holding period return from t=0 to t=1, assuming the stock price equals its intrinsic value next year, would be:

• Expected price at t=1 ($26.18) + Dividend at t=1 ($1.20) - Price at t=0 ($24.89) = $2.49.
• Holding period return = $2.49 / $24.89 = 10% (approximately).

This expected holding period return of approximately 10% is in line with the required rate of return, which is the return required by investors given the risk profile of ABC Corp.