Question

Apple just paid an annual dividend of $3. Analysts expect that the company will increase dividends at a rate of 9% per year during the next three years, and then increase at a constant rate of 2.5% forever. If the discount rate of Apple is 12%, what is the price of Apple’s stock today?

Answer 1

Calculation of value during abnormal stage
Year	Calculation of dividends	Dividends	Discounting factor @12%	PV of dividends
1	$3*109%	3.27	0.892857143	2.919642857
2	$3.27*109%	3.5643	0.797193878	2.841438138
3	$3.5643*109%	3.885087	0.711780248	2.765328188
			Total	8.526409183
Calculation of value during constant stage
P3= (D3*(1+g))/(Re-g)
	(3.885087*(1+0.025))/(0.12-0.025)
	$41.91804395
PV today= $41.91804395/(1.12)^3
	$29.836435711
Value of Apple share today= $(8.526409183+29.836435711)
	$38.362844894
Price of Apple stock today (rounded of to two decimal places)= $38.36
Explaination: The value of stock today is equal to present value of all future cashflows expected from the stock discounted at the required rate of return. In the abnormal stage, the dividend was expected to grow @9% per year so we need to prepare the table to calculate the present value for 1st three years. In the constant stage, as the dividend rate was fixed @ 2.5% perpetuity so we have applied the Gordon formula. But the value so derived is at t=3 so we have pulled back to get the worth today. After both calculations, the value derived in both the stages is added to get the final value of stock today.