Question

A firm's dividends have grown over the last several years. 7 years ago the firm paid a dividend of $2. Yesterday it paid a dividend of $3. What was the average annual growth rate of dividends for this firm?

Answer 1

Solution:
	Average annual growth rate of dividends for this firm is   5.96%
Working Notes:
	Here we use
	Average annual growth rate is the rate at which $2 is compounded to future value in 7 years to $3 , Hence we have to used concept future value of present value of deposit to get the annual rate.
	C0 = Present value = $2    the value 7 years ago
	FV=Future value of the dividend after 7 years = $3   today   dividend amount
	r=annual growth rate of dividends = r=??
	n = no. Of periods = 7 year
	Using future value formula
	FV= C0 x (1+r)^n
	3 = 2 (1+ r)^7
	(3/2) = (1+r)^7
	Taking Log on both side
	Log(3/2) = Log(1+r)^7
	Log(1.5) = Log(1+r)^7
	using relation loga^b = b x Log a
	Log(1.5) = 7 x Log(1+r)	Log(1.5) = 0.176091259
	(0.176091259/7) = Log (1+r)
	here we move log to other side and becomes anti log
	(1+r) = Antilog (0.176091259/7)	0.025155894
	(1+r) = Antilog (0.025155894)	We got from online financial calculator
	(1+r) = 1.0596340223	antilog(0.025155894) =1.0596340223
	r=1.0596340223 - 1
	r=0.0596340223
	r= 5.96340223%
	r=5.96% in two decimal
	r= 5.96340% in 5 decimal
Lets Check is our computed rate is correct.
	Using future value formula
	FV= C0 x (1+r)^n
	3 = 2 (1+ r)^7
	3 = 2 (1+5.96340%)^7
	3 = 2.9999999
	3 = 3
	Hence above computed rate is correct you uses 5 decimal or 2 decimal you will get same answer.
Please feel free to ask if anything about above solution in comment section of the question.