nonconstant dividends
posted by Kurt on .
I have no idea where to begin with this one !
Nonconstant Dividends
Hetfield and Ulrich, Inc., has an odd dividend policy. The company has just paid a dividend of $12 per share and has announced that it will increase the dividend by $7 per share for each of the next 5 years, and then never pay another dividend. If you require a 14 percent return on the company's stock, you will pay $______ per share today?

19 + 26 + 33 + 40 + 47 = 165
165/5 = 33 average yearly dividend
0.14x = 33
x = 235.71 
Ms. Sue, I put in the answer and it says it is wrong. I looked over your work and it looks right... im wondering if maybe multiply instead of divide or something, im trying different ways to alter the answer. thanks for the help.

i figured it out... you have to ^1, ^2, ^3^4^5 for each of the years o the rate of return for each one! thanks

Let's try's Ms Sue's suggestion:
If the dividends accumulate without interest, we have after 5 years,
sum of dividends
= 19 + 26 + 33 + 40 + 47
= 165
This amount should equal the purchase price, P, paid and compounded over 5 years. Thus:
P*1.14*5 = 165
P=$85.70
If the dividends also accumulate at 14% (unlikely?), then
future value of dividends
=19*1.14^4+26*1.14^3+33*1.14^2+40*1.14^1+47*1.14^0
=206.097187
P*1.14*5 = 206.097187
P=$107.04