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

To calculate the price per share today, we need to compute the present value of all the future dividend payments.

Here's how we can approach this problem step-by-step:

1. Determine the future dividend payments: The company will increase the dividend by $7 per share for each of the next 5 years and then stop paying dividends. So, the future dividend payments would be $12, $19 ($12 + $7), $26 ($19 + $7), $33 ($26 + $7), and $40 ($33 + $7).
Year 1: $12
Year 2: $12 + $7 = $19
Year 3: $19 + $7 = $26
Year 4: $26 + $7 = $33
Year 5: $33 + $7 = $40

2. Determine the present value of these future cash flows: To calculate the present value, we need the discount rate, which in this case is 14 percent. We'll use this rate to discount each dividend payment according to the respective year.

Using the formula for present value of a future cash flow:
PV = CF / (1+r)^n
where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods.

Year 1: PV1 = $12 / (1+0.14)^1
Year 2: PV2 = $19 / (1+0.14)^2
Year 3: PV3 = $26 / (1+0.14)^3
Year 4: PV4 = $33 / (1+0.14)^4
Year 5: PV5 = $40 / (1+0.14)^5

3. Sum up the present values: Add all the present values calculated in step 2 to arrive at the total present value of all the future dividend payments.

Total PV = PV1 + PV2 + PV3 + PV4 + PV5

4. Calculate the price per share today: The price per share today is equal to the total present value of all the future dividend payments.

Price per share today = Total PV

Now, you can plug in the values into the equations and solve for the price per share today.