Four Pillars Of Investing - Bernstein - DDM confusion

mgarl10024

Hi,

I'm working my way through William Bernstein's "Four Pillars of Investing" - http://www.efficientfrontier.com/t4poi/t4poi.htm - and am coming unstuck on the DDM calculations.

On pg 48, Bernstein talks about how to figure out the present value of something (the Dow in this case) which pays an initial dividend of $140, and grows at 5% per year. His table shows what happens if you apply a discount rate of 8%, and totals at $4667.67.

So, I fired up a spreadsheet and reproduced his table up to 1000 columns. My numbers match his, but my total is $5040, not $4667.67. That's quite a difference!
Acknowledging that the table is infinite, there's no a single row I can stop at that will give me his figure.

He later goes on to state how the formula
Market Value = Present Dividend/(DR - Dividend Growth Rate) is equivalent, and it does indeed give the expected $4667 as an answer.

So, what am I missing when going about the brute-force method of this calculation, and why is my result different from his?

Any help appreciated!

mgarl10024

Having played with the numbers, I'm fairly sure this is a book error.

The first column has the dividend for year one at $140, and has a discount factor of 1.00.
This suggests that the dividend is being paid at the start and so doesn't need to be discounted. This makes no sense. It should be $140 discounted by 1.08 (8%) and so $129.
The same issue continues down the table. It's like every row is one out.
The new total = $4666.67. Which is correct. Even the book's $4667.67 looks wrong.

Thanks for anyone who tried playing with the numbers too.