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# Nautilus Inc. Message Board

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• astral_tsar astral_tsar Jan 20, 2004 9:26 AM Flag

Fair enough, though perhaps the approach I used is more "unusual" in academic circles than in practice?

What got me "riled up" is a very real content issue here. My objection w/r/t double-counting book value isn't nitpicking, it's the whole ball of wax. Growth comes from reinvestment. Here, I'll show you.

The problem shows up in examples as simple as a savings account. Lemme contrast the "B" approach to a savings account ("A").

B. Assume that I really do receive checks in the mail, with absolute certainty, beginning 1/1/04 and continuing on the first of the year forever. The payments are:
1/1/04 \$1
1/1/05 \$1.05
1/1/06 \$1.05^2 = \$1.1025
1/1/07 \$1.05^3,
1/1/08 ...and so on.

Assume a risk-free discount rate r = 6%. What's the present value of those checks?

Well, net present value turns out to be

\$1/(r-g) = \$1/(6%-5%) = \$100.

Wow. Great deal.

A. Now look deeper. Where might such checks come from? Consider a bank account that contains \$20 and pays g=5% interest on the first day of every year. I leave the interest IN the savings account and let it compound.

Here are the interest payments deposited in the account:
1/1/04: \$1
1/1/05: \$1.05
1/1/06: \$1.1025
1/1/07: ...and so on

Growth "g" is 5%. Exactly the same as the checks. I'm rich! But there's a catch: now I've assumed some real-world mechanism for *producing* the checks. So what's the net present value of leaving my money in that savings account?

Less than \$20.

Right? The account loses the race against the 6% discount rate by 1% per year. I'm losing value. If I leave it there forever under these conditions, the value is zero.

Ok, what if I want checks mailed to me? Well, the values of those checks are determined by the 5% interest rate:
1/1/04: \$1
1/1/05: \$1
1/1/06: \$1
1/1/07: ...and so on.

Present value:

\$1 / 6% = \$16.67.

Still less than \$20. I never take the principal out, remember. All I have is the checks. But now they don't grow!

So if I have total control over the savings account, how close can I get to the \$100 value of case A? \$20. I can withdraw all the money now.

C. How come?
Very simply from the ROI picture. What is the approximate present value of a \$1000 10-year treasury bond that pays 4%? The present value is \$1000! That's how they price these things!

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