# Share repurchases & per-share IV

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"A repurchase of, say, 2% of a company's shares at a 25% discount from per-share intrinsic value produces only a ½% gain in that value at most -- and even less if the funds could alternatively have been deployed in value-building moves." - WEB

It appears that Buffett's formula (I could definitely be wrong) is: % of shares outstanding repurchased x % discount from per-share value.

How do we calculate the change in per-share IV due to share repurchases?

Company IV of 20. 5 shares outstanding. Per-share value is 4. Company repurchases 1 share at a 50% discount. What is the change in per-share intrinsic value? What is the change in Company IV? Show your workings!

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Seems like in your example the new company IV would be 18.  Shares outstanding would then be 4, and IV/share would be 4.5 for a 12.5% increase in IV/share - which is consistent with the math in your Buffett example.  Seems like just yesterday that we were all doing this math with AIG...

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In my example 1/5 of shares outstanding were repurchased (20%) x 50% discount from per-share value

.2 x .5 = .1

The "Buffett formula" says 10% and your math says 12.5%, no?

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In my example 1/5 of shares outstanding were repurchased (20%) x 50% discount from per-share value

.2 x .5 = .1

The "Buffett formula" says 10% and your math says 12.5%, no?

It might be best not to impute arbitrary formulas to Buffett. :-)

Using globalfinancepartners' math on Buffett's example shows an IV increase of about .51%, I believe. Buffett probably just approximated this to 1/2 percent.

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In my example 1/5 of shares outstanding were repurchased (20%) x 50% discount from per-share value

.2 x .5 = .1

The "Buffett formula" says 10% and your math says 12.5%, no?

Yes, I guess my math was different than your formula.  I'll stick with figuring it out the easy way - count whats left and divide by the new share count.  IV is such an abstract and subjective concept that close enough is close enough in my book.

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It might be best not to impute arbitrary formulas to Buffett. :-)

Agreed- and I think I got it wrong on my guess.

I think Global's math is correct.

Thanks

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In my example 1/5 of shares outstanding were repurchased (20%) x 50% discount from per-share value

.2 x .5 = .1

The "Buffett formula" says 10% and your math says 12.5%, no?

It might be best not to impute arbitrary formulas to Buffett. :-)

Using globalfinancepartners' math on Buffett's example shows an IV increase of about .51%, I believe. Buffett probably just approximated this to 1/2 percent.

"Approximately right is better than precisely wrong." -- W.E.B.

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If you purchase 2% of a company's shares outstanding at fair value there is no change in IV because you paid what the shares were worth.

If the shares were repurchased at a 25% discount that would add 1/2% to the total IV [.02 (the # of shares retired) * .25 (the discount to IV) = .005 or 1/2%].

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If the shares were repurchased at a 25% discount that would add 1/2% to the total IV [.02 (the # of shares retired) * .25 (the discount to IV) = .005 or 1/2%].

This is a formula that I was merely guessing Buffett used. I wasn't correct. The math happened to work out in that example, but if you check it for other examples it won't work. I'll illustrate:

Company IV of 20.

5 shares outstanding

Per-share value of 4

Repurchase 3 shares at 50% discount (\$2)

Company spends a total of 6.

Therefore each of the 5 shares spent 1.2. That's \$6/5 shares.

This reduces per share value by 1.2, to 2.8.

There are 5 shares outstanding with 2.8 per-share value.

Now the repurchased shares disappear and the 2 remaining shares absorb the value of the other 3 shares worth 8.4 (3 x \$2.8 )

This increases per-share value by 4.2

Per-share value is now 7 (2.8 + 4.2)

The way simpler way of doing that is saying the company IV started at 20. It spent 6 to repurchase 3 shares. So company IV went down 6, to 14. Shares outstanding went from 5 to 2. Therefore new per-share IV is 7. (\$14/2 shares). Per-share value increased 75%.

The formula you used there would say the answer is 30%, and I promise that's not the case.

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