HYPOTHESIS: IRR OF INVESTING IN A STOCK

by KELVINYIU@YAHOO.COM on 2005-09-25 07:51:17

INTERNAL RETURN RATE OF INVESTING IN A STOCK

Normally no one talks about IRR of investing in a stock. Perhaps due to
uncertain cash flow in future. But I discover that this can be done
with certain reasonable assumptions. I am not sure if any people have
done things similar to what I am trying to do before and please comment
on my hypothesis.

This theory, or hypothesis, is based on the assumption that i) the
payout ratio and return on equity is constant ii) the company tends to
maintain a constant financial leverage (ie borrow more accordingly when
earnings retained). I expect these assumptions to hold on conglomerates
and blue chips since they have relatively stable performance and
strategy.

book(t) = average book value at year t
Payout = payout ratio
ROE = return on equity
earn(t) = per share earning at year t
div(t) = per share dividend at year t
price(t) = average share market price at year t

book(t)
= book(t-1) + ( earn(t-1) - div(t-1) )
= book(t-1) + ( earn(t-1) - Payout*earn(t-1) )
= book(t-1) + earn(t-1)*(1-Payout)
= book(t-1) + book(t-1)*ROE*(1-Payout) {let me assume no
intangible assets here}
= book(t-1) * (1 + ROE*(1-Payout) )

put a = (1 + ROE * (1-Payout))

book(t) = a * book(t-1)
book(t-1) = a * book(t-2)
{and so on...}
book(1) = a * book(0)

substituting,

book(t) = a^t * book(0) ----(#1)

div(t)
= Payout*earn(t)
= Payout*ROE*book(t) {again, let me assume no intangible assets
here}
= Payout*earn(0)*book(t)/book(0)
= Payout*earn(0)*(a^t * book(0))/book(0) {by (#1)}
= Payout*earn(0)*a^t ----(#2)



if the price of a stock is at a certain markup of the book value, so:
price(t)/book(t) = price(0)/book(0)

price(t)
= price(0) * book(t)/book(0)
= price(0) * (a^t * book(0))/book(0)
= price(0) * a^t ----(#3)



Let's find the internal return rate, i, if you purchase the share at
price(0)
price(0) = div(1)/(1+i) + div(2)/(1+i)^2 + ... + div(t)/(1+i)^t +
price(t)/(1+i)^t
price(0) = Payout*earn(0)*a/(1+i) + Payout*earn(0)*a^2/(1+i)^2 + ... +
Payout*earn(0)*a^t/(1+i)^t + (price(0)*a^t)/(1+i)^t
price(0) = Payout*earn(0)*sum[n=1 to t][(a/(1+i))^n] +
price(0)*(a/(1+i))^t
price(0) = Payout*earn(0)*(1-(a/(1+i))^t) / (a/(1+i)) +
price(0)*(a/(1+i))^t


rearranging,
1+i
= a * (1 + earn(0)*Payout/price(0))
= (1 + ROE * (1-Payout)) * (1 + earn(0)*Payout/price(0))



NOTE: the term, price(0)*(a/(1+i))^t, diminishes at t tends to infinity
and the same result is archeived.

Please comment.

Kelvin Yiu
kelvinyiu@yahoo.com
kelvinyiu@kelvinyiu.com