Pvgo Model

Example of the NPVGO model (1)

April 27, 2006

Consider a …rm that has EPS of $5 at the end of the …rst year, a dividend payout ratio of 30%, a can rate of 16%, and a return on carry earnings of 20%. What is the price of a share for this …rm? Dividend emersion model P = Dividend payout ratio is 30%; then Div = 0:3 $5 = $1:5 0:3 = 0:7: Div ; r g

Retention ratio = 1 - Dividend payout ratio = 1 Growth rate, g; g = hard roe Then P = NPVGO model 1.- Value of a cash-cow …rm p= retention ratio = 0:2

0:7 = 0:14

Div $1:5 = = $75 r g 0:16 0:14

EP S $5 = = $31:25 r 0:16

2.- Value of growth opportunities Time 1: investing is 70%$5 = $3:5; at 20% return

1

$3:5 +

$3:5 0:2 $3:5 0:2 $3:5 0:2 + + + ::: = 1:16 (1:16)2 (1:16)3

$3:5 +

$3:5 0:2 0:16 1:14; at

Time 2: investment is 70%$5 = $3:5 that grows at a g = 14%; that is, $3:5 20% return

$3:5

1:14 +

$3:5

1:14 1:16

0:2

+

$3:5

1:14 0:2 + ::: = (1:16)2

$3:5 +

$3:5 0:2 0:16

1:14

Time 3: investment is 70%$5 = $3:5 1:14 ; at 20% return 1:142 1:16
2

1:14 that grows at a g = 14%; that is, $3:5

$3:5 1:142 +

$3:5

0:2 $3:5 +

1:142 (1:16)2

0:2

+::: =

$3:5 +

$3:5 0:2 0:16

1:142

and so on and so forth.



If we sum all the NPV of growing opportunities discounted at time 0 we have $3:5 + $3:5 0:2 0:16 + 1:16
$3:5 0:2 0:16 1:162 $3:5 0:2 0:16 1:163

N P V GO = factoring out

$3:5 +

1:14

+

$3:5 +

1:142

+:::

$3:5 + $3:5 0:2 0:16 ; we have 1:16 N P V GO = $3:5 + $3:5 0:2 0:16 1:16 = $3:5 + $3:5 0:2 0:16 1:16 1 1
1:14 1:16

1+

1:14 1:142 + + ::: = 1:16 1:162 1:16 = 1:16 1:14

=

=

$3:5 + $3:5 0:2 0:16 1:16

$3:5 + $3:5 0:2 0:16 1:16

1:16 = 0:02

$3:5 + $3:5 0:2 0:16 = $43:75 0:02

So summing (1) and (2) we obtain P = EP S + N P V GO = $31:25 + $43:75 = $75 r

2

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