# Equity Topic Test #16 - Vitality Question #4

Hello,

Can anyone explain why when comparing the PVGO using a no growth versus perpetual growth, the correct answer uses EPS for the no growth level perpetuity but Dividends for the growing stream? I thought the PVGO formula was E1/r + PVGO = Value.

Im thinking this may be an error? It seems likes we’re comparing apples and oranges??

Many thanks!!

since the assumption is NO GROWTH., the company isn’t required to keep any Retained earnings(RE) .all of its earnings are assumed to be paid as dividends. so under no growth 100% of earnings are dividends.

It is an opportunity to think outside the box. This question would be a tough one during the exam. The problem is that we don’t know the value, so we have two uknowns.

You are correct that value = E1/r+PVGO. Now E1 is the same as EPS. So if you assume no growth prospects then Value=EPS/r (a perpetuity)

Given growth prospects, you can use the Gordon growth model to find value.

This way you have found two values - one without growth prospects, another one with growth. The difference is the value attributable to growth.

Bingo! Makes sense. Many thanks folks!

I would like to bump this thread and ask a similar, yet related question.

I am so confused why, in the PVGO formula, it’s E1/r instead of E0/r – E1 essentially being E0 times (1+growth rate). I could understand if the formula were E1/r, where E1 was equal to E0, but they are using a growth rate to calculate E1.

If it is a NO GROWTH firm, E0 should be equal to E1; all dividends are being paid out, hence no growth is occurring. If you look at question 8c in Reading 30 on DDM, the answer states that it’s E0, which further adds to my confusion.