Justified leading P/E from price to sales.....

[BaseballRedhawks]

Firm has a justified price to sales ratio of 2.0 times, a net profit margin of 5%, and a long-term growth rate of 4%. The justified leading P/E (based on gordon growth model) is closed to:
Can someone please help with this question?
THANKS!

 

[S2000magician]

If the net profit margin is 5%, then
E0/S0 = 5%.
If P/S is 2.0, then P/E is
P0/E0 = P0/S0 × S0/E0
= P0/S0 ÷ E0/S0
= 2.0 ÷ 0.05
= 40.0.

 

[Would You Look]

S2000magician wrote:
If the net profit margin is 5%, then
E0/S0 = 5%.
If P/S is 2.0, then P/E is
P0/E0 = P0/S0 × S0/E0
= P0/S0 ÷ E0/S0
= 2.0 ÷ 0.05
= 40.0.

Wouldn’t E0 be used for the justified trailing P/E? Hence, should the Justified Leading P/E be 40 ÷ 1.04 = 38.46… alternatively = 2.0 ÷ (.05*1.04) = 38.46. Or, have I forgot this section already (which is most likely the case!).

 

[S2000magician]

Yes.
I was trying to get from P/S to P/E. You may still have to adjust for E1 vs. E0. I don’t know whether the P/S ratio used E0 or E1.

 

[Wjf9838]

38.46 is correct. Keep in mind that P/S ratio = (Profit Margin) X (Trailing P/E).
Therefor you will need to convert a leading P/E to a trailing P/E. To do this, once you get you’re leading P/E of 40 you need to pull the (1+g) out of the leading P/E numerator by multiplying both sides of your equation by [1/(1+g)]. (Or dividing by 1.04 like you did, I just prefer to use reciprocals because it makes canceling out more intuitive).
Hope this helps!