We are going to explore the differences between two different companies, both from the same sector, firms A and B$.$ They differ in their reinvestment abilities. Firm A and Firm B are both financed with equity only.

At the end of their business year, both firms report $$1,000$m in revenue. The net income is $$200$m for both firms. Assume that management is able to maintain a constant net profit margin of $20\%.$

Firm A is capable of achieving $8\%$ revenue growth annually by investing $29\%$ of their net income.

Firm B is capable of achieving $8\%$ revenue growth annually by investing $40\%$ of their net income.

Assume that this difference persists into the future.

a$)$ Find the value of firms A and B$.$ Use a discount rate of $16\%$ for both firms.

Value of firm A in millions:

Value of firm B in millions:

b$)$ The forward P$/$E ratio of a company is the price of a share divided by next year$$s earnings per share, or its value divided by next year$$s earnings. What is the forward P$/$E ratio of firms A and B$?$

P$/$E ratio of firm A:

P$/$E ratio of firm B:

c$)$ Why is the forward P$/$E ratio higher for firm A$?$ Or said differently: Why would shares of firm A be more expensive?

Firm A is able to generate the same degree of growth at a

reinvestment rate. Therefore, the present value of their growth is

$.$