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 $$1,000m$ in revenue. The net

income is $$200m$ 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 $27\%$ 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

$\frac{P}{E}$ ratio of firms A and $B?$

$\frac{P}{E}$ 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