Problem 1. [20 points]

We are going to explore the difference 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 $100m for both firms. Assume that management is able to maintain a constant profit margin of 10%.

Firm A is capable of achieving 5% revenue growth annually by investing 25% of their net income. Firm B is capable of achieving 5% revenue growth annually by investing 50% of their net income.

Assume that this difference persists into the future.

1. Find the value of firms A and B. Use a discount rate of 10% for both firms.

Note: This value is the sum of the value of assets already in place plus the present value of future growth opportunities.

2. The forward P/E ratio of a company is the price of a share divided by next years earnings per share, or its value divided by next years earnings. What is the forward P/E ratio of firms A and B?
3. Comment on your result. Why is the forward P/E ratio higher for firm A? Or said differently: Why would shares of firm A be more expensive?