# Calculating the Value of a Firm with Debt and Equity

## What is the value of the firm if it issued $50 million in debt at a cost of 7% for 5 years and repurchased an equivalent amount of the equity?

## Answer:

The value of the firm would be $100,000,000.## Calculating the Value of a Firm with Debt and Equity

**In this problem, we are given the following information:**

- The corporate tax rate is 30%.
- The firm has no debt in its capital structure.
- It is valued at $100 million.
- The firm issued $50 million in debt at a cost of 7% for 5 years and repurchased an equivalent amount of the equity.

Now, let's calculate the value of the firm:

When the firm takes on debt, the value of the firm increases by the present value of the tax shield on the interest expense. The value of the tax shield is calculated as follows:

**Tax shield = Debt x Interest rate x Corporate tax rate x Discount factor**

= $50,000,000 x 0.07 x 0.3 x 3.433

= $5,411,100

The discount factor is calculated as follows:

**Discount factor = (1 - (1 + r)-t) / r**

where r = cost of debt = 7% and t = time period = 5 years

Therefore, discount factor = (1 - (1 + 0.07)-5) / 0.07 = 3.433

Using the tax shield approach, we can calculate the value of the firm with debt as follows:

**Value of firm = Value of firm without debt + Value of tax shield**

= $100,000,000 + $5,411,100

= $105,411,100

Since the firm is repurchasing an equivalent amount of equity (which is $50 million), the new value of the firm is the sum of the value of the debt and the value of the equity:

**New value of firm = Value of debt + Value of equity**

= $50,000,000 + $50,000,000

= $100,000,000

Therefore, the correct value of the firm in this scenario is $100,000,000.