Question

Math

Posted 2 months ago

```
magine that your firm has an expected FCF of $10M next year. You also expect that the FCFs
will grow at a constant rate of 5% per year indefinitely. Your firm’s capital structure is half equity
and half debt while the cost of equity and cost of debt are 14% and 6%, respectively. If the
corporate tax rate is 20%, what is the PV (Interest Tax Shield)?
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 1

First, we need to calculate the firm's Weighted Average Cost of Capital (WACC). The formula for WACC is given by:
$\text{WACC} = \left( \frac{E}{V} \times r_e \right) + \left( \frac{D}{V} \times r_d \times (1 - T_c) \right)$
where $E$ is the market value of equity, $D$ is the market value of debt, $V$ is the total value ( $E + D$ ), $r_e$ is the cost of equity, $r_d$ is the cost of debt, and $T_c$ is the corporate tax rate

step 2

Given that the firm's capital structure is half equity and half debt, we have:
$\frac{E}{V} = \frac{1}{2} \quad \text{and} \quad \frac{D}{V} = \frac{1}{2}$
The cost of equity $r_e$ is 14%, the cost of debt $r_d$ is 6%, and the corporate tax rate $T_c$ is 20%

step 3

Substituting these values into the WACC formula, we get:
$\text{WACC} = \left( \frac{1}{2} \times 0.14 \right) + \left( \frac{1}{2} \times 0.06 \times (1 - 0.20) \right)$
$\text{WACC} = 0.07 + 0.024 = 0.094 \text{ or } 9.4\%$

step 4

Next, we calculate the Present Value (PV) of the Interest Tax Shield. The formula for the PV of the Interest Tax Shield is:
$\text{PV (Interest Tax Shield)} = \frac{T_c \times D \times r_d}{r_d}$
Since $D$ is half of the firm's value and the firm's value is not given, we can simplify the formula to:
$\text{PV (Interest Tax Shield)} = T_c \times D$
Given $T_c = 0.20$ and $D = \frac{1}{2} \times \text{Firm's Value}$, we get:
$\text{PV (Interest Tax Shield)} = 0.20 \times \frac{1}{2} \times \text{Firm's Value}$
$\text{PV (Interest Tax Shield)} = 0.10 \times \text{Firm's Value}$

step 5

Since the firm's value is not explicitly given, we can express the PV of the Interest Tax Shield as 10% of the firm's value

Answer

The PV (Interest Tax Shield) is 10% of the firm's value.

Key Concept

Present Value of Interest Tax Shield

Explanation

The PV of the Interest Tax Shield is calculated as the product of the corporate tax rate and the firm's debt. Since the firm's debt is half of its value, the PV of the Interest Tax Shield is 10% of the firm's value.

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