To determine the horizon value (also known as the terminal value) at [tex]\( t = 3 \)[/tex] for Gere Furniture, we need to apply the perpetuity growth formula. The free cash flow (FCF) at the end of Year 3 is forecasted to be [tex]$40 million, and the FCF is expected to grow at a constant rate of 5% thereafter. The weighted average cost of capital (WACC) is given as 10%.
The formula for calculating the horizon value at \( t = 3 \) is:
\[ \text{Horizon Value at } t = 3 = \frac{\text{FCF}_{3+1}}{WACC - \text{growth rate}} \]
Where:
- \(\text{FCF}_{3+1}\) is the free cash flow at \( t = 4 \)
- WACC is the weighted average cost of capital
- growth rate is the constant growth rate of the FCF
First, we need to calculate \( \text{FCF}_{3+1} \), which is the FCF for Year 4. Since the FCF is expected to grow at a constant rate of 5%, we find \( \text{FCF}_{3+1} \) by growing the FCF at \( t = 3 \) by the growth rate:
\[ \text{FCF}_{3+1} = \text{FCF}_{3} \times (1 + \text{growth rate}) \]
Plugging in the values:
\[ \text{FCF}_{3+1} = 40 \times (1 + 0.05) = 40 \times 1.05 = 42 \]
Next, we use the perpetuity growth formula to calculate the horizon value at \( t = 3 \):
\[ \text{Horizon Value at } t = 3 = \frac{42}{0.10 - 0.05} = \frac{42}{0.05} = 840 \]
Therefore, the horizon value at \( t = 3 \) is $[/tex]840 million.
The correct answer is:
1) $840
