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Gere Furniture forecasts a free cash flow of [tex]$\$[/tex] 40[tex]$ million in Year 3, i.e., at $[/tex]t=3[tex]$, and it expects FCF to grow at a constant rate of $[/tex]5 \%[tex]$ thereafter. If the weighted average cost of capital is $[/tex]10 \%[tex]$ and the cost of equity is $[/tex]15 \%[tex]$, what is the horizon value, in millions, at $[/tex]t=3[tex]$?

1) $[/tex]\[tex]$ 840$[/tex]
2) [tex]$\$[/tex] 882[tex]$
3) $[/tex]\[tex]$ 926$[/tex]
4) [tex]$\$[/tex] 972[tex]$
5) $[/tex]\[tex]$ 1,021$[/tex]



Answer :

GinnyAnswer
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

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