To determine the Year 0 value of operations for Parker & Sons, we need to follow these steps:
1. Identify Inputs:
- Free Cash Flow (FCF) for Year 1: -[tex]$50 million
- Free Cash Flow (FCF) for Year 2: $[/tex]100 million
- Weighted Average Cost of Capital (WACC): 11% or 0.11
- Growth rate after Year 2: 5% or 0.05
2. Calculate Terminal Value (TV) at the end of Year 2:
- The terminal value represents the value of all future free cash flows beyond Year 2, growing at a constant rate of 5%.
- The perpetuity formula to calculate the terminal value at the end of Year 2 is:
[tex]\[
\text{TV}_{\text{Year 2}} = \frac{\text{FCF}_{\text{Year 2}} \times (1 + \text{growth rate})}{\text{WACC} - \text{growth rate}}
\][/tex]
- Substitute the given values:
[tex]\[
\text{TV}_{\text{Year 2}} = \frac{100 \times (1 + 0.05)}{0.11 - 0.05} = \frac{100 \times 1.05}{0.06} = \frac{105}{0.06} = 1750 \text{ million dollars}
\][/tex]
3. Calculate the present value (PV) of the free cash flows and terminal value:
- Present Value of FCF for Year 1:
[tex]\[
\text{PV}_{\text{FCF for Year 1}} = \frac{\text{FCF}_{\text{Year 1}}}{(1 + \text{WACC})^1} = \frac{-50}{(1 + 0.11)^1} = \frac{-50}{1.11} \approx -45.045
\][/tex]
- Present Value of FCF for Year 2:
[tex]\[
\text{PV}_{\text{FCF for Year 2}} = \frac{\text{FCF}_{\text{Year 2}}}{(1 + \text{WACC})^2} = \frac{100}{(1 + 0.11)^2} = \frac{100}{1.11^2} = \frac{100}{1.2321} \approx 81.162
\][/tex]
- Present Value of Terminal Value at the end of Year 2:
[tex]\[
\text{PV of TV}_{\text{Year 2}} = \frac{\text{TV}_{\text{Year 2}}}{(1 + \text{WACC})^2} = \frac{1750}{(1 + 0.11)^2} = \frac{1750}{1.2321} \approx 1420.339
\][/tex]
4. Sum the present values to find the Year 0 value of operations:
- Total Present Value of Operations:
[tex]\[
\text{Value of Operations} = \text{PV of FCF for Year 1} + \text{PV of FCF for Year 2} + \text{PV of TV for Year 2}
\][/tex]
[tex]\[
= -45.045 + 81.162 + 1420.339 \approx 1456.456
\][/tex]
Thus, the Year 0 value of operations for Parker & Sons is approximately [tex]$\$[/tex] 1,456[tex]$ million. The correct option is:
1) $[/tex]1,456$
