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To estimate the value of a share of Illinois Tool Works Inc. (ITW) common stock using the discounted cash flow (DCF) model, we will follow these steps:
### 1. Calculate the Free Cash Flow (FCF)
Free Cash Flow (FCF) is calculated as net operating profit after tax (NOPAT) minus the change in net operating assets (NOA) for each forecast year.
Given data:
- NOPAT for 2019: \$1,152 million
- NOPAT for 2020: \$1,221 million
- NOPAT for 2021: \$1,294 million
- NOPAT for 2022: \$1,372 million
NOA for each year:
- 2018: \$3,785 million
- 2019: \$4,011 million
- 2020: \$4,252 million
- 2021: \$4,507 million
- 2022: \$4,778 million
- 2023: \$4,873 million
Calculating the FCF for each year:
- FCF for 2019 = NOPAT for 2019 - (NOA for 2019 - NOA for 2018) = \[tex]$1,152 million - (\$[/tex]4,011 million - \[tex]$3,785 million) = \$[/tex]1,152 million - \[tex]$226 million = \$[/tex]926 million
- FCF for 2020 = NOPAT for 2020 - (NOA for 2020 - NOA for 2019) = \[tex]$1,221 million - (\$[/tex]4,252 million - \[tex]$4,011 million) = \$[/tex]1,221 million - \[tex]$241 million = \$[/tex]980 million
- FCF for 2021 = NOPAT for 2021 - (NOA for 2021 - NOA for 2020) = \[tex]$1,294 million - (\$[/tex]4,507 million - \[tex]$4,252 million) = \$[/tex]1,294 million - \[tex]$255 million = \$[/tex]1,039 million
- FCF for 2022 = NOPAT for 2022 - (NOA for 2022 - NOA for 2021) = \[tex]$1,372 million - (\$[/tex]4,778 million - \[tex]$4,507 million) = \$[/tex]1,372 million - \[tex]$271 million = \$[/tex]1,101 million
Thus, the FCF values are:
- 2019: \$926 million
- 2020: \$980 million
- 2021: \$1,039 million
- 2022: \$1,101 million
### 2. Calculate the Terminal Value (TV)
The Terminal Value is the value of the firm at the end of the forecast period assuming a stable growth rate indefinitely.
Using the free cash flow for 2022 and the terminal growth rate:
- Terminal growth rate = 2% (0.02)
- Discount rate (WACC) = 7.35% (0.0735)
Terminal Value (TV) = FCF for 2022 * (1 + growth rate) / (discount rate - growth rate)
[tex]\[ TV = 1,101 \times \frac{1 + 0.02}{0.0735 - 0.02} = 1,101 \times \frac{1.02}{0.0535} \approx 19503.93 \text{ million} \][/tex]
### 3. Discount the FCF and Terminal Value to Present Value (PV)
Using the discount rate:
Discounted FCF:
[tex]\[ PV_{FCF 2019} = \frac{926}{(1 + 0.0735)^1} = 926 / 1.0735 \approx 862.91 \text{ million} \][/tex]
[tex]\[ PV_{FCF 2020} = \frac{980}{(1 + 0.0735)^2} = 980 / 1.1514 \approx 851.13 \text{ million} \][/tex]
[tex]\[ PV_{FCF 2021} = \frac{1,039}{(1 + 0.0735)^3} = 1,039 / 1.2347 \approx 841.62 \text{ million} \][/tex]
[tex]\[ PV_{FCF 2022} = \frac{1,101}{(1 + 0.0735)^4} = 1,101 / 1.324 \approx 832.08 \text{ million} \][/tex]
Discounted Terminal Value:
[tex]\[ PV_{Terminal Value} = \frac{19503.93}{(1 + 0.0735)^4} = 19503.93 / 1.324 \approx 14726.14 \text{ million} \][/tex]
### 4. Calculate the Total Enterprise Value (EV)
Combining the present values of free cash flows and the discounted terminal value:
[tex]\[ EV = PV_{FCF 2019} + PV_{FCF 2020} + PV_{FCF 2021} + PV_{FCF 2022} + PV_{Terminal Value} \][/tex]
[tex]\[ EV \approx 862.91 + 851.13 + 841.62 + 832.08 + 14726.14 \approx 18113.88 \text{ million} \][/tex]
### 5. Determine the Equity Value
Equity Value = Enterprise Value (EV) - Net Non-operating Obligations (NNO)
[tex]\[ Equity Value = 18113.88 - 2482 = 15631.88 \text{ million} \][/tex]
### 6. Calculate the Value Per Share
[tex]\[ Value Per Share = \frac{Equity Value}{Common Shares Outstanding} = \frac{15631.88}{131} \approx 119.31 \][/tex]
Thus, the estimated value of a share of ITW's common stock as of December 31, 2018, is approximately [tex]\(\$119.31\)[/tex].
### 1. Calculate the Free Cash Flow (FCF)
Free Cash Flow (FCF) is calculated as net operating profit after tax (NOPAT) minus the change in net operating assets (NOA) for each forecast year.
Given data:
- NOPAT for 2019: \$1,152 million
- NOPAT for 2020: \$1,221 million
- NOPAT for 2021: \$1,294 million
- NOPAT for 2022: \$1,372 million
NOA for each year:
- 2018: \$3,785 million
- 2019: \$4,011 million
- 2020: \$4,252 million
- 2021: \$4,507 million
- 2022: \$4,778 million
- 2023: \$4,873 million
Calculating the FCF for each year:
- FCF for 2019 = NOPAT for 2019 - (NOA for 2019 - NOA for 2018) = \[tex]$1,152 million - (\$[/tex]4,011 million - \[tex]$3,785 million) = \$[/tex]1,152 million - \[tex]$226 million = \$[/tex]926 million
- FCF for 2020 = NOPAT for 2020 - (NOA for 2020 - NOA for 2019) = \[tex]$1,221 million - (\$[/tex]4,252 million - \[tex]$4,011 million) = \$[/tex]1,221 million - \[tex]$241 million = \$[/tex]980 million
- FCF for 2021 = NOPAT for 2021 - (NOA for 2021 - NOA for 2020) = \[tex]$1,294 million - (\$[/tex]4,507 million - \[tex]$4,252 million) = \$[/tex]1,294 million - \[tex]$255 million = \$[/tex]1,039 million
- FCF for 2022 = NOPAT for 2022 - (NOA for 2022 - NOA for 2021) = \[tex]$1,372 million - (\$[/tex]4,778 million - \[tex]$4,507 million) = \$[/tex]1,372 million - \[tex]$271 million = \$[/tex]1,101 million
Thus, the FCF values are:
- 2019: \$926 million
- 2020: \$980 million
- 2021: \$1,039 million
- 2022: \$1,101 million
### 2. Calculate the Terminal Value (TV)
The Terminal Value is the value of the firm at the end of the forecast period assuming a stable growth rate indefinitely.
Using the free cash flow for 2022 and the terminal growth rate:
- Terminal growth rate = 2% (0.02)
- Discount rate (WACC) = 7.35% (0.0735)
Terminal Value (TV) = FCF for 2022 * (1 + growth rate) / (discount rate - growth rate)
[tex]\[ TV = 1,101 \times \frac{1 + 0.02}{0.0735 - 0.02} = 1,101 \times \frac{1.02}{0.0535} \approx 19503.93 \text{ million} \][/tex]
### 3. Discount the FCF and Terminal Value to Present Value (PV)
Using the discount rate:
Discounted FCF:
[tex]\[ PV_{FCF 2019} = \frac{926}{(1 + 0.0735)^1} = 926 / 1.0735 \approx 862.91 \text{ million} \][/tex]
[tex]\[ PV_{FCF 2020} = \frac{980}{(1 + 0.0735)^2} = 980 / 1.1514 \approx 851.13 \text{ million} \][/tex]
[tex]\[ PV_{FCF 2021} = \frac{1,039}{(1 + 0.0735)^3} = 1,039 / 1.2347 \approx 841.62 \text{ million} \][/tex]
[tex]\[ PV_{FCF 2022} = \frac{1,101}{(1 + 0.0735)^4} = 1,101 / 1.324 \approx 832.08 \text{ million} \][/tex]
Discounted Terminal Value:
[tex]\[ PV_{Terminal Value} = \frac{19503.93}{(1 + 0.0735)^4} = 19503.93 / 1.324 \approx 14726.14 \text{ million} \][/tex]
### 4. Calculate the Total Enterprise Value (EV)
Combining the present values of free cash flows and the discounted terminal value:
[tex]\[ EV = PV_{FCF 2019} + PV_{FCF 2020} + PV_{FCF 2021} + PV_{FCF 2022} + PV_{Terminal Value} \][/tex]
[tex]\[ EV \approx 862.91 + 851.13 + 841.62 + 832.08 + 14726.14 \approx 18113.88 \text{ million} \][/tex]
### 5. Determine the Equity Value
Equity Value = Enterprise Value (EV) - Net Non-operating Obligations (NNO)
[tex]\[ Equity Value = 18113.88 - 2482 = 15631.88 \text{ million} \][/tex]
### 6. Calculate the Value Per Share
[tex]\[ Value Per Share = \frac{Equity Value}{Common Shares Outstanding} = \frac{15631.88}{131} \approx 119.31 \][/tex]
Thus, the estimated value of a share of ITW's common stock as of December 31, 2018, is approximately [tex]\(\$119.31\)[/tex].
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