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To address this financial valuation problem step-by-step, we need to estimate the value per share of AT&T common stock using the Residual Operating Income (ROPI) model. Here's how you can break it down:
### Step 1: Forecast Terminal Period Values
1. Calculate the terminal values for sales, NOPAT, and NOA for 2023 (one year beyond the last forecasted year of 2022) assuming a 2% terminal period growth rate:
- Sales for 2023: [tex]\( \$215,576 \times 1.02 \)[/tex]
- NOPAT for 2023: [tex]\( \$28,404 \times 1.02 \)[/tex]
- NOA for 2023: [tex]\( \$502,856 \times 1.02 \)[/tex]
### Step 2: Calculate ROPI for Each Year
2. Calculate ROPI for each forecasted year using [tex]\( ROPI_t = NOPAT_t - (NOA_{t-1} \times rw) \)[/tex] (where [tex]\( rw \)[/tex] is the discount rate):
- [tex]\( rw = 5.78\% \)[/tex]
Set up a table for calculated ROPI:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Year} & \text{NOPAT} & \text{NOA}_{\text{beg}} & \text{ROPI} \\ \hline 2019 & 23,849 & 398,562 & 23,849 - (398,562 \times 0.0578) \\ 2020 & 25,280 & 422,205 & 25,280 - (422,205 \times 0.0578) \\ 2021 & 26,797 & 447,538 & 26,797 - (447,538 \times 0.0578) \\ 2022 & 28,404 & 474,391 & 28,404 - (474,391 \times 0.0578) \\ \hline \end{array} \][/tex]
### Step 3: Present Value of ROPI
3. Discount the ROPI calculated in Step 2 to present value (as of end of 2018):
- Use the formula [tex]\( \text{PV}_{t} = \frac{\text{ROPI}_t}{(1 + rw)^t} \)[/tex].
### Step 4: Cumulative Present Value of Horizon ROPI
4. Sum the present values from Step 3 to get the cumulative present value of horizon ROPI:
### Step 5: Present Value of Terminal ROPI
5. Calculate the present value of terminal ROPI:
- [tex]\( \text{ROPI}_{\text{terminal}} = \frac{\text{NOPAT}_{\text{terminal}}}{1 + rw} \times \text{terminal growth rate} \)[/tex]
- Sum this to the total present value determined so far.
### Step 6: Calculate the Total Firm Value
6. Sum NOA and the cumulative present value of ROPI from Step 4 and 5
### Step 7: Firm's Equity Value
7. Subtract Net Nonoperating Obligations (NNO) and Noncontrolling Interest (NCI) from the Total Firm Value
- Firm Equity Value = Total Firm Value - NNO - NCI
### Step 8: Value per Share
8. Finally, divide the Firm Equity Value by the number of shares outstanding to get the stock price per share:
- Firm Equity Value = (Total Firm Value - NNO - NCI) / number of shares issued
### Filling in the Excel Table
1. Terminal Values:
- Sales for 2023: [tex]\( \$215,576 \times 1.02 \)[/tex]
- NOPAT for 2023: [tex]\( \$28,404 \times 1.02 \)[/tex]
- NOA for 2023: [tex]\( \$502,856 \times 1.02 \)[/tex]
2. ROPI and PV calculations:
3. Cumulative PV Horizon ROPI.
4. Present value of terminal ROPI (discounted)
5. Firm’s Total Value = NOA + PV of ROPI (both horizon and terminal)
6. Firm’s Equity Value
7. Value per Share = Firm’s Equity Value / Shares outstanding
### Note
Ensure you format all dollar amounts and figures to two decimal places in your Excel file. Just input the final per-share price in the provided space.
This detailed approach helps you break down the valuation problem step-by-step. The breakdown shows how each component of the formula contributes to valuing the stock. Be sure to insert the exact calculated values into the provided table spaces.
### Step 1: Forecast Terminal Period Values
1. Calculate the terminal values for sales, NOPAT, and NOA for 2023 (one year beyond the last forecasted year of 2022) assuming a 2% terminal period growth rate:
- Sales for 2023: [tex]\( \$215,576 \times 1.02 \)[/tex]
- NOPAT for 2023: [tex]\( \$28,404 \times 1.02 \)[/tex]
- NOA for 2023: [tex]\( \$502,856 \times 1.02 \)[/tex]
### Step 2: Calculate ROPI for Each Year
2. Calculate ROPI for each forecasted year using [tex]\( ROPI_t = NOPAT_t - (NOA_{t-1} \times rw) \)[/tex] (where [tex]\( rw \)[/tex] is the discount rate):
- [tex]\( rw = 5.78\% \)[/tex]
Set up a table for calculated ROPI:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Year} & \text{NOPAT} & \text{NOA}_{\text{beg}} & \text{ROPI} \\ \hline 2019 & 23,849 & 398,562 & 23,849 - (398,562 \times 0.0578) \\ 2020 & 25,280 & 422,205 & 25,280 - (422,205 \times 0.0578) \\ 2021 & 26,797 & 447,538 & 26,797 - (447,538 \times 0.0578) \\ 2022 & 28,404 & 474,391 & 28,404 - (474,391 \times 0.0578) \\ \hline \end{array} \][/tex]
### Step 3: Present Value of ROPI
3. Discount the ROPI calculated in Step 2 to present value (as of end of 2018):
- Use the formula [tex]\( \text{PV}_{t} = \frac{\text{ROPI}_t}{(1 + rw)^t} \)[/tex].
### Step 4: Cumulative Present Value of Horizon ROPI
4. Sum the present values from Step 3 to get the cumulative present value of horizon ROPI:
### Step 5: Present Value of Terminal ROPI
5. Calculate the present value of terminal ROPI:
- [tex]\( \text{ROPI}_{\text{terminal}} = \frac{\text{NOPAT}_{\text{terminal}}}{1 + rw} \times \text{terminal growth rate} \)[/tex]
- Sum this to the total present value determined so far.
### Step 6: Calculate the Total Firm Value
6. Sum NOA and the cumulative present value of ROPI from Step 4 and 5
### Step 7: Firm's Equity Value
7. Subtract Net Nonoperating Obligations (NNO) and Noncontrolling Interest (NCI) from the Total Firm Value
- Firm Equity Value = Total Firm Value - NNO - NCI
### Step 8: Value per Share
8. Finally, divide the Firm Equity Value by the number of shares outstanding to get the stock price per share:
- Firm Equity Value = (Total Firm Value - NNO - NCI) / number of shares issued
### Filling in the Excel Table
1. Terminal Values:
- Sales for 2023: [tex]\( \$215,576 \times 1.02 \)[/tex]
- NOPAT for 2023: [tex]\( \$28,404 \times 1.02 \)[/tex]
- NOA for 2023: [tex]\( \$502,856 \times 1.02 \)[/tex]
2. ROPI and PV calculations:
3. Cumulative PV Horizon ROPI.
4. Present value of terminal ROPI (discounted)
5. Firm’s Total Value = NOA + PV of ROPI (both horizon and terminal)
6. Firm’s Equity Value
7. Value per Share = Firm’s Equity Value / Shares outstanding
### Note
Ensure you format all dollar amounts and figures to two decimal places in your Excel file. Just input the final per-share price in the provided space.
This detailed approach helps you break down the valuation problem step-by-step. The breakdown shows how each component of the formula contributes to valuing the stock. Be sure to insert the exact calculated values into the provided table spaces.
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