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Estimating Share Value Using the ROPI Model

Following are forecasted sales, NOPAT, and NOA for AT&T for 2019 through 2022:

Note: Complete the entire question in Excel and format each answer to two decimal places. Then enter the answers into the provided spaces below with two decimal places.

a. Forecast the terminal period values assuming the following terminal period growth rate:
[tex]\[
\begin{aligned}
&\text{Terminal period growth rate} \quad 2\%
\end{aligned}
\][/tex]

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline & \text{Reported} & \text{Forecast Period} & & & & \text{Terminal} \\
\hline & 2018 & 2019 & 2020 & 2021 & 2022 & \text{Period} \\
\hline \text{Sales (\[tex]$ millions)} & \$[/tex]170,756 & \[tex]$181,001 & \$[/tex]191,861 & \[tex]$203,373 & \$[/tex]215,576 & \\
\hline \text{NOPAT (\[tex]$ millions)} & 22,567 & 23,849 & 25,280 & 26,797 & 28,404 & \\
\hline \text{NOA (\$[/tex] millions)} & 398,562 & 422,205 & 447,538 & 474,391 & 502,856 & \\
\hline
\end{tabular}

b. Estimate the value of a share of AT&T common stock using the residual operating income (ROPI) model as of December 31, 2018, using the following assumptions and the information above:

\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|l|}{\text{Assumptions}} \\
\hline \text{Discount rate (WACC)} & 5.78\% & \\
\hline \text{Common shares outstanding} & 7,864.1 & \text{million} \\
\hline \text{Net nonoperating obligations (NNO)} & \[tex]$189,167 & \text{million} \\
\hline \text{Noncontrolling interest (NCI)} & \$[/tex]10,579 & \text{million} \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline & \text{Reported} & \text{Forecast Period} & & & & & \text{Terminal} \\
\hline & 2018 & 2019 & 2020 & 2021 & 2022 & \text{Period} \\
\hline \text{ROPI (NOPAT - [NOABeg} \times \text{rw]) (\[tex]$ millions)} & & & & & & & \\
\hline \text{Present value of horizon ROPI (\$[/tex] millions)} & & & & & & & \\
\hline \text{Cumulative present value of horizon ROPI (\[tex]$ millions)} & & & & & & & \\
\hline \text{Present value of terminal ROPI (\$[/tex] millions)} & & & & & & & \\
\hline \text{NOA (\[tex]$ millions)} & & & & & & & \\
\hline \text{Total firm value (\$[/tex] millions)} & & & & & & & \\
\hline \text{Less NNO (\[tex]$ millions)} & & & & & & & \\
\hline \text{Less NCI (\$[/tex] millions)} & & & & & & & \\
\hline \text{Firm equity value (\[tex]$ millions)} & & & & & & & \\
\hline \text{Shares outstanding (millions)} & & & & & & & \\
\hline \text{Stock price per share (\$[/tex])} & & & & & & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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.

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