give answer in 2 step with explanation at the end of each step and final answer at the end:12. You ar asked value ane share of Orion Corp. using he Abnormal Eaings Growth (AEG) model. Forecasts or sam

Question

give answer in 2 step with explanation at the end of each step and final answer at the end:12. You ar asked value ane share of Orion Corp. using he Abnormal Eaings Growth (AEG) model. Forecasts or samings
per share (EPS) and dividends per share (DPS) are provided below.
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VIPSolutions · Accepted Answer

## Step 1: Calculate the Required Rate of Return (Cost of Equity)

We use the Capital Asset Pricing Model (CAPM) formula:

$$
\text{Cost of Equity} = r_e = \text{Risk-free rate} + \beta \times \text{Market risk premium}
$$

Plug in the values:
- Risk-free rate = 2%
- Market risk premium = 5%
- Beta = 1.2

$$
r_e = 2\% + 1.2 \times 5\% = 2\% + 6\% = 8\%
$$

**Explanation:**  
This 8% is the required rate of return for Orion Corp's equity holders, which we will use to discount future cash flows.

---

## Step 2: Value the Share Using the Abnormal Earnings Growth (AEG) Model

The AEG model values a stock as:

$$
P_ = \text{Book Value}_ + \sum_{t=1}^{\infty} \frac{\text{Abnormal Earnings Growth}_t}{(1 + r_e)^t}
$$

**Abnormal Earnings Growth (AEG)** for year $t$:
$$
\text{AEG}_t = ( \text{EPS}_t - \text{EPS}_{t-1} ) - r_e \times ( \text{Book Value}_{t-1} )
$$

However, since we do not have Book Value directly, but we have DPS and EPS, we can use the following shortcut for a two-stage AEG model (assuming clean surplus accounting and that Book Value increases by Retained Earnings):

Let's compute Book Value at end-2025 ($BV_{2025}$), assuming we're at the end of 2025/now:

- Assume Book Value at end-2025 is $BV_$.
- $BV_{2026} = BV_ + (EPS_{2026} - DPS_{2026}) = BV_ + (6.00 - 2.00) = BV_ + 4.00$
- $BV_{2027} = BV_{2026} + (EPS_{2027} - DPS_{2027}) = BV_{2026} + (7.00 - 2.20) = BV_{2026} + 4.80$

Let’s denote $BV_$ as $B$.  
Now, calculate **Abnormal Earnings Growth** for both years:

### For 2026:
$$
\text{AEG}_{2026} = (EPS_{2026} - EPS_{2025}) - r_e \times BV_
$$
But we do not know $EPS_{2025}$, so assume $EPS_{2025} = EPS_{2026}$ for a conservative estimate, or that the AEG for 2026 is all due to the forecasted jump.

### For 2027:
$$
\text{AEG}_{2027} = (EPS_{2027} - EPS_{2026}) - r_e \times (BV_ + 4.00)
$$

#### **Terminal AEG after 2027:**
Grows at 4% per year.

#### **Present Value of Terminal AEG:**
$$
\text{PV of Terminal AEG} = \frac{\text{AEG}_{2028}}{r_e - g} \cdot \frac{1}{(1 + r_e)^2}
$$
where $g = 4\%$.

---

### **Final Answer:**

**To proceed further, we need the Book Value per share at end-2025.** If not given, we must state the answer in terms of $BV_$:

$$
P_ = BV_ + \frac{\text{AEG}_{2026}}{1.08} + \frac{\text{AEG}_{2027}}{(1.08)^2} + \frac{\text{PV of Terminal AEG}}{(1.08)^2}
$$

- $BV_ = $ Book Value per share at end-2025 (assumed known or must be given)
- The rest is as above.

**If Book Value is provided, plug in values to compute the final price. Otherwise, this is the final structured answer.**

---

**Summary of Steps and Answers:**

1. **Calculated required rate of return:** 8%
2. **Set up AEG model using EPS, DPS, and unknown Book Value ($BV_$), giving the final formula for share price.**

**Final Answer:**  
$$
P_ = BV_ + \frac{\text{AEG}_{2026}}{1.08} + \frac{\text{AEG}_{2027}}{(1.08)^2} + \frac{\text{PV of Terminal AEG}}{(1.08)^2}
$$
where $BV_$ is the book value per share at end-2025. Without this, we cannot compute a numeric price.

VIPSolutions · Answer

# Step 1: Calculate the Required Rate of Return (Cost of Equity)

We use the Capital Asset Pricing Model (CAPM) formula to find the cost of equity:

$$
r_e = \text{Risk-free rate} + \beta \times \text{Market risk premium}
$$

### Given Values:
- **Risk-free rate:** 2%
- **Market risk premium:** 5%
- **Beta:** 1.2

### Calculation:
$$
r_e = 2\% + 1.2 \times 5\% = 2\% + 6\% = 8\%
$$

**Explanation:**  
The calculated cost of equity is 8%. This percentage represents the return investors expect for the risk of holding Orion Corp's equity, which will be used to discount future cash flows.

---

# Step 2: Value the Share Using the Abnormal Earnings Growth (AEG) Model

The AEG model values a stock as follows:

$$
P = \text{Book Value} + \sum_{t=1}^{\infty} \frac{\text{Abnormal Earnings Growth}_t}{(1 + r_e)^t}
$$

### Abnormal Earnings Growth (AEG) Calculation:

### For 2026:
- **EPS for 2026:** 6.00
- **DPS for 2026:** 2.00

Assuming $BV_{2025}$ is unknown, we denote it as $B$.

$$
\text{AEG}_{2026} = (EPS_{2026} - EPS_{2025}) - r_e \times BV_{2025}
$$
Assuming $EPS_{2025} = 6.00$ for a conservative estimate:

$$
\text{AEG}_{2026} = (6.00 - 6.00) - 0.08 \times B = -0.08B
$$

### For 2027:
- **EPS for 2027:** 7.00
- **DPS for 2027:** 2.20

$$
\text{AEG}_{2027} = (EPS_{2027} - EPS_{2026}) - r_e \times (B + 4.00)
$$

Calculating $AEG_{2027}$:

$$
\text{AEG}_{2027} = (7.00 - 6.00) - 0.08 \times (B + 4.00) = 1.00 - 0.08B - 0.32 = 0.68 - 0.08B
$$

### Terminal AEG after 2027:
Assuming it grows at 4% per year.

### Present Value of Terminal AEG:
$$
\text{PV of Terminal AEG} = \frac{\text{AEG}_{2028}}{r_e - g} \cdot \frac{1}{(1 + r_e)^2}
$$
Where $g = 4\%$.

---

### Final Share Price Formula:
$$
P = B + \frac{-0.08B}{1.08} + \frac{0.68 - 0.08B}{(1.08)^2} + \frac{\text{PV of Terminal AEG}}{(1.08)^2}
$$

### Summary of Results:
1. **Calculated required rate of return:** 8%
2. **Formulated share price equation based on AEG and assumed Book Value ($B$).**

**Final Answer:**
$$
P = B + \frac{-0.08B}{1.08} + \frac{0.68 - 0.08B}{(1.08)^2} + \frac{\text{PV of Terminal AEG}}{(1.08)^2}
$$
This requires the Book Value at end-2025 to compute a numeric price.

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