To calculate the intrinsic value of ABC Corp using the two-stage Dividend Discount Model (DDM), we will first project the dividends over the two growth stages: the high growth stage of 8% and the stable growth stage of 4%.
Step 1: Calculate the expected dividends for the high growth phase (Years 1-5)
- Dividend for Year 1 (D1): R6.00 (as given)
- Dividend for Year 2 (D2): D1 × (1 + g) = R6.00 × (1 + 0.08) = R6.48
- Dividend for Year 3 (D3): D2 × (1 + g) = R6.48 × (1 + 0.08) = R7.00
- Dividend for Year 4 (D4): D3 × (1 + g) = R7.00 × (1 + 0.08) = R7.56
- Dividend for Year 5 (D5): D4 × (1 + g) = R7.56 × (1 + 0.08) = R8.15
Dividends for the first five years:
- D1 = R6.00
- D2 = R6.48
- D3 = R7.00
- D4 = R7.56
- D5 = R8.15
Step 2: Calculate the present value of dividends during the high growth phase (Years 1-5)
We will discount each dividend back to present value using the required rate of return of 12%:
\[ PV(D1) = \frac{6.00}{(1 + 0.12)^1} = \frac{6.00}{1.12} \approx 5.36 \]
\[ PV(D2) = \frac{6.48}{(1 + 0.12)^2} = \frac{6.48}{1.2544} \approx 5.17 \]
\[ PV(D3) = \frac{7.00}{(1 + 0.12)^3} = \frac{7.00}{1.404928} \approx 4.98 \]
\[ PV(D4) = \frac{7.56}{(1 + 0.12)^4} = \frac{7.56}{1.57351936} \approx 4.80 \]
\[ PV(D5) = \frac{8.15}{(1 + 0.12)^5} = \frac{8.15}{1.7623416} \approx 4.63 \]
Total present value of dividends for Years 1-5: \[ PV = 5.36 + 5.17 + 4.98 + 4.80 + 4.63 \approx 24.94 \]
Step 3: Calculate the present value of dividends during the stable growth phase (Year 6 onwards)
To find the present value of all future dividends during the stable growth phase, we first need to calculate the dividend for Year 6, which will grow at 4% perpetually.
\[ D6 = D5 \times (1 + g_{stable}) = 8.15 \times (1 + 0.04) = 8.15 \times 1.04 = R8.49 \]
The present value of dividends starting from Year 6 can be calculated using the Gordon Growth Model:
\[ PV(D6) = \frac{D6}{r - g_{stable}} = \frac{8.49}{0.12 - 0.04} = \frac{8.49}{0.08} \approx 106.13 \]
Since this amount is as of Year 5, we need to discount it back to the present value:
\[ PV(D6) = \frac{106.13}{(1 + 0.12)^5} = \frac{106.13}{1.7623416} \approx 60.19 \]
Step 4: Calculate the total intrinsic value of the stock
Add the present value of the high-growth phase and the present value of the stable growth phase:
\[ Total\ PV \approx 24.94 + 60.19 = 85.13 \]
Step 5: Compare the intrinsic value with the current market price
The calculated intrinsic value of ABC Corp using the two-stage DDM is approximately R85.13. The current market price of the shares is R75.00.
Conclusion:
Since the intrinsic value (R85.13) is greater than the current market price (R75.00), ABC Corp shares can be considered undervalued. This suggests a potential buying opportunity for investors, as the stock is trading below its estimated intrinsic value.
Justification: \[ \text{Intrinsic Value} = R85.13 > \text{Market Price} = R75.00 \] This indicates that the shares offer a value premium that could lead to price appreciation, making it an attractive investment option.