Question

New Millennium Company’s stock sells at a P/E ratio of 21 times earnings. It is expected to pay dividends of $2 per share in each of the next 5 years and to generate an EPS of $5 in year 5. Using the dividends-and-earnings model and a 12% discount rate, compute the stock’s justified price.

a) $35.71
b) $41.67
c) $45.45
d) $49.38

Answer 1

The justified price of New Millennium Company’s stock is computed by finding the present value of dividends for the next five years and the present value of the price of the stock in year five, based on the P/E ratio and discounting these amounts using a 12% discount rate.

Step-by-step explanation:

To calculate the justified stock price using the dividends-and-earnings model and a 12% discount rate, we will first find the present value of the dividends expected to be paid over the next five years. In this problem, the dividends are $2 per share each year. We also need to account for the earnings in year 5, which are projected to be $5 per share. Since the stock is trading at a P/E ratio of 21, the expected price in year 5 would be 21 times the earnings, which is $105. We calculate the present value (PV) of the dividends and the PV of the expected price in year 5 by discounting them back to present value using the discount rate of 12%.

The calculation of the present value of dividends is as follows:

1. Year 1 PV = $2 / (1 + 0.12)^1
2. Year 2 PV = $2 / (1 + 0.12)^2
3. Year 3 PV = $2 / (1 + 0.12)^3
4. Year 4 PV = $2 / (1 + 0.12)^4
5. Year 5 PV = $2 / (1 + 0.12)^5

We also need to calculate the PV of the expected stock price in year 5:

Year 5 Stock Price PV = $105 / (1 + 0.12)^5

Once we have all the present value calculations done, we add them up to get the total present value. This total present value represents our justified price for the stock.