Question

A prospective investor is evaluating the share of a company. He is considering three scenarios. Under the first scenario the company will maintain to pay its current dividend per share without any increase or decrease. Another possibility is that the dividend will grow at an annual rate of 6% in perpetuity. Yet another scenario is that the dividend will grow at a high rate of 12% for the first 3 years; a medium rate of 7% for the next 3 years and thereafter, at a constant rate of 4% perpetually. The last year's dividend per share was 3 and the current market price of the share is 80. If the investor's required rate of return is 10%, calculate the value of the share under each of the assumptions. Should the share be purchased?

Answer 1

1)

First scenario:

Present value = Annual dividend / required rate

Present value = 3 / 0.1

Present value = $30

2)

Second scenario:

Present value = D1 / required rate - growth rate

Present value = (3 * 1.06) / 0.1 - 0.06

Present value = 3.18 / 0.04

Present value = $79.5

3)

Third scenario:

Year 1 dividend = 3 * 1.12 = 3.36

Year 2 dividend = 3.36 * 1.12 = 3.7632

Year 3 dividend = 3.7632 * 1.12 = 4.21478

Year 4 dividend = 4.21478 * 1.07 = 4.50982

Year 5 dividend = 4.50982 * 1.07 = 4.82551

Year 6 dividend = 4.82551 * 1.07 = 5.16329

Year 7 dividend = 5.16329 * 1.04 = 5.36982

Value at year 6 = D7 / required rate - growth rate

Value at year 6 = 5.36982 / 0.1 - 0.04

Value at year 6 = 5.36982 / 0.06

Value at year 6 = 89.49706

Present value = 3.36 / (1 + 0.1)¹ + 3.7632 / (1 + 0.1)² + 4.21478 / (1 + 0.1)³ + 4.50982 / (1 + 0.1)⁴ + 4.82551 / (1 + 0.1)⁵ + 5.16329 / (1 + 0.1)⁶ + 89.49706 / (1 + 0.1)⁶

Present value = $68.84

Share should not be purchased as all three methods show present value to be lower than the market price. This states that share price is overvalued.