Question

20. Assume that you plan to buy a share of ABC stock today and to hold it for 3 years. Your expectations are that you will not receive a dividend at the end of Year 1 and 2, but you will receive a dividend at the end of Year 3. In addition, you expect to sell the stock for $100 at the end of Year 3. The stock recently paid a dividend of $7. If your required rate of return on the stock is 12 percent, how much should you be willing to pay for this stock today? If the stock sells for $74 today, what would your expected rate of return from the stock be? (Assume that the company's growth rate is 5 percent)

Answer 1

Let’s call today as Year 0

The stock recently paid a dividend of $7, so D0 = $7

Further, the Company growth rate, g = 5%, so the dividends are expect to grow at growth rate of the Company.

So, expected dividend at Year 3 (3 years from now) will be : D0 *( (1+g)^3)

= $7 *( (1+0.05)^3)

= $8.10

Further, expected selling price of stock at Year 3 = $100

So, total inflows expected from the stock investment = $100 + $8.10 = $108.10

Further, we expect a 12% return on capital, so discounting this $108.10 receivable after 3 years to present time with our discount rate,

The value of stock today should be $108.10 /( (1+0.12)^3 ) = $76.95

So, I would be willing to pay $76.95 for this stock today.

If the stock sells for $74 today, the expected rate of return would be something more than 12% because with higher discount rate we would get lesser value of stock today.

Putting the values in the formula as above,

$74 = $108.10 / (1+r)^3

(1+r)^3 = 1.46

1+r = 1.1347

So, r = 0.1347 or 13.47%