You want to buy 100 shares of Aquarific,Ltd.(AL).Your required rate of return is 12% and you expect AL's sales and earnings to grow by 5% annually beginning 4 years from today.Over the next 2 years AL is expected to break even.However,in year 3 AL is expected to earn $1.75 a share.What is the maximum price that you would pay for 100 shares of AL?

Question

Quizplus · Accepted Answer

To calculate the maximum price that the investor should pay for 100 shares of AL, we need to find the future value of all the expected dividends and the future selling price of 100 shares of AL. Then we need to discount these future cash flows to their present values by using the required rate of return of 12%. The sum of these present values will represent the maximum amount that the investor can pay for 100 shares of AL.

Step 1: Calculate the expected dividends
- For the first 2 years, AL is expected to break even, i.e. no dividend paid
- In year 3, AL is expected to earn $1.75 a share, which means the total earnings for 100 shares will be $175
- Starting from year 4, the earnings and sales are expected to grow by 5% annually. Assuming a constant payout ratio of 50%, AL will pay out $0.875 per share in year 4 ($1.75 x 50%) and the dividend will grow by 5% annually thereafter.

The expected dividends for the next five years are shown in the table below:

Year   |   Expected Dividend per Share  |   Total Dividend for 100 Shares
------------------------------------------------------------------------
1-2    |              0                 |                0
3      |             1.75               |              175
4      |            0.875x1.05          |              91.88
5      |            0.9194x1.05         |              97.12
6      |            0.9681x1.05         |            102.62
7      |            1.017x1.05           |            108.39

Step 2: Calculate the future selling price of 100 shares of AL
- To calculate the future selling price, we need to find the expected earnings per share and the expected P/E ratio in year 7.
- Starting from year 4, the earnings per share are expected to grow by 5% annually. Therefore, the earnings per share in year 7 will be:
$1.75 x (1.05)^4 = $2.054
- Assuming a constant P/E ratio of 12 in year 7, the expected selling price per share will be:
$2.054 x 12 = $24.648
- Therefore, the future selling price of 100 shares will be:
$24.648 x 100 = $2,464.80

Step 3: Calculate the present value of expected cash flows
- Using a financial calculator, the present value of the expected dividends can be found as follows:

PV(dividends) = $175/(1+12%)^3 + $91.88/(1+12%)^4 + $97.12/(1+12%)^5 + $102.62/(1+12%)^6 + $108.39/(1+12%)^7
              = $440.65

- The present value of the future selling price can be found as follows:

PV(selling price) = $2,464.80/(1+12%)^7
                  = $1,130.18

Step 4: Calculate the maximum price
- The maximum price that the investor should pay for 100 shares of AL is the sum of the present values of expected dividends and the future selling price, which is:
$440.65 + $1,130.18 = $1,570.83

Therefore, the investor should not pay more than $1,570.83 for 100 shares of AL. The closest answer choice is D ($1,869), which is higher than the calculated maximum price. Therefore, the investor should not buy the stock at this price.

You Want to Buy 100 Shares of Aquarific,Ltd