Apocalyptica Corporation is expected to pay the following dividends over the nex

Question

Apocalyptica Corporation is expected to pay the following dividends over the next four years: $6.80, $17.80, $22.80, and $4.60. Afterwards, the company pledges to maintain a constant 5.75 percent growth rate in dividends, forever.

If the required return on the stock is 8 percent, what is the current share price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Apocalyptica Corporation is expected to pay the following dividends over the next four years: $6.80, $17.80, $22.80, and $4.60. Afterwards, the company pledges to maintain a constant 5.75 percent growth rate in dividends, forever.

Explanation / Answer

The two stage model can be used to value companies where the first stage has an unstable initial growth rate and there is a stable growth in the second stage which lasts forever. The first stage may have a positive, negative, or a volatile growth rate and will last for a finite period while the second stage is assumed to have a stable growth rate for the rest of the life of the company. In this model, it is assumed that the dividend paid by a company also grows in the exact way i.e. in two such stages.

In the problem , the dividend for the next four years are given. Lets compute the dividend for 5th Year.

Dividend for 5th year = $ 4.60 * Growth Rate

= $ 4.60* 1.0575

= $ 4.86

Assuming this as the constant dividend for the rest of the company’ life of the company, we arrive at the present values as follows:

P0 = D / (i – g)

Where, P0 = Value of the stock / equity

D = Per-Share dividend paid by the company at the end of each year

i = Discount rate, which is the required rate of return* which an investor wants for the risk associated with the investment in equity as against investment in a risk-free security.

g = Growth rate

*One of the most commonly used ways of calculating required rate of return is by using the Capital Asset Pricing (CAPM) model.

Now using the formula for calculating value of the firm, we can arrive at the present value at the end of 4th year for all future cash flows as follows:

Value    = $ 4.86 / (8% – 5.75%)

= $ 216.20

Table Showing Present Values

$3.38

Present value calculations in the above table are arrived at as follows:

$ 6.3 = $ 6.80 / (1 + 8%) 1

$ 15.26 = $ 17.8 / (1 + 8%) 2

$ 18.10 = $ 22.8/ (1 +8%) 3

$ 3.38= $ 4.60/ (1 + 8%) 4

$ 158.91= $ 216.20(1 + 8%) 4

The sum of all the present values will be the value of the current share price which comes to $201.95

Tenor Cash Flow Discount Rate Present Value 1 $6.8 8% $6.30 2 $17.8 8% $15.26 3 $22.8 8% $18.10 4 $4.60 8%

$3.38

4 $216.20 8% $158.91 Total Present Value $201.95

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