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# Assumption Company Z s earnings and dividends per share

Assumption: Company Zâ€™s earnings and dividends per share are expected to grown indefinitely by 5 percent a year. If next yearâ€™s dividend is \$10 and the market capitalization rate is 8 percent, what is the current stock price?

Company Z-prime is like Z in all respects save one: its growth will stop after year 4. In year 5 and afterward, it will pay out all earnings as dividends. What is Z-primeâ€™s stock price? Assume next yearâ€™s EPS is \$15.
Price = Next Year Dividend/(Market Capitalization Rate - Growth Rate)

= \$10/(0.08-0.05) = \$333.33

P0 = [D1/(1+r)1]+[D2/(1+r)2]+[D3/(1+r)3]+[D4/(1+r)4]+[D5/r]

P0 = [\$10/(1.08)]+[\$10.5/(1.17)]+[\$11.025/(1.26)]+[\$11.58/(1.36)]+[\$12.16/0.08]

= \$187.46
Customer: replied 11 years ago.
Reply to Manal's Post: Thanks for part of the answer, but I still need some clarification. Should this value be multiplied by NPV factor for year 5 (.
68060?

Also, is this a value in year 5? if so, the value of this stock today should be

9.26+9.00+8.75+8.51+ (187.46*NPV for a year 50)?

Can you clarify?

Thank you, Customer
No, see in year 5 will remain constant and would not grow. Therefore it can be treated as an Ordinary Perpetuity with a cash flow equal to D5 forever. Since we do not know the number of years the stock will pay a dividend, we calculate the present value of those cash flows using the formula Dividend divided by the Rate of Return which is (D5/R). Also, the \$9.26,\$9,...etc represent the presnt value of the dividend so no need to discount the values.

I hope this clarifies it.

Regards
Customer: replied 11 years ago.
Thank you.
Customer: replied 11 years ago.
Reply to Manal's Post: Sorry, one more question on this question :-/... you said since we do not know how the number of years the stock will pay a dividend,... etc

If there is no growth, I would think the year 5 would be the last year they paid dividends. Will this alter an answer?

Thank you, Customer
If that was the last year they are going to pay dividends, then yes, this would alter the solution because then you would divide D5 by (1.08)^5. i.e. it would be treated as the dividends in the first year where we calculate the PV of the dividend each year. Your assumption is not correct though because in the question it says "In year 5 and afterward, it will pay out all earnings as dividends". I just noticed something though, teh problem says "Assume next yearâ€™s EPS is \$15

Now EPS is growing at the same rate as dividends, therefore it is growing by 5% as well. This means that the 5th year EPS would equal \$18.23. In the first 4 years though, the dividends would remain as calculated, but in the 5th year the firm will pay all its earnings as dividends, hence the dividend per share = EPS. From this the stock price should be

P0 = [\$10/(1.08)]+[\$10.5/(1.17)]+[\$11.025/(1.26)]+[\$11.58/(1.36)]+[\$18.23/0.08]

= \$263.34

I have overlooked that part i am sorry.

Customer: replied 11 years ago.
Reply to Manal's Post: should it be 17.36 since 15 is for next year? (EPS)?
No, the problem states that it "Company Z-prime is like Z in all respects save one". This means that in the first 4 years, it will pay dividends just like the first company (\$10 for next year, increasing by 5% per year until year 4), after that it will pay all EPS as dividends. The EPS in year 5 = \$18.23. So the first 4 years it will pay a dividend like the first company, but in year 5 it will pay an EPS, and there will be no further growth.

Customer: replied 11 years ago.
Reply to Manal's Post: I will horrible asking another question, but I want to understand this...how did you arrive to 18.23?

Did you multiply 15 by 0.05 for each year (including 1?)

Please do not say that. I am here to answer any and every question you have, this is why i am here so please do not hesitate to ask as much as you want.

Yes, see EPS for next year = \$15, Year 2 = \$15 x 1.05 = \$15.75, year 3 = \$15.75 x 1.05 = \$16.54, and so on