Pn = price at time n; Dn = dividend at time n; Yn = Earnings in period n; r = re

Question

Pn = price at time n; Dn = dividend at time n; Yn = Earnings in period n; r = retention ratio = 1-Dn/Yn = dividend payout ratio
En = Equity at the end of year n; k = discount rate, g = dividend growth rate = r x ROE; ROE = Yn/E(n-1)

1. Using the discounted dividend model, calculate the price Po if
D1=20, k = 0.15 and g= r x ROE = .8 *.15 = .12 and Y1 = 100 per share

2. What then will P5 be if:
D6 = 20, k = 0.15 and g = r*ROE = .8 * .15 = 0.12?

3. If P5 = your results from part B, and assuming no dividends are paid until P6, what would be P0? P1? P2?

4. Again, assuming the facts from Part 2, what is the relationship between P2 and P1? Explain why this is the result.

Explanation / Answer

1. P0= D1/k-g = P0 = 20/0.15 - 0.12 = $667

2. P5 = D6/k-g = 20/0.15 - 0.12 = $667

3. P0 = EPS(1-r)/k-g = 100(1- 0.8)/0.15 - 0.12 = $667

P0, P1,P2 = $667

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