Question

P&G Corporation will pay an annual dividend of $0.50 one year from now. Analysts expect this dividend to grow at 10% per year thereafter until the fifth year. After that, growth will level off at 1.5% per year, The firm's equity cost of capital is 7%.

a. According to the dividend-discount model, what is the value of a share of P&G stock?

b. Assume the company prefers to target a retention ratio of 0.50. What was the return on equity for the first 5 years and beyond? If the company's turnover and leverage ratios were constant, can you explain (calculate) what happened to ROE and why?

C. There is another group of analysts that disagrees the assumption about the above differential growth model. Although they agree with the cost of capital, the share price, and the annual dividend to be paid one year from now, they believe that the dividends will have only one long- term constant growth rate. What is this growth rate?

d. Explain why these two groups of analysts have such differ ent assumptions in their models.

Answer 1

Answer a:

Stage 1 : Explicit forecast period = 1st 5 years

D1/Re-g [1-(1+g/1+Re)n]

Where,

D1= Expected dividend = $0.50

Re = Cost of capital = 7%

g = Growth rate = 10%

n = No .of years

threfore,

0.50/0.07-0.10 [1-(1.07/1.10)5]

= -16.67 * [1-0.847123]

= $ -2.548 (approx)

Stage 2 : Horizon period = Beyond 5 years

P5 = D6 /Re-g

D6 = 0.50*(1.10)4*1.015

= 0.50*1.4641*1.015

= 0.74303075

P5 = 0.74303075/0.07-0.015

= 0.74303075/0.055

= $13.51 (approx)

Present value of P5 = 13.51/(1.07)5

= $9.63 (approx)

Intrinsic value = $(9.63 - 2.548)

= $ 7.082 (approx)