Question

Church Inc. is presently enjoying relatively high growth because of a surge in the demand for its new product. Management expects earnings and dividends to grow at a rate of 22% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends to zero, i.e., g = 0. The company’s last dividend, D0, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. What is the current price of the common stock?

Answer 1

This can be worked out as under:

rakhivasavada :

Required Rate of Return r(m) = r(f) + b r(p), where r(f) is the risk free rate and the r(p) is the risk premium and b is beta and therefore:

r(m) = 3.00 + 1.20 * 5.5 = 9.6%.

rakhivasavada :

Hence current price P(0),

= D1/(1+k) +D2/(1+k)^2 + D3/(1+k)^3 + D4/(1+k)^4 + P4/(1+k)^4

D1 = D0 * 1.25 = 1.25*1.25 = 1.25^2

D2 = 1.25D1 = 1.25^3

D3 = 1.25D2 = 1.25^4

D4 = 1.25D3 = 1.25^5

D5 = 1*D4 = 1.25^5 (g = 0, so (1+g) =1)

P4 = D5/k = 1.25^5/0.096

So, P(0)

= 1.25^2/1.096 +1.25^3/1.096^2 +1.25^4/1.096^3 +1.25^5/1.096^4 +1.25^5/(0.096*1.096^4)

= 29.05

rakhivasavada :

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rakhivasavada :

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Answer 2

The current price of the common stock of Church Inc. is $28.85.

The following information have been given:

Company’s last dividend, D0 = $1.25

Beta = 1.20

Market risk premium = 5.50%

Risk-free rate = 3.00%

The price today will be calculated thus:

P = D × 1.22⁴ × (1 - g)/(k-g) = D × (1 - g) / (rfr + beta(rm - rfr ) -g]

P = 1.25 × 2.2153346 / (0.03 + 1.2(0.055)

P = 2.77/0.096

P = 28.85

Therefore, the current price of the common stock is $28.85.

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