Question

step by step of all equations used and explanations claearly

.     (a) Suppose Carter Chemical Company's management conducts a study and concludes that if Carter expands its consumer products division (which is less risky than its primary business, industrial chemicals), the firm's beta will decline from 1.1 to 0.9. However, consumer products have a somewhat lower profit margin, and this will cause Carter's growth rate in earnings and dividends to fall from 7 percent to 6 percent. Should management make the change? Assume the following:

ER_M= 10% ;  R_F=7.5%; D₀=$2.

(b)      Assume all the facts as given in part (a), except the one about the changing beta coefficient. By how much would the beta have to decline to cause the expansion to be a good one? (Hint: set P₀under the new policy equal to P₀under the old one, and find the new beta that produces this equality.)

Answer 1

a) First list down the information provided in question:

Following steps needs to be followed to solve the question:

Step No. 1: Calculation of Cost of equity (K_e) under current scenario (without expansion)

As per CAPM model

Cost of Equity (Ke) = R_F + b*(R_M - R_F)

= 0.075 + 1.1 * (0.10 - 0.075)

= 0.075 + 0.0275 = 10.25%

Step No. 2: Calculation of Cost of equity (K_e) under revised scenario (post expansion)

Cost of Equity (Ke) = R_F + b*(R_M - R_F)

= 0.075 + 0.9 * (0.10 - 0.075)

= 0.075 + 0.0225 = 9.75%

Step No. 3: Calculation of Firm's current price (P₀) under current scenario (without expansion)

As per dividend growth model or Gordon's growth model

Current Stock price (P₀ )= D₁ / (K_e - g)

= D₀*(1+g) / (K_e - g)

= $ 2*(1+0.07) / (0.1025-0.07)

= $ 2.14 / 0.0325 = $ 65.85

Step No. 4: Calculation of Firm's current price (P₀) under revised scenario (post expansion)

Current Stock price (P₀ )= D₁ / (K_e - g)

= D₀*(1+g) / (K_e - g)

= $ 2*(1+0.06) / (0.0975-0.06)

= $ 2.12 / 0.0375 = $ 56.53

Conclusion: Post expansion, the firm's stock price will reduce from $ 65.85 to $ 56.53, therefore the expansion is not advisable.

b) Information available for part b:

Following steps needs to be followed to solve the question:

Step No. 1: Calculation of Cost of equity (K_e) using revised firm's current price (P₀) under revised scenario (post expansion):

Current Stock price (P₀ )= D₁ / (K_e - g)

Hence, K_e = (D₁ / P₀) + g

= ($2.12/$65.85) + 0.06 = 9.22%

Step No. 2: Calculation of b using Cost of equity (K_e) under revised scenario (post expansion):

Cost of Equity (Ke) = R_F + b*(R_M - R_F)

Hence, b = (K_e - R_F) / (R_M - R_F)

= (0.0922 - 0.075) / (0.10-0.075) = 0.688

Conclusion: Post expansion, to sustain firm's stock price, b will have to reduce to 0.688 from 1.1.

Trust the same will serve your purpose.

Should you need any clarifications, please feel free to comment.