Question

Cost of Common Equity

The future earnings, dividends, and common stock price of Carpetto Technologies Inc. are expected to grow 4% per year. Carpetto's common stock currently sells for $25.50 per share; its last dividend was $2.00; and it will pay a $2.08 dividend at the end of the current year.

1. 
   
2. Using the DCF approach, what is its cost of common equity? Round your answer to two decimal places.
   %
3. 
   
4. If the firm's beta is 1.30, the risk-free rate is 3%, and the average return on the market is 12%, what will be the firm's cost of common equity using the CAPM approach? Round your answer to two decimal places.
   %
5. 
   
6. If the firm's bonds earn a return of 9%, based on the bond-yield-plus-risk-premium approach, what will be r_s? Use the midpoint of the risk premium range discussed in Section 10-5 in your calculations. Round your answer to two decimal places.
   %
7. 
   
8. If you have equal confidence in the inputs used for the three approaches, what is your estimate of Carpetto's cost of common equity? Round your answer to two decimal places.
   %

Answer 1

Given:

Dividend growth rate (g) = 4%

Common Stock value (P₀) = $25.50 per share

Dividend just paid (or) Last dividend (D₀) = $2

Current year dividend to pay (D₁) = $2.08

(a) Cost of Common Equity (R) = [D₁ / P₀] +g

Cost of Common Equity (R) = [$2.08 / $25.50] + 0.04

Cost of Common Equity (R) = 0.1215 = 12.15%

Cost of Common Equity (R) = 12.15%

(b) Beta = 1.3

Risk-free rate (R_f) = 3%

Return on the Market (R_M) = 12%

Calculating Firm’s Cost of Common Equity using the CAPM approach:

Cost of common equity (R_E) = [R_f + β (R_M – R_f)]

Cost of common equity (R_E) = [3% + 1.3 (12% - 3%)]

Cost of common equity (R_E) = [3% + 1.3 (9%)]

Cost of common equity (R_E) = [0.03 + 1.3 (0.09)]

Cost of common equity (R_E) = 0.147 = 14.7%

Cost of common equity (R_E) = 14.7%

(c) r_s= Bond rate + Risk premium

Risk premium = R_M – R_f

r_s= 9% + 9% = 18%

d) The firm’s cost of equity estimated to be equal to the average of all the three methods.

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