Question

Cost of Common Equity:

Cost of Retained Earnings, rs:

Suppose that (1) the risk-free return is 5.5%; (2) the average stock return (i.e. the market return) is 11.5%; (3) your firm stock’s beta (i.e. stock’s risk) is 0.8; (4) the next dividend payment will be $1; (4) the growth rate of the dividend is 6%; (5) the current market price of the stock is $25; (6) the yield of your firm’s long-term bond is 6.5%; and (7) the risk premium on your firm’s stock over your firm’s bond is 4%.

Given the information above, calculate the cost of retained earnings using (1) Capital Asset Pricing Model, CAPM, approach; (2) Bond-yield-plus-risk-premium approach; and (3) Discounted Cash Flow, DCF, approach.

(1) CAPM approach:

(2) Bond-yield-plus-risk-premium approach:

(3) DCF approach:

What is the range of your estimations? What is the midpoint of this range (i.e. the final estimation of the cost of retained earnings)?

Cost of New Common Stock, re:

The flotation cost of issuing new common stock, F, is 15% of the issue price. According to the previously provided information of your outstanding common stock, estimate the cost of new common stock using the DCF approach.

According to the DCF approach cost of new common stock calculated above, (1) figure out the flotation cost adjustment for new common stock; and then (2) considering the cost of retained earnings from all three approaches, adjust for this flotation cost. What is the cost of new common stock?

Answer 1

a) The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for stocks.

CAPM : Rf+ (Rm-Rf)*B

Rf = Risk Free

Rm-Rf= Market Risk Premium

B = Beta sensitivity of stock to the market return

Hence, Cost = 5.5+ (11.5-5.5)*0.8

= 10.30%

b) The bond yield plus risk premium (BYPRP) approach is another method we can use to determine the value of an asset, specifically, a company's publicly traded equity. BYPRP allows us to estimate the required return on an equity by adding the equity's risk premium to the yield to maturity on company's long-term debt.

Cost = Yield of bonds + risk premium on stock over your firm’s bond

= 6.5 + 4

= 10.5%

c) DCF approach attempts to figure out the value of an investment today, based on projections of how much money it will generate in the future. We may use Gordon Growth Model to find the cost of equity

Cost = (Expected Dividend / Price of share)% + Growth

= 1/25 *100 + 6

= 10%

Cost of Retained Earnings ranges from 10% to 10.5%. Midpoint shall be 10.25%

d) Cost of floatation is 15%. Hence if we raise new stock at 25$(Current Price), effectively 15% of $25 will be cost of floatation i.e 3.75. Effectively we will receive 25-3.75 = 21.25

Cost of Equity Using DCF = 1/ 21.25*100 +6

= 10.71%