Question

The stock of Gao Computing sells for $50, and last year's dividend was $3.13. Security analysts are projecting that the common dividend will grow at a rate of 7% a year. A flotation cost of 10% would be required to issue new common stock. Gao's preferred stock sells for $32.61, pays a dividend of $3.30 per share, and new preferred stock could be sold with a flotation cost of 8%. The firm has outstanding bonds with 20 years to maturity, a 12% annual coupon rate, semiannual payments, $1,000 par value. The bonds are trading at $1,171.59. The tax rate is 25%. The market risk premium is 6%, the risk-free rate is 6.5%, and Gao's beta is 1.2. In its cost-of-capital calculations, Gao uses a target capital structure with 45% debt, 5% preferred stock, and 50% common equity.a. Calculate the cost of each capital component—in other words, the after-tax cost of debt, the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs). Use both the CAPM method and the dividend growth approach to find the cost of equity.b. Calculate the cost of new stock using the dividend growth approach.c. Assuming that GAO will not issue new equity and will continue to use the same tar-get capital structure, what is the company's WACC?

P₀ $50.00

D₀ $3.13

g 7%

Flotation cost for common 10%

P_pf $32.61

D_pf $3.30

Flotation cost for preferred 8%

Bond maturity 20

Payments per year 2

Annual coupon rate 12%

Par $1,000.00

Bond price $1,171.59

Tax rate 25%

Beta 1.2

Market risk premium, RP_M 6.0%

Risk free rate, r_RF 6.5%

Target capital structure from debt 45%

Target capital structure from preferred stock 5%

Target capital structure from common stock 50%

Cost of debt:

Semiannual yield = RATE = ? (Is this 5%?)

Annual  B-T r_d          = ?

A-T r_d          = ?

Cost of preferred stock (including flotation costs):

D_pf             /          Net P_pf        = r_pf          = ?

Cost of common equity, dividend growth approach (ignoring flotation costs):

D₁          /           P₀            +             g         = r_s         = ?

Cost of common equity, CAPM:

r_RF  + b  × RP_M   = r_s         = ?

b. Calculate the cost of new stock using the dividend growth approach (include flotation costs).

D₀× (1 + g)    /       P_{0 ×}(1 - F)      +             g         = r_e         = ?

c. Assuming that Gao will not issue new equity and will continue to use the same capital structure, what is the company's WACC?

w_d 45.0%

w_pf 5.0%

w_s 50.0%

100.0%     

w_d× A-T r_d   +       w_pf× r_pf    +        w_s× r_s       = WACC?

Answer 1

cost of debt:

cost of debt is its YTM

coupon = 1000*12%*(1/2) = 60

number of periods = 20*2 = 40

present value = 1171.59

future value = 1000

[N = 40 ; PMT = 60 , PV = -1171.59 ; FV = 1000] compute I/Y

I/Y = 5%

above rate is semi annual

annual rate = 5%*2 = 10%

after tax cost of debt = beforetax cost*(1-tax)

= 10%*(1 - 25%)

= 7.50%

Cost of prefrred stock:

using the formula given

cost = 3.30 / 32.61*(1 - 8%) = 11%

cost of common equity:

Dividend growth approach:

using the formula given

= [3.13*(1+7%) / 50] + 7%

= 13.70%

CAPM approach

= 6.5% + 1.2*6%

= 13.70%

cost of new stock:

= [3.13*(1+7%) / 50*(1-10%)] + 7%

= 14.44%

WACC:

=(0.45*7.50%) + (0.05*11%) + (0.5*13.70%)

= 10.78%