Question

source of capital	Target market proportions
long term debt	20%
preffered stock	10
common stock equity	70

A firm has determined its optimal capital structure which is composed of the following sources and target market value proportions.

Debt: The firm can sell a 12-year, $1,000 par value, 7 percent semiannual coupon bond for $950. A flotation cost of
2 percent of the face value would be required. Note: Floatation cost only occurs if new security needs to be offered.
Preferred Stock: The firm has determined it can issue preferred stock at $75 per share par value. The stock will pay a $10 annual dividend. The cost of issuing and selling the stock is $3 per share.
Common Stock: A firm's common stock is currently selling for $18 per share. The dividend expected to be paid at the end of the coming year is $1.74. Its dividend payments have been growing at a constant rate for the last four years. Four years ago, the dividend was $1.50. It is expected that to sell, a new common stock issue must be underpriced $1 per share in floatation costs. Additionally, the firm's marginal tax rate is 21 percent.

The firm's after-tax cost of existing debt is closest to________. (See Table 9.1). Hint: No need to consider floatation cost.

The weighted average cost of capital up to the point when retained earnings are exhausted (i.e. Do not issue any new security) is closest to________. (See Table 9.1)

If the target market proportion of long-term debt is increased to 30 percent — decreasing the proportion of preferred stock to 0 percent, what will be the revised weighted average cost of capital? Assuming all funds will be coming from existing investors and so no floatation cost will occur. (See Table 9.1)

Answer 1

For debt:

Face Value = $1,000

Current Price (PV) = $950

Coupon rate = 7 percent semiannually

Thus, coupon amount (PMT) = 7%/2*1000 = $35

Number of years = 12

Number of periods (Nper) = 12*2 = 24

The yield-to-maturity (YTM) is calculated as:

= Rate(Nper, PMT, PV, FV, Type)

= Rate(24, 35, -950, 1000, 0)

= 3.8220%

Tax rate = 21%

Solution 1) Before-tax cost of debt (Kd) = YTM of the bond

After-tax cost of debt = Before-tax cost of debt*(1 - Tax Rate%)

= 3.8220%*(1 - 21%)

= 3.0194%

Solution 2) Cost of preferred equity (Kpe) = Annual dividend/Current price per share

= 10/75 = 13.333%

Dividend growth rate (g) = (Final Value/Initial Value)^(1/n) - 1

n = number of years

Final Value (FV) = 1.74

Initial Value (IV) = 1.50

Since 1.74 is expected to the be end of the next year and 1.50 is paid before 4 years from today, hence, n = 5

g = (1.74/1.5)^(1/5) - 1

g = 3.0129%

Cost of equity (Ke) = D1/P + g

D1 = Expected Dividend = 1.74

P = Current price = 18

Ke = 1.74/18 + 3.0129%

Ke = 12.6796%

Weighted average cost of capital (WACC) = Wd*Kd*(1 - tax%) + Wpe*Kpe + We*Ke

Where, Wd, We and Wpe = weights of debt, equity and preferred equity respectively

Kd, Kpe and Ke are cost of debt, preferred equity and equity respectively.

Wd = 20%

Wpe = 10%

We = 70%

WACC = 20%*3.8220%*(1 - 21%) + 10%*13.333% + 70%*12.6796%

= 0.006039 + 0.013333 + 0.088757

= 0.108129

= 10.8129%

Solution 3) Since the weight of the preferred equity is reduced to 0% and weight of debt has been increased to 30%

Therefore, Wd = 30%

Wpe = 0%

We = 70%

WACC = 30%*3.8220%*(1 - 21%) + 70%*12.6796%

9.782%

Please comment in case of any doubts or clarifications. Please Thumbs Up!!