If our firm were to raise funds now in a certain mix of debt, preferred stock, retained earnings and common stock, then what would be our overall cost of capital?Definitions
- ko= WACC, the average cost of capital after taxes.
- D = market value of debt in our capital structure
- RE = net income that has not been paid out in dividends
- CS = market value of common stock in our capital structure
- PFD = market value of pfd stock in our capital structure
- kd = the cost of debt funds before taxes
- ke = the cost of equity for retained earnings
- kc = the cost of equity for common stock
- kp = the cost of equity for preferred shares
- t = tax rate
Cost of debt funds:- Debt that is placed with banks and insurance companies at kd% interest rate per year have no flotation costs and incur an after tax cost of capital of kd*(1-t).
- New bond issues placed at face value with an investment banker havning a coupon rate of kd% and flotation costs of fb% have an after tax cost of capital of kd*(1-t)/(1-fb).
- We will set the coupon rate to the YTM of a similar bond currently selling in the market.
- The tax advantage (1-t) applies only when the firm has a positive NIAT. This will be assumed.
Cost of pfd stock:- If we sell preferred shares for Pp we must pay pay dividends of Dp per year which would meet the investors' required rate of return according to the perpetuity, kp = Dp/Pp .
- However, our cost of capital will be higher when flotation and adminstrative costs of fp% are incurred: kp = {Dp/Pp}/(1-fp).
Cost of Retained Earnings: - We know what our investors require as a rate of return when they buy our common stock. So when managers invest their earnings investors must be given the same rate of return.
- If we can't generate this rate by reinvesting, we must give the earnings to our stockholders as dividends.
- The CAPM method can be used when kf, (km-kf) and b can be estimated. Cost of RE is: ke = kf + b*(km - kf).
- Alternately, when the growth rate of dividends, g, can be estimated and Po is known the discounted cash flow equation can be used to compute: ke = Do(1+g)/Po + g.
Cost of Issuing Common Stock: - If we issue new shares at Po we incur flotation costs of fc%.
- Simply adjust cost of retained earnings for flotation costs, kc = ke/(1-fc).
Example Problem:Funds are required to sustain growth in sales projected for next year. We have retained $100 million from our NIAT of $150 million and we will be paying out the balance in dividends. We will issue $200 million in bonds with a coupon rate of 10% and KKK have agreed to handle the entire sale for a flotation cost of $50 per bond. We will issue $80 million in additional common stock with a flotation cost of 10% and $20 million in preferred shares at $100 per share paying dividends of $11 per year and incurring flotation costs of 5%. Use the CAPM method for computing the cost of equity with a § of 0.80, a risk free rate of 7% and a market risk premium of 8.3%. Our tax rate is 34%. Compute ko.
Solution:
- kd = 10%* (1-.34)*1000/(1000-50) = 6.95%
- ke = 7% + 0.80*8.3 = 13.64%
- kc = 13.64/.9 = 15.16%
- kp = [11/100]/0.95 = 11.58%
- ko = {200*.95*6.95 + 20*.95*11.58 + 100*13.64 + 80*0.90*15.16}
- Ö {200*.95 + 20*.95 + 100 + 80*.90} = 3996.04/341.55 = 11.69
MCC - Marginal Cost of Capital In practice the cost of capital is affected by two additional factors:
- we wish to maintain a fixed proportion between debt, preferred, and common equity (retained earnings and common stock) (D:PFD:CE)
- we can only obtain fixed finite sums at a given cost of capital. Additional funds require higher costs.
The MCC (marginal cost of capital) questions the managers must answer - What will it cost to raise our first dollar at our D:PFD:CE ratio
- how much money can we raise at this rate.
- After this amount is exhausted, what will be our new cost of capital
- how much money can we raise at that rate
- and so on.
We define the following terms:- d = % debt we wish to maintain in our OCS
- p = % pfd stock desired in our OCS
- c = % common equity in our OCS.
- Di debt funds are available at rate kdi
- Pi pfd stock funds are abailable at cost Kpi
- Ei common equity funds available at cost Kei
- Fdi = Di/d = total funds that can be raised by using up all Di.
Example ProblemOur firm has a capital structure consisting of $750 in debt, $375 in preferred, and $1375 in equity. We believe that this is our optimal capital structure and would like to maintain this ratio when we raise funds tofinance new projects.
We find that we can borrow up to $150 from the bank at a before tax cost of 12%. Additional debt funds can be generated by issuing bonds. We find that a bond of similar quality is currently selling at $1100. It has a coupon rate of 18% and matures in 5 years. The Greedy Bunch, Inc., (TGB) our investment brokers, have agreed to handle this sale at a total flotation cost of $65 per bond.
An insurance company has agreed to buy $37.5 of preferred stock at $50 each. A pfd of similar quality is currently selling in the market for $75 and pays dividends of $14.25. Additional issues of pfd can be sold at the same dividend rate but will incur a $2.50 per share flotation cost.
We expect to retain $66 from current earnings to support our expansion program. Our stock is currently selling for $22.80 per share. We paid dividends of $2 this year and we feel that our investors are expecting our earnings and dividends to grow an an annual rate of 14%.
TGB advises us that they can generate an additional $154 of equity funds by selling common stock at $20 per share. They will charge a flotation cost of $1 per share.
If we issue additional shares, we feel that our investors will de-evaluate our stock to $16 due to dilution effects.
Our tax rate is 30%
- Construct the MCC schedule
- Compute the WACC for raising $300
