Copyright © 1999 Addison Wesley Longman CHAPTER CHAPTER 12 The Cost of Capital Copyright © 1999 Addison Wesley Longman 1

Objectives 1. Compute the cost of debt 2. Compute the cost of preferred stock 3. Compute the cost of equity 4. Compute the weighted average cost of capital.

Why Compute an Average Cost of Capital? Because it will let you make better project selection decisions.

For example Suppose a project is identified that will return 12%. You learn you can borrow the funds to start the project for 10%. You might reasonably accept the project.

Now suppose A project becomes available that will return 16%, but you find out that you can no longer borrow, instead you must issue equity with a cost of 20%. You might reasonably reject this project.

Table 12.1 Choosing Investment Projects Business Expected Cost of Cost of Average Cost Opportunity Return Borrowing Equity of Money Sun Glass Hut 12% 10% 15% Custom Shoe 16% 20% 15%

You have accepted a 12% project and rejected a 16% project, simply because the 12% project became available first.

Average Cost of Funds If you had used the average cost of funds (15%) you would have rejected the 12% and accepted the 16%

After Tax Cost of Debt Review the equation for the price of a bond: Kd = cost of debt

In Chapter 8 we called Kd the yield to maturity The after-tax cost of debt: Kd (1 – T) = cost of debt Kd is multiplied by (1 – T) because interest is tax deductible for the firm.

Cost of Preferred Stock: Ppreferred = Div / Kp Kp = Div / Ppreferred

Example If a firm pays a $2.00 dividend on preferred stock selling for $20.00, what is the cost of preferred? Kp = $2/$20 = 10%

Cost of Equity The cost of equity is more difficult to accurately estimate since the inputs are less certain.

We estimate Ke three ways: 1. CAPM 2. Gordon growth model 3. Bond yield plus premium

Ke : CAPM Ke = Rf +  (Rm – Rf ) The Ke on the left side of the equality is the return required by shareholders.

Gordon Growth Model Po = Div1 Ke – g Ke – g = Div1 Po Ke = Div1 + g Po

Bond Yield Plus Premium Kd represents the risk of the firm’s debt  is the equity risk premium, or the additional risk that stock has over stock (from 3% to 5%) Ke = Kd + 

Cost of Equity Summary CAPM Ke = Rf +  (Rm – Rf ) Gordon Growth Model Ke = Div1 + g Po Bond Yield Plus Premium Ke = Kd + O

To find the cost of equity Compute using all three methods. Reconcile the methods. Weight any method you feel has better inputs more heavily than a method with questionable inputs.

Weighted average cost of capital after tax WACCAT = Wd Kd (1 – T) + Wp Kp + We Ke Wd , Wp , and We are the proportions of debt, preferred, and equity in the firm’s target capital structure.

Example Compute the WACCAT given that: Kd = 10%, Kp = 12%, and Ke = 14% The firm has 30% debt, 10% preferred and 60% equity. The tax rate is 40%.

Example You are buying a $100K. You plan to borrow $80K at 8% and cash in mutual funds that have been yielding 12% to cover the rest. You are in the 28% mtr. What is your WACCAT?

Solution WACCAT = .30(10%)(1 – .4) + .1(12%) + .6(14%)

Marginal Cost of Capital Schedule As additional funds are raised the cost of those funds often increases. The graph showing the cost of each additional dollar is the marginal cost of capital schedule.

Investment Opportunity Schedule The Investment Opportunity Schedule can be combined with the marginal cost of capital schedule Select those projects that return more than they cost

FIGURE 12.1 Marginal Cost of Capital and Investment Opportunity Schedules

To Prepare a Marginal Cost of Capital Schedule 1. Compute the points where the cost of funds increase—called break points 2. Compute the new weighted cost of funds at each break point

Computing Break Points Divide the amount of funds that are limited by the percentage they make up of the capital structure.

Computing Break Points BPi = TCi Wi BPi = break point for a particular type of capital, I

TCi = amount of funds of a particular type of capital available at a particular cost

Example A firm can raise $5 million in retained earnings with a cost of 12%. New equity will cost 13%. Debt costs 7%. The firm capital structure is 19.42% debt and 80.58% equity.

Prepare the cost of capital schedule assuming T = 40%

Solution BPi = $5 million = $6,205,013.65 .8058 Between $0 and $6,205,013.65 the funds will cost the same. After $6,205,013.65 the cost of funds will rise.

FIGURE 12.2 Finding the Break Point = FIGURE 12.2 Finding the Break Point 3

Solution, cont. Next, compute the cost of capital above and below the break point: WACCAT = Wd Kd (1 – T) + Wp Kp + We Ke WACCATo – BP1 = .1942 (.07)(1 – .4) + (.8058)(.12) WACCATo – BP1 = .1049 = 10.49%

Solution, cont. WACCATABOVE BP1 = .1942(.07)(1 – .4) + (.8058)(.13)

FIGURE 12.3 WMCCAT for Harley-Davidson 4