My summary from Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition. While I am sitting somewhere and nothing to do, better reading what I’ve been summarizing….:-) than dreaming what the future bring....?
WACC is about an adjustment when the project is financed with both debt and equity. Suppose a firm uses both debt and equity to finance its investments. If the firm pays RB for its debt financing and Rs for its equity, what is the overall or average cost of its capital? The cost of equity is Rs. the cost of debt is the firm’s borrowing rate, RB, which we can often observe by looking at the yield to maturity on the firm’s debt. If a firm uses both debt and equity, the cost of capital is a weighted average of each. This work out to be:
((S / S+B) x Rs ) + ((B / S+B) x RB)
The weights in the formula are, respectively, the proportion of total value represented by equity:
(S/S+B)
And the proportion of the total value represented by debt:
(B/S+B)
If the firm had issued no debt and was therefore an all-equity firm, its average cost of capital would equal its cost of equity, Rs. At the other extreme, if the firm had issued so much debt that its equity was valueless, it would be an all-debt firm, and its average cost of capital would be its cost of debt, RB.
Interest is tax deductible at the corporate level, the aftertax cost of debt is:
Cost of debt (after corporate tax) = RB x (1-tc)
Where tc is the corporation’s tax rate.
Assembling these results, we get the average cost of capital (after tax) for the firm:
Average cost of capital = (S/S+B) x Rs + (B /S+B) x RB x (1-tc)………….…..(13.5)
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Example 13.5
Consider a firm whole debt has a market value of $40 million and whose stock has a market value of $60 million (3 million outstanding shares of stock, each selling for $20 per share). The firm pays a 5 percent rate of interest on its new debt and has a beta of 1.41. The corporate tax rate is 34 percent. (Assume that the security market line (SML) holds, that the risk premium on the market is 9.5 percent [somewhat higher than the historical equity risk premium], and that the current Treasury bill rate is 1 percent. What is the firm’s RWACC ?
To compute the RWACC using Equation 13.5, we must know:
The after tax debt, RB x (1-tc)
The cost of equity, Rs
And, The proportions of debt and equity used by the firm.
The pretax cost of debt is 5 percent, implying an aftertax cost of 3.3 percent [=5% x (1 – 0.34)].
We calculate the cost of equity capital by using the SML:
Rs= RF + β x (RM – RF)
= 1% + 1.41 x 9.5%
= 14.40%
We compute the proportions of debt and equity from the market value of debt and equity. Because the market value of the firm is $100 million (= $40 million + $60 million), the proportions of debt and equity are 40 and 60 percent, respectively.
The cost of equity, Rs, is 14.40 percent, and the after tax cost of debt , RB x (1-tc) is 3.3 percent. B is $40 million and S is $60 million. Therefore:
RWACC = S/S+B) x Rs + (B /S+B) x RB x (1-tc)
= [(40 / 100) x 3.3%) + (60 / 100) x 14.40%)
= 9.96%
The above calculations are presented in table form below:
1 | 2 | 3 | 4 | 5 |
financing component | market value | weight | cost of capital (after corporate tax) | weighted cost of capital |
debt | $ 40.000.000 | .40 | 5% x (1-.34)= 3.3% | 1.32% |
equity | $ 60.000.000 | .60 | 1% + 1.41 x 9.5% = 14.40% | 8.64 % |
$ 100.000.000 | 1.00 | 9.96% |
Example 13.6
Project evaluation and the WACC.
Suppose a firm has a current and a target debt equity ratio of 0.6, a cost of debt of 5.15 percent, and a cost of equity of 10 percent. The corporate tax rate is 34 percent. What is the firm’s weighted average capital cost?
Our first step calls for transforming the debt – equity (B/S) ratio to debt – value ratio. A B/S ratio of 0.6 implies 6 parts debt for 10 parts equity. Because value is equal to the sum of the debt plus the equity, the debt – value ratio is 6 (6/6+10) = 0.375. Similarly, the equity – value ratio is 10/(6+10) = 0.625. The RWACC then be:
RWACC = S/S+B) x Rs + (B /S+B) x RB x (1-tc)
= 0.625 x 10 % + 0.375 x 5.15% x 0.66 = 7.52%
Suppose the firm is considering taking on a warehouse renovation costing $60 million that is expected to yield cost savings 0f $12 million a year for six years. Using the NPV equation and discounting the six years of expected cash flows from the renovation at the RWACC, we have:
NPV = -$60 + ($12/1+RWACC) + …….+ ($12/(1+RWACC)6)
= - 3.71
Should the firm take on the warehouse renovation? The project has a negative NPV using the firm’s RWACC , this means that the financial markets offer superior investments in the same risk class (namely, the firm’s risk class). The answer is clear: The firm should reject the project.
Questions and problems (connect)
12. WACC Kose, Inc has a target debt- equity ratio of 0.65. its WACC is 11.2 percent, and the tax rate is 35 percent.
a. If Kose’s cost of equity is 15 percent, what is its pretax cost of debt?
b. instead you know that the aftertax cost of debt is 6.4 percent, what is the cost of equity?
Answer:
a. Using the equation to calculate WACC, we find:
WACC = 0.112 = (1/1.65)(0.15) + (0.65/1.65)(1-0.35)RD
RD = 0.0824 or 8.24%
b. Using the equation to calculate WACC, we find:
WACC = 0.112 = (1/1.65) RE + (0.65/1.65) (0.64)
RE = 0.1432 or 14.32%
source:
Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.
