3.7 Solutions to WACC Problems
WACC1 represents the current capital cost. The capital weight for each component is multiplied by its respective cost, and the numbers are aggregated. Here again are the earlier assumptions.
| Long-Term Debt (LTD) | $100,000 | Corporate Tax Bracket | 40% |
| Preferred Stock | 10,000 | Interest Rate in Debt | 8% |
| Common Stock @ Par | 10,000 | Cost of Preferred Stock | 9% |
| Additional Paid-in-Capital | 40,000 | Cost of Retained Earnings | 12% |
| Retained Earnings | 40,000 | Cost of Common Stock | 14% |
| Total Equity + LTD | $200,000 | ||
If the firm increases its equity, the solution will depend on whether the company did so by means of internal (WACCRE) or external (WACCC/S) equity. The outcomes will differ. The solutions are also provided below.
| WACC1 | WACCRE | WACCC/S | |
| RE | 40 | 40 + 10 | – |
| C/S | 50 | – | 50 +10 |
| Total Capital | 200 | 210 | 210 |
Problem #1:
WACC1 = (100/200) (.08) (1-.40) + (10/200) (.09) + (40/200) (.12) + (50/200) (.14) = .0875
Problem #2a: Increase in retained earnings (internal capital)
WACCRE = (100/210) (.08) (.6) + (10/210) (.09) + (50/210) (.12) + (50/210) (.14) = .089
Problem #2b: Increase in common stock (external capital)
WACCC/S = (100/210) (.08) (.6) + (10/210) (.09) + (40/210) (.12) + (60/210) (.14) = .09
Obviously, if one uses external, rather than internal, equity, the WACC will be higher.
In either case, the WACC is higher because the firm is increasing its weighting in “expensive” equity. That is to say, the WACC would rise because the component, which was increased in proportion to the total capital, bore a greater cost than the initial WACC.
Should the firm choose to use debt, rather than equity, its WACC, ceteris paribus, would decrease relative to the initial case (problem #1); this WACC would work out to be 8.34%. Its solvency ratios, however, would also deteriorate, and, in a very bad case, the potential resulting reduction in creditability (“default risk”) could cause incremental debt capital costs to increase. (Interestingly, this would result in higher equity costs as well because equity is junior to debt. We will discuss this notable effect below under “The Levered Beta.”).
- What if the company raised capital by issuing more debt?
- Since debt is cheapest, the WACC would decrease. The percentage of debt relative to total capital would incerase.
- What if the company reduced capital by buying back stock? What would the new WACC be?
- If the company buys back stock the equity will be reduced. In Problem #2b, the percentage of common stock relative to total capital was 60/200 = 30%. Let’s say that the company buys back $30,000 in common stock. Now the new common stock percentage would be 30/170 = 17.6%.
