Answer:
The marginal cost of capital is 10.18%( 10.2% when rounded to 1 decimal place)
Step-by-step explanation:
The requirement, in this case, is to ascertain the firm's cost of capital, its weighted average cost of capital, which is the sum of the after-tax cost of each component source of capital multiplied by their weight in the firm's capital structure, on the premise that the first $67 million would be from the internal equity, retained earnings
Balance of investment(after retained earnings)=$155-$67
Balance of investment(after retained earnings)=$88 million
Out of the $88 million,$74 million would be financed by debt which is a before-tax cost of 5.0% and the $14 million($88-$74) would be from additional debt which has a pretax cost of debt of 9.0% because raising additional debt is cheaper compared preferred equity and external equity whose costs are 15.0% and 22.0% respectively.
The after-tax costs of debt are computed thus:
after-tax cost for 5.0%=5.0%*(1-25%)
after-tax cost for 5.0%=3.75%
after-tax cost for 9.0%=9.0%*(1-25%)
after-tax cost for 9.0%=6.75%
WACC=(value of internal equity/total investment*cost of internal equity)+ (value of initial debt/total investment*after-tax cost of debt)+(value of additional debt/total investment*after-tax cost of debt)
WACC=(67/155*18.0%)+(74/155*3.75%)+(14/155*6.75%)
WACC=10.18%