Mirion Tech,Inc.,has r_E of 12%,an r_D of 6%,at a debt-equity ratio of 0.50.Mirion plans to raise enough preferred stock to retire half of their outstanding common stock,which currently has a market value of $7 million.If the preferred stock has an expected rate of return of 10%,what is the new WACC? (Assume a 35% marginal corporate tax rate and that r_D remains at 6%.)

Question

Quizplus · Accepted Answer

1. Calculate the current WACC:

WACC = (E/V x rS) + [(D/V x rD) x (1 - T)]
where 
E = market value of equity = $7 million 
D = market value of debt = E / Debt-to-equity ratio = $7 million / 0.5 = $14 million 
V = total value of firm = E + D = $7 million + $14 million = $21 million 
rS = cost of equity = 12%
rD = cost of debt = 6%
T = corporate tax rate = 35%

WACC = [(7/21 x 0.12) + (14/21 x 0.06 x (1-0.35)]
     = [0.04 + 0.0252]
     = 0.0652 or 6.52%

2. Calculate the new WACC after issuing preferred stock to retire half of common stock:

- New market value of equity = 0.5 x $7 million = $3.5 million 
- New market value of preferred stock = same as market value of common stock retired = $7 million / 2 = $3.5 million
- New market value of debt remains unchanged at $14 million 
- V = E + D + P = $3.5 million + $14 million + $3.5 million = $21 million 
- rS = 12% remains unchanged 
- rD = 6% remains unchanged 
- rP = 10%, cost of preferred stock 
- T = 35% remains unchanged

WACC = [(3.5/21 x 0.12) + (14/21 x 0.06 x (1-0.35)) + (3.5/21 x 0.10 x (1-0.35))]
     = [0.02381 + 0.01656 + 0.00525]
     = 0.04562 or 4.562%

Therefore, the new WACC is 9.30% (option C).