Question

**Problem #2**

**Assume that a conglomerate wishes to consider
establishing a new division. Those companies within industry in
which the proposed division will be part, reflect an average 'beta'
of 1.20 and a Market Value based Debt/Asset ratio 0.40. The
conglomerate is anticipating a Market Value based Debt/Asset ratio
for their new division of 0.67. With a prevailing risk-free rate of
6%, an historic excess market return of 7.50%, and a corporate tax
of 21%, calculate the weighted after-tax cost of capital for the
division, given Kd = 12%.**

Answer #1

**Solution**

1). Levered beta for the industry = 1.20; Debt/Asset (D/A) = 0.40, so Equity/Asset (E/A) = 1-0.40 = 0.60

D/E = 0.40/0.60 = 0.67

Unlevered beta for the industry = levered beta/(1 + (1-Tax rate)*D/E) = 1.20/(1+ (1-25%)*0.67) = 0.80

The required D/A ratio for the new division is 0.67. Thus, E/A = 1-0.67 = 0.33

D/E = 0.67/0.33 = 2.00

Relever the unlevered industry beta to get the beta for the new division: unlevered beta*(1+(1-Tax rate)*D/E)

= 0.80*(1+(1-25%)*2) = 2.00

Cost of equity (ke) (using CAPM) = risk-free rate + beta*market risk premium = 6% + (2*7.50%) = 21%

kd = 12%

WACC = (D/A*kd*(1-Tax rate)) + (E/A*ke)

= (0.67*12%*(1-21%)) + (0.33*21%) = 13.28%

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