Question

Southern Healthcare and BestWell are for-profit HMOs that operate in Florida and Georgia. Currently,
both are identical in every respect except that Southern is unleveraged while BestWell has $10 million
of 5 percent bonds. Both HMOs report an EBIT of $2 million and pay corporate tax at a rate of 30
percent. The cost of equity to Southern is 10 percent. Assume that all of the MM assumptions hold.
a. What total value would MM estimate for each HMO?
b. What is the value of the equity of each HMO?
c. What is the required rate of return on equity for each HMO?
d. What is the corporate cost of capital for each HMO?

Answer 1

a)

Total Value of Southern Healthcare = EBIT(1-tax rate) / Required return on equity

Here EBIT = $2 million

Tax rate = 30%

Required rate of return on equity = 10%

= $2 million(1-30%) / 10%

= $1.4 million / 10%

=$14 million

Total Value of Bestwell = Total Value of Southern Healthcare + PV of interest tax shield

PV of interest tax shield = Total debt x Tax rate

= $10 million x 30%

= $ 3 million

Thus Total Value of Bestwell = 14 million + 3 million

= $ 17 million

b) Value of equity of Southern Healthcare = Total Value of Southern Healthcare = $14 Million

Value of equity of bestwell = Total Value of Bestwell - Total Debt

= $17 million - 10 million

= $ 7 million

c) Required rate of return on equity for Southern Healthcare = 10%

Required rate of return on equity for bestwell = R_u + [(R_u - Rd) x (D/E) x (1 - tax rate)]

R_u = Cost of equity of unlevered firm = 10%

R_d = Interest rate = 5%

D = Total value of Debt = $10 million

E = Total value of equity =$ 7 million

Tax rate = 30%

Thus Required rate of return on equity for bestwell = 10% + [(10%-5%) x (10/7) x (1-0.3)]

= 10% + [ 5% x 1.4286 x 0.7]

= 10% + 5%

= 15%

d) Cost of capital for Southern Healthcare = 10%

Cost of capital for Bestwell = [Cost of equity x E/(D+E) ] + [Interest rate(1-tax rate) x D/(D+E) ]

Cost of equity = 15%

Interest rate = 5%

D = Total value of Debt = $10 million

E = Total value of equity =$ 7 million

Tax rate = 30%

Cost of capital for Bestwell = [15% x 7/(7+10)] + [5%(1-0.3) x 10/(7+10)]

=[15% x 7/17] + [3.5% x 10/17]

= 6.18% + 2.06%

= 8.24%