Question

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HCA HealthCare is considering an acquisition of Mission Health. Mission Health is a publicly traded company, and its current beta is 1.30. Mission Health has been barley profitable and had paid an average of only 20% in taxes during the last several years. In addition, it uses little debt, having a debt ration of just 25%. If the acquisition were made, HCA would operate Mission Health as a separate, wholly owned subsidiary. Mission Health would pay taxes on a consolidated basis, and the tax rate would therefore increase to 35%. HCA also would increase the debt capitalization in the Mission Health subsidiary to 40% of assets, which would increase its beta to 1.5. HCA estimates that Mission Health, if acquired, would produce the following net cash flows to HCA's shareholders (in millions of dollars):

Year		Free Cash Flows to Equityholders
1		$1.30
2		$1.50
3		$1.75
4		$2.00
5+		constant growth rate at 6%

These cash flows include all acquisition effects. HCA's cost of equity is 14%; its beta is 1.0; and its cost of debt is 10%. The risk free rate is 8%

A. What discount rate should be used to discount the estimated cash flow? (Hint: Use HCA's cost of equity to determine the market risk premium)

B. What is the dollar value of Mission Health to HCA's shareholders?

Answer 1

A.

HCA cost of equity = 14

cost of equity = risk free rate + market risk premium *beta

14 = 8 + MRP*1

MRP = 6

Cost of equity for Mission helath = 8 + 6 *1.50 = 17%

discount rate used to discount the cash flows = weighted average cost of capital

=0.4* 10 * ( 1 - 0.35) + 0.6*17

= 12.80%

B.

FCFF for year 5 = 2*1.06 = 2.12

Present value of cash flows = present value of cash flows from year 1 to 4 + present value of terminal value

terminal value = FCFF for year 5 / ( wacc - growth rate )

= 2.12 / ( 0.128 -0.06) = 31.18

Dollar value of Mission Health to HCA's shareholders = 1.3 /1.128 + 1.5/1.128^2 + 1.75/1.128^3 + 2/1.128^4 + 31.18/1.128^4

= 24.05 million