Questions

What is the firm's current debt/equity ratio?
What is SAP AG's current debt/capital ratio?
What is SAP's unlevered beta?
What is SAP's cost of equity? Its weighted average cost of capital?
How much additional debt should SAP take on, if the additional debt is used to purchase shares at the current market price?
What is SAP's weighted average cost of capital after the additional debt?
How much does SAP's value increase as a result of the lower cost of capital?
What will be the increase in the share price for SAP after the company takes on new debt?

What would be the free cash flows to the acquired firm, SDF, if SAP completes the acquisition? |
What is the net present value of SAP's investment in SDF?

Suggested solution

Current debt/equity (D/E) ratio = debt/(share price*shares outstanding): 2.42%
Current debt/capital (D/C) ratio = debt/(debt +share price*shares outstanding):
2.36%
The levered beta is found from: Betalev=Betaunlev(1+(1-tax rate)(D/E)
The current unlevered beta is Betaunlev=Betalev/(1+(1-tax rate)(D/E))= 1.13
Cost of equity (Expected return on equity) = Risk free rate + beta(Market expected return - Risk free rate) = 10.33%

WACC = (Cost of equity)(Equity/Capital) + (Cost of debt(1-tax rate))(Debt/Capital) = 10.14%

We can calculate, for different debt levels, the cost of equity, the cost of debt, and the WACC:
(You can download the spreadsheet sapcase.xls.)
 
 

Additional debt	Value of Equity Remaining	Shares (millions)	New Rating	Interest rate	Levered Beta	Cost of Equity	After-tax Cost of Debt	Cost of Capital
0	82,659	107.04	AAA	4.40%	1.15	10.33%	2.44%	10.14%
10000	72,659	94.09	AA	4.85%	1.24	10.81%	2.69%	9.66%
15000	67,659	87.62	A	5.10%	1.29	11.11%	2.83%	9.45%
20000	62,659	81.14	BBB	8.50%	1.36	11.46%	4.72%	9.71%
30000	52,659	68.19	BB	12.00%	1.52	12.35%	6.66%	10.20%

Optimal additional debt: DEM 15 billion
At the optimal capital structure, with DEM 15 billion of debt, SAP's WACC becomes 9.45%

It's about DEM 6 billion.

Old cost of capital: 10.14%. New cost of capital: 9.45%
Change in firm value is a perpetuity = CF/r = cost savings/discount rate
= Old firm value(Old cost of capital-New cost of capital)/New cost of capital
Annual cost savings = old firm value(Old cost of capital-New cost of capital) = 584 DEM million
Permanent increase in firm value = Annual cost savings/Cost of capital = 584/9.45% = DEM 6,180 million

Increase in stock price = increase in firm value/shares outstanding
= DEM 70.54 or 9.1%

To evaluate the proposed acquisition, we must find the FCFF (free cash flow to firm) and discount this at the cost of capital:
 

EBIT		600
Subtract tax at 44%		-267
Add depreciation		100
FCFF		433

Free cash flows = DM 433 million per year.

Present value of this perpetuity = FCFF/cost of capital = 433/9.45% = 4,584 million
NPV = Value-Cost = = 4,584-3,000 = DEM 1,584 million
Under old capital structure with a higher cost of capital, NPV = DEM 1,272 million