8/13/2019 Gross vs Net

1/4

Component Capital Inves After-tax Ear Value PE P/BV

Operating As 1000 125 1250 10.00 1.25

Cash 250 10 250 25.00 1.00

Firm 1250 135 1500 11.11 1.20

8/13/2019 Gross vs Net

2/4

Gross Debt Approach Net Debt Approach

Debt = $500.00 $250.00

Equity = $991.25 $924.77

Cash = $250.00

Unlevered beta of operating assets = 1.42 1.42

Levered beta 1.849762241 1.650326352

Cost of equity 13.25% 12.25%

Cost of debt 6.28% 7.80% ! Cost of debt

Cost of capital 10.07% 10.64%

Operating Assets $1,241.25 $1,174.77

Cash $250.00 $0.00

Firm Value $1,491.25 $1,174.77

Debt $500.00 $250.00

Equity Value $991.25 $924.77

Operating Earnings = 125 125

Cash Earnings = 10 10

Tax Rate = 40% 40%

Riskfree rate = 4.00% 4.00%

Risk premium = 5.00% 5.00%

Cost of debt for the firm = 5.90% 5.90%

8/13/2019 Gross vs Net

3/4

used has to be adjusted to reflect assumptions about cash holdings.

The gross and net debt approaches make different assumptions about how the cash in a firm is f

In the net debt approach, cash is entirely funded with riskfree debt and the operating assets are

of the equity and the remaining debt. In the gross debt approach, cash is funded with the same

equity as the operating assets of the firms.

The upshot of this is that the cost of debt that we use in the cost of capital for the two approach

to reflect these assumptions. In the net debt approach, the debt carried by the operating assets i

the safest asset (cash) is fully funded with debt. In the gross debt approach, the cost of debt will

cash shelters some of the debt. In neither case, can the stated cost of debt for the entire firm (w

and operating assets) be used in the cost of capital.

When the tax rate is 0% and the costs of debt are adjusted to reflect the different risks (which t

the two approaches will yield the same value for equity. As the tax rate rises, the two approache

net debt approach yielding a lower value. This is because the net debt approach assumes that an

debt used to fund cash is fully offset by the tax that will have to be paid on the interest income f

8/13/2019 Gross vs Net

4/4