EFN507 Chap.6 WACC, Capital Cash Flows and Adjusted Present Value
WACC, Capital Cash Flows and Adjusted Present Value
One identity, three methods
Week 4 derives the cost of capital from the split of operating cash flow among lenders, shareholders and the tax office. Discounting unlevered after-tax free cash flow at a single rate produces the after-tax WACC, in which the interest tax saving appears only through the (1 − t) on the cost of debt.
Putting the tax saving into the cash flow instead gives the capital cash flow, discounted at a pre-tax WACC that never mentions the tax rate.
Adjusted present value keeps the unlevered cash flow at the unlevered rate and adds the tax shield valued separately.
Pairing and rebalancing
The prescribed reading insists that all methods give the same value when each cash flow is paired with its own rate; pairing them wrongly double counts or drops the tax shield.
If the firm rebalances to a target debt ratio, the tax shield becomes risky and the Miles and Ezzell rate replaces the fixed-debt formula.
What this chapter covers
- 01
The cash flow identity X = XD + XE + XG and the tax on X − XD
- 02
Deriving the after-tax WACC for free cash flows
- 03
Capital cash flows and the pre-tax WACC
- 04
Adjusted present value with two discount rates
- 05
The cost of equity under MM with corporate tax
- 06
Miles and Ezzell when debt is rebalanced to a target
Worked example · free
One levered firm valued three ways
- +2APV: unlevered value 700 ÷ 0.10 = $7,000 plus a tax shield of 0.3 × 2,000 = $600 gives $7,600.
- +1Cost of equity: 10% + (10% − 6%) × (2,000 ÷ 5,600) × 0.7 = 11.0%.
- +2After-tax WACC: (2,000 ÷ 7,600)(6%)(0.7) + (5,600 ÷ 7,600)(11%) = 9.21%; 700 ÷ 0.0921 = $7,600.
- +1Capital cash flow: 880 × 0.7 + 120 = $736 at a pre-tax WACC of 9.68% also gives $7,600.
Key terms
- Weighted average cost of capital
- The after-tax rate at which unlevered free cash flows are discounted to give the levered firm's value.
- Interest tax shield
- The tax saved because interest is deductible, equal to the tax rate times the interest paid.
- Unlevered cost of capital
- The required return on the firm's assets if it were financed entirely by equity.
- Miles and Ezzell formula
- A cost of capital for a firm that rebalances its debt to a constant share of value every period.
WACC, Capital Cash Flows and Adjusted Present Value FAQ
Why does the after-tax WACC multiply the cost of debt by one minus the tax rate?
Because free cash flows ignore the interest tax saving, the benefit of debt has to enter somewhere. Scaling the cost of debt down by the tax rate credits the firm with that saving through the discount rate rather than the cash flow.
When is APV easier than the WACC?
When the amount of debt follows its own schedule, such as a loan repaid over the project's life or a subsidised loan. APV values the unlevered project and each financing side effect separately, so the changing debt does not force a new WACC every year.
What rate discounts the cash flows to equity holders?
The cost of equity itself. Cash flow after interest and tax is what shareholders receive, so dividing it by their required return gives the value of the equity; adding the debt then gives firm value.
Why is the tax shield discounted at the cost of debt in APV?
With a fixed amount of permanent debt, the interest saving is as certain as the interest payments, so it carries the risk of the debt. A level perpetuity of t × rD × D discounted at rD is worth exactly t × D.
How does the WACC change as the firm borrows more?
Under the fixed-debt assumptions the after-tax WACC equals the unlevered rate times one minus the tax rate times the debt-to-value ratio, so it falls as leverage rises. Nothing in this model offsets that, which is why distress costs are introduced later.
What changes when the firm rebalances to a target ratio?
Future debt depends on future firm value, so the tax shields become risky and should be discounted at a higher rate. The Miles and Ezzell formula gives a cost of capital above the fixed-debt one, so the shield adds less value.
Exam move
Derive the after-tax WACC from the cash flow identity on a blank page, then value one perpetual firm by APV, free cash flow, capital cash flow and equity cash flow, and confirm all four values agree.
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