Advanced Cost of Capital and Capital Structure

Advanced Cost of Capital and Capital Structure

Syllabus tag: KASNEB CPA | Advanced Level | CA33 Advanced Financial Management | Topic 5 Advanced Cost of Capital and Capital Structure

Lesson objectives

By the end of this topic, you will be able to:

• Explain why a single WACC is inadequate for a project in a different industry
• Ungear and regear a beta
• Compute a project-specific discount rate
• Apply the adjusted present value method
• Say when APV is preferable to a WACC-based NPV

Why this matters

CA22 discounted every project at the company WACC. That is right only where the project carries the same business risk and the same financing mix as the existing business. This topic supplies the two methods for when it does not.

The problem with a single WACC

A company WACC reflects two things: the business risk of what the company currently does, and the financial risk created by how it is financed.

A project in a different industry has different business risk. A project financed differently has different financial risk. Discounting it at the company WACC misprices it — and the direction of the error is predictable. Using a rate that is too low makes bad projects look acceptable.

Ungearing and regearing beta

The equity beta of a listed company reflects both business and financial risk. To isolate business risk, remove the gearing:

Asset beta = Equity beta × E / [E + D(1 − t)]

A proxy company in the target industry has an equity beta of 1.6, equity of 600 and debt of 400, with tax at 30%:

Asset beta = 1.6 × 600 / [600 + 400(0.7)] = 1.6 × 600 / 880 = 1.0909

That figure is the business risk of the industry, stripped of the proxy company's financing choices.

Now regear it to the financing the investing company will actually use — say 50% equity, 50% debt:

Equity beta = Asset beta × [1 + D(1 − t) / E]

= 1.0909 × [1 + 50(0.7) / 50] = 1.0909 × 1.7 = 1.8545

Project cost of equity by CAPM, risk-free 9% and market return 16%:

Ke = 9 + 1.8545(16 − 9) = 21.98%

The logic in three steps: take a proxy from the right industry, strip out its gearing, put in your own.

The proxy must be chosen carefully. It should operate wholly in the target industry — a diversified conglomerate's beta reflects a mixture and tells you nothing about any one activity.

:::checkpoint A company uses the equity beta of a listed competitor without ungearing it. The competitor is more heavily geared than the investing company. State whether the resulting discount rate is too high or too low, and what that does to the NPV. :::

Adjusted present value

APV separates the project from its financing entirely.

APV = Base case NPV + PV of financing side effects

Step 1 — the base case. Value the project as if all-equity financed, discounting at the ungeared cost of equity.

A project costing KES 40,000,000 with inflows of 12, 14, 16 and 15 million, ungeared cost of equity 14%:

Base case NPV = KES 979,610

Step 2 — the financing side effects.

The tax shield on debt of 18,000,000 at 10% with tax at 30%:

Annual shield = 18,000,000 × 10% × 30% = 540,000 PV over four years at the cost of debt = KES 1,711,727

Issue costs of 800,000 are deducted.

Step 3 — combine.

	KES
Base case NPV	979,610
PV of tax shield	1,711,727
Issue costs	(800,000)
APV	1,891,337

The project is marginal on its own merits and clearly acceptable once the financing benefit is counted. That separation is the whole value of the method — it shows how much of the return comes from the project and how much from the way it was funded.

Choosing between the methods

Use a WACC-based NPV where the project has similar business risk and the financing mix is stable. It is quicker and the audience will find it familiar.

Use APV where:

• The financing mix changes over the project's life, so a single WACC cannot apply
• The project carries subsidised or unusual financing — a development loan at below-market rates
• Financing side effects are material and identifiable — issue costs, grants, guarantees
• The project is a leveraged buyout, where gearing falls steadily as debt is repaid

The discount rate for the tax shield is itself examinable. Using the cost of debt treats the shield as being about as risky as the debt that creates it. Some texts use the ungeared cost of equity on the ground that the shield is only as certain as the taxable profits. Either is acceptable if stated and applied consistently.

:::checkpoint A leveraged buyout is financed with 80% debt at the outset, falling to 30% over five years as cash flows repay it. Explain why a single WACC cannot be used and how APV handles the changing structure. :::