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Adjusting WACC when gearing changes
时间:2008-12-31

INTRODUCTION

When discounting a project's cash flow at company's WACC (weighted average cost of capital), we assume that:

1.   Same Business Risk:

The project's business risk is the same as it of company's other asset and remains so for the life of the project.

2.   Same Financial Risk: - Gearing Ratio.

The project supports the same gearing ratio as company's capital structure, which remains constant for the life of the project.

After study of F9 or P4, students are familiar with calculation of adjusted WACC when business risk differs. This article is going to discuss another topic - how to adjust the WACC when financial risk (gearing ratios) changes:

DEGEARING AND REGEARING OF THE BETA

Firstly we should review the concept of beta; there are two types of beta, equity beta and asset beta. Equity beta represents the systematic business risk and financial risk of a company, and asset beta reflects only the business risk of a company. If a company is all equity financed, the equity beta is exactly equal to asset beta.

As long as a company operates in its existing business, its asset beta remains constant. However, the equity beta will change as company's gearing (financial risk) change, the higher gearing ratio, the higher equity beta.

Therefore, we still could use the techniques of 'degearing and regearing' to adjust the company's WACC when gearing ratios changes, there are five steps:

Step1: calculate the beta asset (business risk) of company by degearing the beta equity. The formula is as following:


In this step, the beat asset is unknown variable, and Debt and Equity is used the market value before the gearing changed.

If you are not given beta debt, we normally assume beta debt is zero .The formula can be simplified as:


Step 2: calculate the new beta equity by regearing the new debt / equity ratio, the formulae is same but the beta equity is unknown variable:


or (if beta debt is not given)

The Debt and Equity is used the new gearing ratio after company adjusting its capital structure.

Steps 3: calculating the cost of equity (Ke) by using CAPM model:


Step 4: Estimate cost of debt (Kd) at new gearing ratio. We should note that the cost of debt may rise if gearing ratio increase, as company's credit rating may fall under a higher gearing ratio and debtholders require higher return.

Step 5: Calculating the WACC under a new gearing ratio.

WACC =

Example 1: S plc

S plc is a light weapons manufacturer whose equity: debt ratio is 79:21. The corporate debt yields 3% after tax. The beta value of the company's equity is 1.2. The average return on the stock market is 10.5% and return on treasury bill is 4%. The corporation tax rate is 30%.

The company is considering to increase its gearing ratio to 50% (gearing ratio is defined as D/(D+E) on market value basis). Company estimate the after tax cost of debt may rise to 3.5% after gearing increase.

Required:

Calculate the company's WACC after gearing change

Existing WACC calculation

Ke =4 + (10.5 -4)×1.2 = 11.8%

WACC =

Adjusting WACC after gearing change

Step1: calculate the beta asset (business risk) of company


Step 2: calculate the new beta equity by regearing the new debt / equity ratio



Steps 3: calculating the cost of equity (Ke) by using CAPM model:


Step 4: Estimate cost of debt (Kd) at new gearing ratio.


Step 5: Calculating the WACC in a new gearing ratio.


ADJUST THE WACC WHEN BETA IS NOT GIVEN

In some P4 examination questions, students are not told the information of beta whereas just giving the information of cost of equity (Ke), we still can degear and regear the Ke by using Modigliani and Miller's formulae, the steps are following:

Step1: calculate the cost of equity at zero debt (Keu) by using M+M proposition

(Given in exam)

Keu is unknown variable, D/E ratio is used the market value before the gearing changed.

Step 2: Estimate cost of debt (Kd) at new gearing ratio.

Step 3: calculate the new cost of equity (Keg) by regearing the new debt / equity ratio, the formulae is same as step 1, but the Keg is unknown variable:


The Debt and Equity is used the new gearing ratio after company adjusting its capital structure.

Step 4: Calculating the WACC in a new gearing ratio.

WACC =

Example 2: D plc (beta is not given)

D plc is a heavy weapons manufacturer whose equity: debt ratio is 60:40. The corporate debt yields 6% before tax. The current cost of equity is 12.4%.

The company is considering to increase its gearing ratio to 50% (gearing ratio is defined as D/(D+E) on market value basis). Company estimate the before tax cost of debt may rise to 6.2%. Corporation tax is 30%.

Required:

Calculate the company's WACC after gearing change

Existing WACC

WACC =

WACC = 9.12%

Adjusting WACC after gearing change

Step1: calculate the Keu of company



Step 2: Estimate cost of debt (Kd) at new gearing ratio.

Kd = 6.2%

Step 3: calculate the new cost of equity (Keg) by regearing the new debt / equity ratio.



Step 4: Calculating the WACC in a new gearing ratio.

WACC =

WACC = 8.82%

Notes: In examination question, if students are not given the cost of debt after changing capital structure, it is reasonable to assume that the cost of debt remain unchanged if gearing level dose not change too much. For example, in this question, if the cost of debt under new gearing of 6.2% is not given, we can still use existing cost of debt of 6% at step 3.

THE ASSUMPTIONS AND RECOMMENDATION 

Some students may argue that we should use adjust present value (APV) method to evaluate a project when gearing / financial risk changes. This is correct. APV does not seek to adjust the discount rate; it evaluates both a project and its proposed financing package separately.

APV = Base case NPV + PV of financing side effects

In practice, we assume that the formulas for degear and regear are used in the circumstance where the capital structure changes in a relative small and steady manner, but if the firm plans significant changes in capital structure, the formula will not work, and you should turn to the APV method.

To sum up, I recommend to students that: in real exam if you are given the new gearing ratio after capital structure changed, we should use degear and regear formulas, if you are not told the new gearing ratio, use APV method.

REFERENCE

1. Brealey / Myers / Allen Corporate Finance: 8th edition, McGraw Hill International Edition, pp 516-525, 2006.

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