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Traditional NPV& WACC Modigliani and Miller meet CAPMPWC Course Notes P62

ACCA Paper P4

Also suitable for ICAEW, ICAS, CFA etc

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Traditional NPV We are going to calculate the discount factor to be used in an NPV

calculation

Before you listen to this please make sure you are comfortable with CAPM and M&M

Wyke plc is a company that makes ice cream in Scotland

Wyke wants to expand into Europe. Europe has no surplus demand for ice cream but their market research shows that South Europe needs freezers. Wyke decides to investigate freezer distribution in S Europe.

Aranalde is a Spanish firm that distributes freezers throughout South Europe

Wyke has prepared a cashflow for the proposed freezer distribution business but does not know at what rate to discount it

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Traditional NPVWyke Aranalde

Equity Beta Geared 1.1 1.2

Gearing Ratio (Book Value, D:E)

1:1 3:7

Gearing Ratio (Market Value,D:E)

1:4 1:1

Cost of Debt % 6 6

AssumptionsCorporate debt is risk free, corporate tax is charged at 30%The project will be financed in the same ratio as existing capital in WykeReturn on treasury bills is 6%, return on the market portfolio 9%

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Traditional NPVTo Note

This technique is a combination of CAPM and M&M

We need a beta which reflects 2 things, the business risk of the new industry and the gearing risk of the project (here existing Wyke business)

CAPM says that risk (Beta) is related to market risk.

M&M say that is a direct linear function of gearing

If debt is risk free then the debt beta is zero

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Traditional NPV Calculation of for Wyke Freezer Distribution in S Europe

Therefore we take the beta of the new industry (Aranalde) and we remove the effect of Aranalde’s gearing.

This gives us an asset beta which reflects the freezer industry risk ungeared

We then include the (Wyke) project gearing, this will give us the that reflects the project gearing and the industry risk

Put new in CAPM and we get project

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Traditional NPV

𝛽𝑎=¿ ¿

We use the formula

+

So we need an asset beta which reflects the business risk of freezer distribution in Europe. If we take Aranalde’s beta it will reflect the business risk but also Aranalde’s gearing, so we degear Aranalde’s equity beta

𝛽𝑎= 1

1+(1𝑥 0.7 )   1.2=0.71

We must always use market values, the value of the equity to debt is 1:1. Aranalde’s beta reflects the business risk, the tax rate is 30%. The asset beta tells us the ungeared beta of the Freezer distribution industry. Debt is risk free so debt beta is zero

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Asset Beta

Remember your beta reflects 2 things. Market risk (CAPM) & gearing (M&M)

M&M said that the relationship between gearing and is linear, so we can take it out

therefore is a beta that only represents business risk with no gearing

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Traditional NPV

So the asset beta reflects the business risk but Wyke will use debt finance in part to fund the project we need therefore to factor that it

𝛽𝑎=¿ ¿

Debt is risk free so 2nd half of the equation is omitted

The asset beta therefore, as said , gives us the risk for an ungeared business distributing freezers in S Europe. But our business will not be ungeared, therefore we have to put in our project gearing

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Re-gearing the Asset Beta

Putting into the equation Wyke’s own gearing we get

𝛽𝑎=¿ ¿

Debt is risk free so 2nd half of the equation is omitted

0.71= 4/(4+0.7) , therefore = 0.83

Having got the equity beta we can derive the of the project = 6 + 0.83(9-6)= 8.5%The project though will be funded with debt and equity so we need WACCWACC (8.5x0.8) + (6x 0.2)= 8%The discount rate is therefore 8%