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Adjusted Present ValueModigliani and Miller meet CAPMPWC Course Notes P62

ACCA Paper P4

Also suitable for ICAEW, ICAS, CFA etc

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APV We are going to undertake a project appraisal calculation

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

The APV is an alternative to NPV

It can give a different decision from NPV

It is not used in real life but is frequently examined

IT IS BASED ON MODIGLIANI & MILLER

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APV

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 cash flow for the proposed freezer distribution business but does not know at what rate to discount it

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APVWyke 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

Other Information• Corporate debt is risk free, corporate tax is charged at 30%• The project will be financed in the same ratio as existing capital in Wyke• Return on treasury bills is 6% pa, return on the market portfolio 9% pa• The project shows an initial investment will be required of $7.5m• Net cash flows will be $1.1m for 5 years• Issue costs will be 2% for debt and 5% for equity, both of gross sum raised• Debt will be a 5 year loan payable at the end of the project

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APVTo 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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APV Step 1

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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APV Step 1

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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APV Step 1 REMEMBER M&M1 Capital Structure is independent of gearing

Therefore degearing regearing etc will have no effect on WACC according to M&M, so we discount out cash flow at derived from the ungeared β

Β = 0.71

Therefore = 0.71(6+ (9-6))= 6.39%

Using 6%

Inflows are 5.6371 x 1.1m= 6.2m

Initial investment 7.5m

Therefore net (1300k)

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APV Step 2- The Tax ShieldStep 3 Things That Shouldn’t Exist!

Step 2 Tax Shield But M&M said that debt raised was tax deductible, so we

take into account the tax relief on debt interest 7.5m x 20% x 30% x 5.6371= 2537 Step 3- Market Inefficiencies Issue costs Equity [(6m/0.950)-6m]= 316 Debt [(1.5m/0.98)-1.5m]= 31 Total issue costs (347)

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APV Summary

Cash flow (1300) Tax Shield 2537 Other Items (347) Result +890

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Comparison of NPV and APV

NPV

Steps Take of Newco, take out Newco

gearing Gives for new industry. for project finance to get of

project Put in CAPM , get Combine with to get WACC That is your discount rate Discount cash flow If positive accept

APV Steps

Take of Newco, take out Newco gearing

Gives for new industry.

This is your discount rate

Discount cash flow

Calculate PV of tax savings due to use of debt

Calculate benefits/costs of anything else ie issue costs

Add up 3 sections, if positive accept