Adjusted Present Value
Modigliani and Miller meet
CAPM
PWC 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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APV
Wyke
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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APV
To 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 𝐾𝑒 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 𝑘𝑒 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 𝛽 that
reflects the project gearing and the industry risk

Put new 𝛽 in CAPM and we get project 𝑘𝑒
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APV Step 1
We use the formula
𝛽𝑎=
𝑉𝑒
𝑉𝑒+𝑉𝑑 (1−𝑇)
𝛽𝑒
+
𝑉𝑑
𝑉𝑒+𝑉𝑑 (1−𝑇)
𝛽𝑑
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
𝛽
1
𝑎=
1.2 =0.71
1+(1𝑥0.7)
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 7the ungeared beta of the
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Freezer distribution industry. Debt is risk free so debt beta is zero
Asset Beta

Remember your beta reflects 2 things. Market risk
(CAPM) & gearing (M&M)

M&M said that the relationship between gearing and
𝐾𝑒 is linear, so we can take it out

β 𝑎 therefore is a beta that only represents business
risk with no gearing
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APV Step 1

REMEMBER M&M1

Therefore degearing regearing etc will have no effect on WACC
according to M&M, so we discount out cash flow at 𝐾𝑒 derived from
the ungeared β

Β = 0.71

Therefore 𝐾𝑒 = 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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Capital Structure is independent of gearing
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APV Step 2- The Tax Shield
Step 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




APV
Steps
Take β 𝑒 of Newco, take out Newco
gearing
Gives β 𝑎 for new industry.
Regear β 𝑎 for project finance to get
β 𝑒 of project

Put β

Combine with K 𝑑 to get WACC
That is your discount rate
Discount cash flow
If positive accept



𝑒
in CAPM , get K
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𝑒

Steps

Take β 𝑒 of Newco, take out Newco
gearing

Gives β

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
𝑎
for new industry.
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