Traditional NPV& WACC
Modigliani and Miller meet
CAPM
PWC Course Notes P62
ACCA Paper P4
Also suitable for ICAEW, ICAS, CFA etc
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1
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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2
Traditional NPV
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
Assumptions
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%, return on the market portfolio 9%
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3
Traditional NPV
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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4
Traditional NPV

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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5
Traditional NPV
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 6the 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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7
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
Debt is risk free so 2nd
𝑉𝑒
𝛽𝑎=
half of the equation is
𝛽
𝑉𝑒+𝑉𝑑 (1−𝑇) 𝑒
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=
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𝑉𝑒
𝑉𝑒+𝑉𝑑 (1−𝑇)
𝛽𝑒
Debt is risk free so 2nd
half of the equation is
omitted
0.71= 4/(4+0.7) 𝛽𝑒 , therefore 𝛽𝑒 = 0.83
Having got the equity beta we can derive the 𝑘𝑒 of the project
𝑘𝑒 = 6 + 0.83(9-6)= 8.5%
The project though will be funded with debt and equity so we
need WACC
WACC (8.5x0.8) + (6x 0.2)= 8%
9
The discount rate is therefore 8%