# S2_2 - Art Durnev

## GROWING ECONOMIES

1

### Cost of Equity, Flexible Approach

General Model

where

R f

SR

denotes risk-free rate,

MRP

the world market risk premium, specific risk of the investment, and

A

.

Four Different Models

 two inputs (

R f

and by all four models

MRP

) on the basis of

worldwide markets

are shared

 two other inputs

SR

and

A

differ across the models

1.

The Lessard Approach

2.

The Godfrey-Espinosa Approach

3.

The Goldman Sachs Approach

4.

The SalomonSmithBarney Approach

2

### The Lessard Approach

 measures specific risk (

SR

) as the product of a project beta (

β p

) and a country beta (

β c

):

SR

where

β p

and

β c

capture the risk of industry and country, respectively.

 cost of equity when investing in industry

p

and country

c

is:

β p

(

β c

) is estimated as the beta of the industry (country) with respect to the world market, and no further adjustment (

A

is assumed to be zero)

3

### The Godfrey-Espinosa Approach

 Two adjustments with respect to CAPM:

1)

R f

by the yield spread of a country relative to the U.S. (

YS c

)

A

=

YS c

2)

Measuring risk as 60% of the volatility of local market relative to world market

(

σ c

/

σ w

)

SR

= (0.60)·

(

σ c

/

σ

W

)

where

σ c

and

σ w

of country

c

are the standard deviation of returns of stock market and world, respectively.

● cost of equity when investing in industry

p

and country

c

is:

● this model ignores the specific nature of the project, but all that matters is the country in which the foreign company invests

4

### The Goldman Sachs Approach

● one adjustments with respect to

Godfrey-Espinosa Approach

:

● replacing 0.60 by one minus the observed correlation between the stock market and bond market of the country

c

.

SR

=

(1–

SB

)

·

(

σ c

/

σ

W

) where

SB

is the correlation between stock and bond markets

.

● cost of equity when investing in country

c

is:

● intuition of the model

SB

= 0

 no correlation, two sources of risk (stock and bond)

SB

= 1

YS c

captures all relevant risk

0<

SB

<1

 the model incorporates both risk from bond and stock markets, but not double counting sources of risk

5

### The SalomonSmithBarney Approach

 account for the risk of investing in Specific Industry and/or Country

 adjustments with respect to previous models :

1)

2)

3)

Political risk (

1

: between 0 and 10)

Risk of accessing capital markets (

2

: between 0 and 10)

Financial importance of the project (

3

: between 0 and 10)

A

= { (

1+

2+

3

) / 30}·

YS c

 intuition of the model

1 is a rough estimate of the likelihood of expropriation (e.g., oil industry)

2 is low for large firms and high for small undiversified firms

3 is low for large firms investing in relatively small projects and high for small firms investing in relatively large projects

6

### The SalomonSmithBarney Approach – continued

 intuition of the model

 worst scenario

A

=

YS c

; the best case

A

= 0

For example, a large international firm investing a small proportion of its capital in an industry unlikely to be expropriated (

A

= 0)

A small undiversified company investing a large proportion of its capital in an industry likely to be expropriated would have to incorporate a full adjustment for political risk (

A

=

YS c

)

 quantify

SR

(specific risk) with the project beta, then the cost of equity when investing in industry

p

and country

c

is:

 this model, different from three previous ones, can allow discount rate to depend on not only specific project but also the company

7