Question

A U.S. based MNC has the following two sets of information, one for its domestic operations and one for its global operations:

Domestic:

Standard deviation of the company’s return = 18% p.a.

Covariance of the company’s return with the U.S. stock market returns = 270

Global:

Standard deviation of the company’s return = 24% p.a.

Covariance of the company’s return with the global stock market returns = 144

In addition, the following market information is available:

U.S. stock market risk premium = 12% p.a.

Standard deviation of the U.S. stock market = 20% p.a.

The risk-free rate in the U.S. = 3% p.a.

Expected return on the global stock market = 20% p.a.

Standard deviation of the global stock market = 30% p.a.

Show whether the cost of equity for domestic operations is higher or lower than that of global operations. Analyze on all levels and for all components and explain the difference in the two costs?

Answer 1

The cost of equity can be calculated with the help of the CAPM (capital asset pricing model) model. Cost of equity can be represented as K(e) and can be calculated as:

K(e)= RFR+Beta*MRP

Where,

• RFR is Risk-free rate
• MRP is Market risk premium and calculated as Equity market returns minus Risk-free rate.

Let us first look at the cost of equity for domestic operations:

As given in the question:

Domestic:

Standard deviation of the company’s return = 18% p.a.

The covariance of the company’s return with the U.S. stock market returns = 270

U.S. stock market risk premium = 12% p.a.

The standard deviation of the U.S. stock market = 20% p.a.

The risk-free rate in the U.S. = 3% p.a.

To calculate the cost of equity, we need to first find the beta (not given):

Beta can be calculated as covariance of the return of an asset with the return of the benchmark divided by the variance of the return of the benchmark over a certain period.

The formula is, Beta= Covariance (Ra, Rb) / Variance (Rb)

Ra- Return of an asset, Rb- Return of the benchmark.

Again, Variance is not given and can be calculated as Squared of standard deviation. We need a Variance of the return of the benchmark.

Variance (Rb) = (The standard deviation of the U.S. stock market)^2 = (20% p.a.)^2 = 4%

Let us go back to find the Beta,

Beta = Covariance (Ra, Rb) / Variance (Rb) = 2.7/4 = 0.675

Please note: I am assuming it is 270 basis points as 270 is not a possible number.

Now we have all the data to find the cost of equity using the CAPM model:

K(e) = RFR+Beta*MRP = 3%+(0.675*12%) = 11.1%

Hence, the cost of equity for domestic operations is 11.1%.

Let us now look at the cost of equity for global operations:

As given in the question:

Standard deviation of the company’s return = 24% p.a.

The covariance of the company’s return with the global stock market returns = 144

The risk-free rate in the U.S. = 3% p.a.

Expected return on the global stock market = 20% p.a.

Standard deviation of the global stock market = 30% p.a.

To calculate the cost of equity, we need to first find the beta (not given):

Beta can be calculated as covariance of the return of an asset with the return of the benchmark divided by the variance of the return of the benchmark over a certain period.

The formula is, Beta= Covariance (Ra, Rb) / Variance (Rb)

Ra- Return of an asset, Rb- Return of the benchmark.

Again, Variance is not given and can be calculated as Squared of standard deviation. We need a Variance of the return of the benchmark.

Variance (Rb) = (The standard deviation of the Global stock market)^2 = (30% p.a.)^2 = 9%

Let us go back to find the Beta,

Beta = Covariance (Ra, Rb) / Variance (Rb) = 1.44/9= 0.16

Please note: I am assuming it is 144 basis points as 144 is not a possible number.

Now we have all the data to find the cost of equity using the CAPM model:

K(e) = RFR+Beta*MRP = 3%+(0.16*17%) = 5.72%

MRP here is calculated as

Expected return on the global stock market = 20% p.a. minus The risk-free rate in the U.S. = 3% p.a.

Hence, the cost of equity for global operations is 5.72%.

Therefore, the cost of equity for domestic operations is higher than that of global operations.