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### The Cost of Capital for Foreign Investments

P.V. Viswanath

International Corporate Finance

Based on Alan Shapiro, “Multinational Financial Management”

The cost of capital

- In what follows, we will assume that the subsidiary or project cashflows have been restated in dollars. Hence the issue is coming up with a discount rate that is appropriate for dollar flows.
- In principle, the cost of capital used should be a forward-looking rate. However, in practice, the components of the cost of capital are often estimated using historical data.
- While this is unavoidable, historical estimates should be used with care.
- An alternative method is to use the Adjusted Net Present Value approach, where the project is valued as a stand-alone all equity project and impact of the the different financing frictions are added to this base value.

P.V. Viswanath

The WACC

- If the financial structure and risk of a project is the same as that of the entire firm, then the appropriate discount rate is the Weighted Average Cost of Capital (WACC):

- where
- ko = WACC
- L = the firm’s debt-to-assets ratio (debt ratio)
- id = before-tax cost of debt
- ke = cost of equity
- t = marginal tax rate of the firm
- However, in using the WACC for project selection, the L used must be the target debt ratio.

P.V. Viswanath

The cost of equity

- According to the CAPM, the required rate of return on an asset is given as:

- Rf = risk-free rate
- bi = beta of asset i, a measure of its non-diversifiable risk.
- In principle, the CAPM applies to all assets, but in practice –
- It is used to estimate the cost of equity
- It is rarely used to estimate the cost of debt because it is very difficult to estimate a beta for debt securities.

P.V. Viswanath

Beta Risk of Foreign Projects

- Foreign projects in non-synchronous economies should be less correlated with domestic markets.
- Paradox: LDCs have greater political risk but offer higher probability of diversification benefits.
- Where there are barriers to international portfolio diversification, corporate international diversification can be beneficial to shareholders.
- Studies have shown that international index movements explain returns on domestic companies, after accounting for the domestic component of US indexes. This suggests that there is a significant benefit from the ability of multinational corporations to invest abroad.

P.V. Viswanath

Issues in estimating cost of capital for foreign projects

- In order to estimate a beta for the foreign subsidiary, a history of returns is required. Often this is not available. Hence, a proxy may have to be used, for which such information is available.
- Should corporate proxies be local companies or US companies?
- The beta is the estimated slope coefficient from a regression of the stock returns against a base portfolio, which is the global market portfolio, according to the CAPM. However, this assumes that markets are integrated.
- In practice, is the relevant base portfolio against which proxy betas are to be estimated, the US market portfolio, the local portfolio, or the world market portfolio?
- Should the market risk premium be based on the US market or the local market or the world market?
- How should country risk be incorporated in the cost of capital?

P.V. Viswanath

The Correct Approach in Principle

- If we assume that the multinational in question is a US multinational with investors who are globally diversified, then, in principle, the beta of the foreign subsidiary should be estimated with respect to a global market portfolio, and a global market risk premium should be used.
- Furthermore, if cashflows are measured in dollars, the right risk-free rate to be used is also the US Treasury rate.

P.V. Viswanath

The Correct Approach in Principle

- However, in practice,
- US investors may not be globally diversified, and
- It may be easier to obtain US data than global data
- Consequently, US MNEs often evaluate projects from the viewpoint of a US investor, who is not diversified internationally.
- Furthermore, a recent study (2004) showed that a cost of capital estimated using a domestic CAPM model is insignificantly different from a cost of capital computed using global risk factors.
- Consequently, the base portfolio used for beta estimation is a US index (such as the S&P 500).
- Furthermore, since US projects are evaluated using a US base portfolio, foreign projects can be compared to a US project, if the base portfolio is the same US market in both cases.

P.V. Viswanath

Proxy Companies

- Since we want a proxy as similar as possible to the project in question, it makes sense that we use a local company.
- The return on an MNC’s local operations will depend on the evolution of the local economy.
- Using a US proxy is likely to produce an upward biased estimate for the beta.
- This can be seen by looking at the definition of the foreign market beta with respect to the US market:
- Foreign companies are likely to have lower correlation with the US market than US companies.

P.V. Viswanath

Proxy Companies

- If foreign proxies in the same industry are not available (say because of data issues), then a proxy industry in the local market can be used, whose beta is expected to be similar to the beta of the project’s US industry.
- Alternatively, compute the beta for a proxy US industry and multiply it by the unlevered beta of the foreign country relative to the US. This will be valid, if:
- The US beta for the industry is the same as that of that industry in the foreign market as well, and
- The only correlation, with the US market, of a foreign company in the project’s industry is through its correlation with the local market and the local market’s correlation with the US market.

P.V. Viswanath

The Relevant Market Risk Premium

- Again, in principle, one would want the global risk premium. However, if the base portfolio used is a US one, then the market risk premium, too, should be based on the US market.
- As before, US markets have much more historical data available, and it is a lot easier to estimate forward-looking risk premiums for the US market.

P.V. Viswanath

Summary

- Find a proxy firm/portfolio in the country in which the project will be located.
- Calculate its beta relative to the US market.
- Multiply this beta by the risk premium for the US market to get a project risk premium.
- Add this risk premium to the long-term US nominal risk-free rate to obtain a dollar cost of equity capital.

P.V. Viswanath

Country Risk Premiums

- The previous approaches that use US base portfolios and/or US proxies effectively ignore country risk, assuming that it is diversifiable. However, this may not be the case. In fact, with globalization, cross-market correlations have increased, leading to less diversifiability for country risk.
- Furthermore, it may not be enough to look at the beta alone of a foreign project\'s beta, because this only deals with contribution to volatility.
- Skewness or catastrophic risk may be significant in the case of emerging markets. The impact of a project on the negative skewness of the equityholder\'s portfolio could be significant and should be taken into account.

P.V. Viswanath

Country Risk Premiums

- For example, India\'s beta could be negative, but it would not be appropriate to discount Indian projects at less than the US risk-free rate.
- If investors do not like negative skewness (i.e. the likelihood of catastrophic negative returns), we should augment the CAPM with a skewness term.
- An alternative would be to estimate a country risk premium based on the riskiness of the country relative to a maturity market like the US, and to incorporate this into the cost of equity of the project.

P.V. Viswanath

Estimating Country Premiums

- Country Premiums may be estimated by looking at the rating assigned to a country’s dollar-denominated sovereign debt.
- One can then look at the spread over US Treasuries or a long-term eurodollar rate for countries with such ratings (sovereign risk premium). This spread would be a measure of the country risk premium.
- One could also look at the spread for US firms’ debt with comparable ratings.
- Optionally, one might then adjust this spread by the ratio of the standard deviation of equity returns in that country to the standard deviation of bond returns – to convert a bond premium to an equity premium.

P.V. Viswanath

Using the Country Premium

- The country risk premium that is obtained can then be used in two ways:
- One, it could be added to the cost of equity of the project. This assumes that the country risk premium applies fully to all projects in that country
- Two, one could assume that the exposure of a project to the country risk is proportional to its beta. In this case, one would add the country risk premium to the US market risk premium to get an overall risk premium. This would then be multiplied by the beta as before to obtain the project-specific risk premium.

P.V. Viswanath

Using the Country Risk Premium

- Finally, one could take the US market risk premium and multiply it by the ratio of the volatility of stock returns in the foreign country to the volatility of stock returns in the US.
- This is the country-risk adjusted market risk premium.
- As before, then, this market risk premium would be multiplied by the beta of the project to get the project-specific risk premium.

P.V. Viswanath

Adjusting for Country Risk

- Suppose the market risk premium in US markets is 5.5%
- The market risk premium in Germany is 8%
- The yield on US 10 year treasuries is 5%
- The yield on German government bonds is 6%
- The world nominal risk-free rate (computed as the lowest risk-free rate that can be obtained globally, for borrowing in dollars – or otherwise adjusted for exchange rate risk) is also assumed to be 5%

P.V. Viswanath

Adjusting for Country Risk

- Project beta with respect to the German market is 1.2
- Beta with respect to US market is 1.0
- Beta with respect to an international equity index is 1.1
- The volatility of returns (std devn) on a broad-based US market index is 25% per year.
- The volatility of returns on a broad-based German index is 35% per year.
- The volatility of returns on a broad-based world index is 30% (returns measured in dollars)

P.V. Viswanath

Adjusting for Country Risk

- Reqd. ROR = US Riskfree rate + bi(Market Risk Premium)
- If the investors in the project are investors who hold domestic (US) diversified portfolios, then we use US quantities.
- If country risk is diversifiable or can otherwise be ignored,
- Reqd ROR = 5% + 1 (5.5) = 10.5%, and country risk premium is set at zero.
- If the investors are internationally diversified, then
- Reqd ROR = 5% + 1.1 (5.5) = 11.05%, and country risk premium is set at zero.
- If we take a weighted average of the two rates (in this example, we use 65-35 weights), we get 0.65(10.5) + (0. 53)(11.05) = 10.6925%

P.V. Viswanath

Adjusting for Country Risk

- If we believe that country risk is not diversifiable and/or is not otherwise captured in the beta computation or that it captures other kinds of risk that go beyond variability risk, we need to adjust for country risk.
- Add sovereign risk premium to the required rate of return:(If we are worrying about country risk premiums, we’re probably discounting the existence of a single international asset pricing model, since it implies an integrated world; strictly speaking, we could still hold that an international asset pricing model holds, but it is not a mean-variance model. We will ignore this here.)
- This gives us 5% + (8 - 5) + 1(5.5) = 13.5%

P.V. Viswanath

Adjusting for Country Risk

- If we assume that the country risk premium is shared by the project only to the extent that it moves with the market, then we’d get
- Required ROR = 5% + 1(5.5 + 3) = 13.5% (in this case, the rate doesn’t change) from 1.
- If we say that the country risk premium is shared by the project only to the extent that it moves with its local market:
- Reqd ROR = 5% + 1 (5.5) + (1.2)(3) = 14.1%,
- Amplifying CAPM beta by volatility ratio:
- Amplified beta = 1x(35/30)
- Hence the required rate of return is = 5% + 1(35/30)(5.5) = 11.42%

P.V. Viswanath

The Cost of Debt Capital

- Suppose Alpha S.A., a French subsidiary of a US firm borrows €10m. for 1 year at an interest rate of 7%. If the current rate is $0.87/€, this would be a $8.7m. loan.
- If the end-of-year rate is expected to be $0.85/€, the dollar cost of the loan is only 4.54%, since (10.7)(0.85)/8.7 = 1.0454.
- In general, the dollar cost of a foreign currency loan with an interest rate of rL and a depreciation of the home currency of c% per year is given by rL(1 + c) + c.
- If the loan is taken by a foreign subsidiary and the interest can be deducted for tax purposes, where the tax rate is ta, then the effective dollar rate is r = rL(1+c)(1‑ta) + c.

P.V. Viswanath

The Cost of Debt Capital

- In general, the effective dollar interest rate is, r, where:
- c is the annual rate of appreciation of the local currency
- rL is the coupon rate of the loan
- ta is the affiliate’s marginal tax rate

- However, the solution to this general problem is the same as the solution to the single period problem.
- Finally, we put the cost of debt and the cost of equity together to get the WACC.

P.V. Viswanath

Problem 3, Chapter 14

- IBM is considering having its German affiliate issue a 10-year $100m. Bond denominated in euros and priced to yield 7.5%. Alternatively, IBM’s German unit can issue a dollar-denominated bond of the same size and maturity and carrying an interest rate of 6.7%.
- If the euro is forecast to depreciate by 1.7% annually, what is the expected dollar cost of the euro-denominated bond? How does this compare to the cost of the dollar bond?

P.V. Viswanath

Problem 3, Chapter 14

- The pre-tax $ cost of borrowing in euros at a interest rate of rL, if the euro is expected to depreciate against the dollar at an annual rate of c, is rL(1 + c) + c. There is a “depreciation penalty applied to the interest (first term) and to the principal (second term).
- In this case, we get an expected $ cost of borrowing euros of 7.5(1-0.017)-1.7 or 5.67. This is below the 6.7% cost of borrowing $s.
- If the German unit is taxed at ta, the ta, is r = rL(1+c)(1‑ta) + c. Thus, if ta = 35%, r = 7.5(1-0.017)(1-0.35) - 0.017, or 4.78%.

P.V. Viswanath

Establishing a Worldwide Capital Structure

- As capital structure theory teaches us, the capital structure for the global firm as a whole should be determined, based on:
- Volatility of worldwide earnings
- Bankruptcy cost
- Marginal Tax rate
- Nature of business and product/service.
- Since foreign operations may provide diversification and reduce earnings variability, an MNE may able to use more debt than a purely domestic corporation.

P.V. Viswanath

Foreign Subsidiary Capital Structure – I

- The capital structure of the foreign subsidiary is relevant only if the parent company is willing to allow the subsidiary to default on its debt; else there is only one capital structure.
- Even though, formally, there may be different capital structures for the parent and the subsidiary, in effect there is a single capital structure, that of the consolidated corporation.
- Alternatively, if the subsidiary issues debt, collateralized by its own assets or cash flows from local projects, without recourse to the parent, one can talk of a subsidiary capital structure.

P.V. Viswanath

Foreign Subsidiary Capital Structure – II

- If the parent is borrowing the money and investing it in the subsidiary, then it does not really matter whether the investment in the subsidiary is called debt or equity.
- This is also equivalent to the case where the subsidiary borrows the money directly from a bank, instead of the parent borrowing it (assuming that the debt is guaranteed by the parent).
- In all these cases, the global debt-equity ratio will be the same – that of the parent.

P.V. Viswanath

Other Considerations

- Borrowing in the local currency can help reduce foreign exchange exposure. This may reduce the volatility or beta risk of the cashflows expressed in dollars. It should, in any case, reduce bankruptcy risk.
- Borrowing globally may be cheaper from a tax point of view; local government subsidies may be available, too.
- Lending money to a subsidiary might mean easier repatriation of profits to the parent than structuring the investment in the subsidiary as equity.
- Raising funds locally can be useful if there is political risk. In case of expropriation, the parent can default on loans by local banks to the subsidiary.
- If funds can be raised in the foreign market with payment to be made with local cashflows alone and no recourse to the parent, this could reduce the likelihood of expropriation, as well.

P.V. Viswanath

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