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«What is the riskfree rate? A Search for the Basic Building Block Aswath Damodaran Stern School of Business, New York University ...»

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The Scenario In many countries (and their associated currencies), the biggest roadblock to finding a riskfree rate is that the government does not issue long term bonds in the local currency. So, how do they borrow? Many choose to use commercial bank loans, the World Bank or the IMF for their borrowing, thus bypassing the rigors of the market; this is true for most of the countries that comprise sub-Saharan Africa, for instance. Quite a few governments issue long term bonds, but in the currencies of more mature markets, rather than their own currencies. From 1992 to 2006, the Brazilian government issued long-term bonds denominated in US dollars rather than Brazilian Reais. In 2008, only 3 of the 12 South American countries had long-term bonds denominated in local currencies. Finally, there are governments that issue long term bonds, but then proceed to either offer special incentives to domestic investors (such as tax breaks) or use coercion to place these bonds, resulting in rates on these bonds that are not realistic.

Common (and dangerous) practices When there are no long term government bonds in the local currency that are widely traded, analysts valuing companies in that market often take the path of least resistance when estimating both cash flows and discount rates, resulting in currency mismatches in their valuations. With discount rates, analysts decide that is easier to estimate riskfree rates and risk premiums in a mature market currency; with Latin American companies, for instance, the currency of choice is the US dollar and the discount rates are estimated in US dollars. With cash flows, analysts either stick with local currency cash flows or convert those cash flows at the current exchange rate into a mature market currency; with Latin American companies again, the cash flows in the local currency are converted into US dollars using current exchange rates. If the value of the company is computed using these cash flows and discount rates, the resulting value will be fatally flawed because the expected inflation built into the cash flows will be different from the expected inflation built into discount rates. Consider, for instance, a Mexican company where the cash flows are estimated in pesos and the discount rate is estimated in the US dollars. Since the expected inflation rate in pesos is about 5% and the inflation rate built into the US dollar discount rate is only 2%, we will over value the company. Note that converting the peso cash flows into dollar cash flows, using currency exchange rates, does nothing to alleviate this problem.

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Note that the terminal value is computed at the end of year 3:

Terminal value = 60.50 (1.06)/ (.09-.06) = $ 2,137.67 By using the current exchange rate to convert future BR cash flows into US dollars, we have in effect built in the 6% inflation rate in BR into the expected cash flows, while using a discount rate that reflects the 2% inflation rate in US dollars. In addition, the terminal value has been computed using a growth rate in nominal BR and a discount rate in US dollars. Not surprisingly, the mismatch in inflation rates leads us to over value the company.

Possible solutions If the government does not issue long-term local currency bonds (or at least ones that you can trust to deliver a market interest rate), we have two solutions that preserve consistency. One is to estimate discount rates in a mature market currency (rather than the local currency) and then convert the cash flows into the mature market currency as well. The other is to try to estimate a local currency discount rate, troubles with the riskfree rate notwithstanding.

Mature market currency valuation:

Since the value of a company, done right, should not be a function of what currency we choose to do the valuation in, one solution is to value the company in an alternate (mature market) currency. If getting a riskfree rate in Brazilian Reais is too difficult to do, a Brazilian company can be valued entirely in US dollars or Euros. To do this right, we have to first estimate the discount rate in US dollars. As we noted in the last section, the right riskfree rate to use will be the US treasury bond rate (and not the tenyear $ denominated Brazilian bond rate, which has an embedded default spread in it). To be consistent, the cash flows, which will generally be in Reais, will have to be converted into US dollar cash flows. This conversion has to be made using the expected US dollar/ Reai exchange rate and not the current exchange rate. While forward or futures markets may provide estimates for the near term, the best way to estimate future exchange rates is

by using purchasing power parity, based on expected inflation in the two currencies:

(1 + Expected Inflation Rate Brazilian Reai ) t Expected Reais/ $ in period t =Current Rate* (1 + Expected Inflation Rate US $ ) t Using this expected exchange rate will ensure that the inflation built into the expected cash flows is consistent with the inflation embedded in the discount rate.

€ Illustration 2: Valuing in Mature Market Currency Let us revisit the valuation in illustration 2. Instead of using the current exchange rate, we will use the expected BR/$ exchange rate, estimated using the inflations rates of 6% in BR and 2% in US dollars, to convert the cash flows into dollars:

Cash flow in Exchange Exchange Cash fow in Present Year BR Rate (BR/$) Rate ($/BR) US $ Value 1 100 2.0784 0.481132075 $48.11 $44.14

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The higher inflation rate in BR leads to a depreciation in the currency’s value over time.

In addition, the terminal value is computed using the US dollar cash flow of $53.91 million in year 3 and an expected growth rate of 2% (reflecting the inflation rate in US

dollars and not in BR):

Terminal value = $53.91 (1.02)/ (,09-.02) = $785.49 million The value that we derive for the firm today is $735.17 million (1,470.35 million BR) and it reflects more consistent assumptions about inflation in the cash flows and discount rates and is much lower than the value of $1,789.55 million that we derived in illustration 1.

Local Currency valuation The valuation can be done in the local currency, with the discount rate converted into a local currency discount rate; the expected cash flows in this case will remain in the local currency. There are three ways in which we can overcome the absence of a local currency, long term government bond rate as a starting point. In the first two, we try to estimate a local currency risk free rate, with estimates of inflation, and in the third, we convert a foreign currency discount rate, using expected inflation rates.

o The build-up option: Since the riskfree rate in any currency can be written as the sum of expected inflation in that currency and the expected real rate, we can try to estimate the two components separately. To estimate expected inflation, we can start with the current inflation rate and extrapolate from that to expected inflation in the future. For the real rate, we can use the rate on the inflation indexed US treasury bond rate, with the rationale that real rates should be the same globally. In 2005, for instance, adding the expected inflation rate of 8%, in India, to the interest rate of 2.12% on the inflation indexed US treasury would have yielded a riskfree rate of 10.12% in Indian rupees.

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9 In cases where only a one-year forward rate exists, an approximation for the long term rate can be obtained by first backing out the one-year local currency borrowing rate, taking the spread over the oneyear treasury bill rate, and then adding this spread on to the long term treasury bond rate. For instance, with a one-year forward rate of 39.95 on the Thai bond, we obtain a one-year Thai baht riskless rate of 9.04% (given a one-year T.Bill rate of 4%). Adding the spread of 5.04% to the ten-year treasury bond rate of 5% provides a ten-year Thai Baht rate of 10.04%.

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The terminal value is estimated using the nominal growth of 6% in BR and the BR cost

of capital:

Terminal Value = 121 (1.06)/ (.1327-.06) = 1763.1428 million BR Note that the value of the firm is 1,470.35 million BR. Identical to the valuation that we obtained when we valued the company in US dollars in illustration 2.

The government is not default free We have hitherto assumed that governments are default free, at least when it comes to borrowing in the local currency. That assumption, reasonable thought it may seem, can be challenged in some countries where investors build in the likelihood that of default risk into government bonds.

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To the extent that we accept Moody’s assessment of country risk, the long term, local currency bonds issued by each of these governments will have default risk embedded in them, with the risk being greater in the Brazilian government bond than it is in the Chinese government bond.

Common (and dangerous) practices When there are local currency long term bonds, analysts often choose to use the market interest rate on these bonds, notwithstanding the default risk embedded in them, as riskfree rates. To illustrate, the interest rate on long term, rupee denominated bonds issued by the Indian government in October 2008, which was 10.7%, would be used as the riskfree rate in computing the rupee cost of equity and capital for an Indian company.

As table 2 shows, India’s local currency rating of Baa3 suggests that there is default risk in the Indian rupee bond, and that some of the observed interest rate can be attributed to this risk. While it may seem reasonable that rupee discount rates should be higher to reflect the Indian government risk, the danger of building it into the riskfree rate is that the risk may end up being double counted. Analysts who use 10.7% as the riskfree rate for rupee discount rates often also use higher equity risk premiums for India; in fact, one approach to adjusting equity risk premiums in emerging markets is to add the default spread for the country to mature market equity risk premiums.

The Solution Since the problem in this case is that the local currency bond rate includes a default spread, the solution is a fairly simple one. If we can estimate how much of the current market interest rate on the bond can be attributed to default risk, we can strip this default spread from the rate to arrive at an estimate of the riskfree rate in that currency.

Using the Indian rupee bond again as the illustration, we used the local currency rating for India as the measure of default risk to arrive at a default spread of 2.6%. Subtracting this from the market interest rate yields a riskfree rupee rate of 8.10%.

Riskfree rate in Indian rupees = Market interest rate on rupee bond – Default SpreadIndia = 10.70% - 2.60% = 8.10% How did we go from a rating to a default spread? In table 3, we have estimated the typical default spreads for bonds in different sovereign ratings classes. One problem that we had in estimating the numbers for this table is that relatively few emerging markets have dollar or Euro denominated bonds outstanding. Consequently, there were some ratings classes where there was only one country with data and several ratings classes where there were none. To mitigate this problem, we used spreads from the CDS market, referenced in the earlier section. We were able to get default spreads for almost 40 countries, categorized by rating class, and we averaged the spreads across multiple countries in the same ratings class.10 An alternative approach to estimating default spread is to assume that sovereign ratings are comparable to corporate ratings, i.e., a Ba1 rated country bond and a Ba1 rated corporate bond have equal default risk. In this case, we can use the default spreads on corporate bonds for different ratings classes. Table 3 also 10 For instance, Turkey, Indonesia and Vietnam all share a Ba3 rating, and the CDS spreads as of September 2008 were 2.95%, 3.15% and 3.65% respectively. The average spread across the three countries is 3.25%.

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