A decision of uncertainty:

## Introduction:

The chosen scenario in this case is an investment decision, the paper assumes that a business is faced with a decision to invest in municipal bonds available in the market, two municipal bonds with the highest yield to maturity are considered from yahoo finance (2010) and they include Jefferson county bonds and Columbia Ballpark bonds. The following is a discussion on the appropriate decision to be made given that the firm wants to invest in bonds that will yield higher returns and also have lower risk levels, whereby the level of risk is indicated by bond rating.

Research:

Given that the firm wants to invest in five year municipal bonds and that it has to choose only one bond then information regarding al the three bonds were collected, yahoo finance contained information about bonds and after researching on the available five year bonds issued by Jefferson country (IMP)and Columbia Ballpark bonds had the highest yield to maturity value, the following is summary of the information retrieved:

The Jefferson County (IMP) bond rating is CCC, YTM value is 9.465%, coupon rate is paid semi annually and the value is 5% and finally the price is \$80.71. Columbia ballpark bond which is a 5 year bond and the rating of this bond is AA, YTM value is 3.766%, coupon rate is paid semi annually and the value is 5.00% and finally the price is \$106.07.

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Decision of Uncertainty

Ratings are important in that they provide information regarding the probability that the issuers of the bond will default, there are a number of organizations that rate bonds and they include S\$P, Moody and Fitch, in this paper these ratings were retrieved from Moody (2009) website and the following table summarizes the probabilities that the different bond rates will default:

municipal default rates

rate

DEFUALT RATE (5 YEAR)

AAA

0.0000%

AA

0.0467%

A

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Decision of Uncertainty

0.0230%

BAA

0.1350%

BA

1.4445%

B

13.4901%

CAA

15.9469%

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Decision of Uncertainty

The information was retrieved from Moody’s (2009), from the above it is evident that the probability that an AAA 5 year bond will default is 0%, the probability that a CAA bond will default is 15.95%, from the above therefore it is evident that Jefferson county (IMP) is rated

CCC which is equivalent to CAA in the above scale, this means that there is a 15.95% probability of default, and for the Columbia Ballpark bonds is rated AA and this means that there is a 0.0467% chance of defaulting pay.

Interpreting data:

Using the above information a decision is constructed retaking into consideration the yields and price of each bond, Bayer’s theorem is used to calculate the probabilities, this is because probabilities on bond ratings are provided and therefore probability would be the most appropriate method to use.

bond

years

coupon

rate

yield  to maturity

price

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Decision of Uncertainty

value

returns

Jefferson country (IMP)

5

5%

9.47%

80.71

207.5639

126.8539

Columbia  Ballpark bonds

5

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Decision of Uncertainty

5%

3.77%

106.07

233.6751

127.6051

From the above calculations it is evident that approximately all the bonds have the same expected returns, however their price and default rates differ, the following table summarizes the joint probabilities of investing in the two bonds:

The probability of the company investing in Jefferson county (IMP) bonds is 0.5, probability of the firm investing in Columbia Ballpark bonds is also 0.5, the table below shows the probability of default for the two bonds:

J

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Decision of Uncertainty

defaults

15.95%

does  not default

84.05%

C

defaults

4.70%

does  not default

95.30%

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Decision of Uncertainty

Given that the probability of choosing Jefferson county (IMP) bonds is 0.5 and the probability of the firm investing in Columbia Ballpark bonds is also 0.5, then the probability values are determined as follows:

 – Invests in Jefferson county bonds and the company defaults = 0.5 * 0.1595 = 0.07975 – Invests in Jefferson county bonds and the company does not default= 0.5 * 0.8405= 0.42025 and the company defaults = 0.5 * 0.47 = 0.0235 – Invests in Columbia Ballpark bonds – Invests in Columbia Ballpark bonds and the company does not default= 0.5 * 0.9530=

0.4765

The table below summarizes the results:

J

C

defaults

0.07975

0.0235

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Decision of Uncertainty

0.10325

does  not default

0.42025

0.4765

0.89675

0.5

0.5

1

From the table the probability that the company buys the two bonds and will not be paid the full amount is 0.10325, the probability that the company will buys both bonds and will be paid the full amount is 0.89675, this table therefore indicates that there is a high possibility that if the company buys the two bonds then there is a 89.7% that it will be paid the full amount.

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Decision of Uncertainty

Decision:

From the above calculations it is evident that the company will have an equal chance of choosing each of the bonds, from the discussion the best decision would be to purchase Columbia Ballpark bonds which have a relative high returns value and the probability that the bond will be paid in full is 0.4765 whereas the probability that Jefferson county bonds will be paid is 0.42025.

## References:

McClave, J. and Terry, S. (2008) Statistics for business and economics, New Jersey: prentice hall

Moody’s (2009) municipal Bond rating, retrieved on 7th February, from http://www.moodys.com /cust/content/content.ashx?source=StaticContent/Free%20pages/Credit%20Policy%20Resear ch/documents/current/2001700000407258.pdf

Yahoo finance (2010) Municipal bonds, retrieved on 7th February, from http://reports.finance.y ahoo.com/z1?b=1&amp;cpl=-1.000000&amp;cpu=-1.000000&amp;mtl=60&amp;mtu=60&amp; pr=0&amp;rl=-1&amp;ru=-1&amp;sf=y&amp;so=d&amp;stt=-&amp;tm=1&amp;yl=-1.000000&a mp;ytl=-1.000000&amp;ytu=-1.000000&amp;yu=-1.000000

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