High Yield Municipal Bonds

Initial data in this research was a list of three investments (real estate development, retail franchise
for Just Hats, a boutique-type store selling fashion hats for men and women, High Yield Municipal
Bonds) with different payoffs. The aim of the analysis was to find out whether to consult the expert,
who can predict favorable or unfavorable market conditions, or not to consult. In other words, is the
expert’s decision worth paying or not.
The method for evaluating the value of expert’s information was Decision Tree method.
Executive Summary
The research used Decision Tree to find out whether it is better to hire a consultant, or invest in one
out of three options with the highest payoff.
The analysis showed, that if the expert will ask more than $0.525 million for the services, it is not
worth paying for it, it is better to invest in the real property development.
Otherwise, if the requested sum will be equal or less than $0.525, it is a good opportunity to find out
whether market opportunities are favorable or unfavorable, and the payoff in some cases can reach
$6.125 million (including expert fees), which is the greatest value among all investment
Opportunities for Investment
Initial investment opportunities consisted of three options with different payoffs and probability of
the state of market (favorable/unfavorable):
 Real estate investment:
a) Favorable NPV: $7.5 million, Pr = 0.5;
b) Unfavorable NPV: $2.0 million, Pr = 0.5;


 Retail franchise for Just Hats:
a) Favorable NPV: $4.5 million, Pr = 0.75;
b) Unfavorable NPV: $2.5 million, Pr = 0.25;
 High Yield Municipal Bonds:
a) NPV: $2.25 million, Pr = 1.0.
Below this information is shown as a decision tree:

Image 1. Decision tree for three different options.

The Expert

There is a 4 th way for investment: consult the expert. The expert can predict favorable/unfavorable
state of the market, but his/her predictions are not always correct. The prediction of each state has a
different probability.
Table 1. Expert prediction probabilities.

  True State of the Market
Expert Prediction Favorable Unfavorable
Predicts “Favorable” .9 .3
“Unfavorable” .1 .7

Decision Tree
Decision trees are a form of multiple variable (or multiple effect) analyses. All forms of multiple
variable analyses allow one to predict, explain, describe, or classify an outcome (or target). An
example of a multiple variable analysis is a probability of sale or the likelihood to respond to a
marketing campaign as a result of the combined effects of multiple input variables, factors, or
dimensions. Decision trees attempt to find a strong relationship between input values and target
values in a group of observations that form a data set. They are constructed through successive
recursive branches, where a branch is contained within the parent branch and is usually
accompanied by peers that are formed at the same level of the decision tree. Because of this, a
defining characteristic of a decision tree is that it clearly and graphically displays the
interrelationships among the multiple factors that form the decision tree model, as viewed from
branch to branch and between branches at any level of the decision tree. (De Ville, 2006)
Decision trees are useful because they provide a clear, documentable and discussible model of either
how the decision was made or how it will be made. (Eriksen, et al 2001)

Decision trees are often used for calculating the expected NPV of investment. (Keeney, et al 1993)
In this research, it is used for evaluating the value of the expert’s information.
In the sheet ‘Expanded Solution No Probability’ in Excel spreadsheet decision tree for this research
is shown. Each branch shows the expected payoff for different situations (for example, $7.5 million
for investment in real estate in case market is favorable).
The analysis showed, that expected returns for each option for investment are the following:
 Real estate development: $4.75 million;
 Retail franchise for Just Hats, a boutique-type store selling fashion hats for men and women:
$4 million;
 High Yield 10-Year Municipal Bond: $2.25 million;
 Consult the expert: $5.275 million.
Value of Information
The value of information can be a useful thing in the strategy of investment with uncertain
outcomes, which is widely spread in the modern world. (Goetz, 2011)
The expected value of the information can be calculated as following:

Where EV – expected value, EP – expert payoff, MPI – maximum payoff from all investments.
In this research, .
So, million.

To sum up, if the expert will ask more than $0.525 million for services, it is not worth paying
him/her. It is better to invest in the real estate development, because the payoff in this case will be
$4.75 million.
In other case, the profit from investment into expert consulting services might be higher, than any
other investment. For example, the payoff can reach $6.125 million (look at the sheet ‘Expanded
Solution No Probability’ in Excel).
The aim of the research was to find out: is there a need to hire the expert to consult about market
state. The analysis, conducted with the help of Decision Tree, showed, that in case the expert will
ask more than $0.525 million for the services, there is no need to pay for it. Otherwise, the expert
may be hired and there is a chance for the highest payoff among all investment opportunities.


References List
De Ville, B. (2006). Decision Trees for Business Intelligence and Data Mining: Using SAS
Enterprise Miner. SAS Press Series. 8-15.
Eriksen, S., Huynh, C., Keller, L. R. (2001). Decision trees. Kluwer Academic Publishers. 1.
Goetz, T. (2011). The Decision Tree: How to make better choices and take control of your
health. Rodale. 115-117.
Keeney, R.L. and Raiffa, H. (1993). Decisions with Multiple Objectives: Preferences and
Value Tradeoffs, Cambridge University Press, Cambridge, United Kingdom. 85-87.

BUS520-Expected Value of Information.

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