Guaranteed Return Mr. Juan Tobias Rich (Toby to his friends) has recently inherited $50,000 from the estate of his great-aunt. He has never had capital to invest before, so he is not quite sure what to do. His friend Mr. Richard Stuffy is an investment counselor for a local stock brokerage firm, Bullfinch and Bearwallow. In their initial talk, Toby said, “I want to invest the entire inheritance, but no more now. I am living very well on my salary, and I really have no need for the money in the near-term. My goal is to combine this with a good chunk of my future raises, so that I can retire early— in 25 years or so.” Richard believes Toby will follow his savings plan. Toby in two years saved enough for the down payment on a house, which he purchased last year. Toby’s capital is too limited for many forms of independent investment. On the other hand, his possibilities go far beyond a certificate of deposit or a few shares of stock. As is normal practice with new clients, Richard has developed three distinctly different investment alternatives (in this case, each is for $50,000). Richard uses his client’s reactions to the investment choices to develop clearer goals for each client’s investment strategy. The first of these alternatives is the financing of a second mortgage on a commercial structure. The risk on this investment is relatively low because the loan is secured by the building. It runs for a 25-year period, with annual payments at a 15% annual rate. The borrower pays the cost of title and fire insurance as well as the fees to the bank that acts as the intermediary for payments. The second alternative is the purchase of 25-year bonds issued by the local power authority. These bonds carry a face rate of 9% with interest paid annually. However, interest rates for this class of bond have risen in recent years (currently 11%) so that the bonds are selling at a discount from their face value. The power authority has recently announced some cost overruns on the nuclear facility that is under construction. In reaction to this news and fearful of more substantial problems, their bonds in particular are being discounted more heavily—to correspond to a 14% rate of return. Thus, if the bonds are paid off, this is a rare opportunity, but there is some risk of default. The third alternative is as a limited partner in a business run by some friends of Toby and Richard. The business is a spin-off from a local high-tech firm, which is still in the embryonic stage. Their friends hope to take the firm public (sell stock and become publicly held) within three years. At this point, the investor’s capital would be returned with substantial interest. However, the company may go bankrupt instead. If this happens, Toby can expect to get back about 20 cents on the dollar. Although many intermediate states are possible, Richard believes that the two extreme possibilities provide adequate guidance. He estimates that there is a 40% chance of success and that the o.

1. Guaranteed Return
Mr. Juan Tobias Rich (Toby to his friends) has recently inherited $50,000 from the estate of his
great-aunt. He has never had capital to invest before, so he is not quite sure what to do. His
friend Mr. Richard Stuffy is an investment counselor for a local stock brokerage firm, Bullfinch
and Bearwallow. In their initial talk, Toby said, “I want to invest the entire inheritance, but no
more now. I am living very well on my salary, and I really have no need for the money in the
near-term. My goal is to combine this with a good chunk of my future raises, so that I can retire
early— in 25 years or so.” Richard believes Toby will follow his savings plan. Toby in two years
saved enough for the down payment on a house, which he purchased last year.
Toby’s capital is too limited for many forms of independent investment. On the other hand, his
possibilities go far beyond a certificate of deposit or a few shares of stock. As is normal practice
with new clients, Richard has developed three distinctly different investment alternatives (in this
case, each is for $50,000). Richard uses his client’s reactions to the investment choices to
develop clearer goals for each client’s investment strategy.
The first of these alternatives is the financing of a second mortgage on a commercial structure.
The risk on this investment is relatively low because the loan is secured by the building. It runs
for a 25-year period, with annual payments at a 15% annual rate. The borrower pays the cost of
title and fire insurance as well as the fees to the bank that acts as the intermediary for payments.
The second alternative is the purchase of 25-year bonds issued by the local power authority.
These bonds carry a face rate of 9% with interest paid annually. However, interest rates for this
class of bond have risen in recent years (currently 11%) so that the bonds are selling at a discount
from their face value. The power authority has recently announced some cost overruns on the
nuclear facility that is under construction. In reaction to this news and fearful of more substantial
problems, their bonds in particular are being discounted more heavily—to correspond to a 14%
rate of return. Thus, if the bonds are paid off, this is a rare opportunity, but there is some risk of
default.
The third alternative is as a limited partner in a business run by some friends of Toby and
Richard. The business is a spin-off from a local high-tech firm, which is still in the embryonic
stage. Their friends hope to take the firm public (sell stock and become publicly held) within
three years. At this point, the investor’s capital would be returned with substantial interest.
However, the company may go bankrupt instead. If this happens, Toby can expect to get back
about 20 cents on the dollar. Although many intermediate states are possible, Richard believes
that the two extreme possibilities provide adequate guidance. He estimates that there is a 40%
chance of success and that the original investment will increase tenfold if the investment is a
success.

2. Toby’s (8%) mortgage is his only outstanding debt. Therefore, a fourth alternative would be to
pay $50,000 of it off early. Each of these investments has a higher rate of return, but he is not
certain how he should pick the right one. The question is further complicated by Richard’s
comment that the current capital shortage has pushed interest rates and other returns up from the
normal rate of 10% for relatively risk-free investments.
What steps would you first take to perform an after taxes analysis to determine a better
investment for the following example:
Toby is in a 35% bracket for income taxes (state and federal combined), and only 40% of a
capital gain is likely to be taxable at retirement.
Note:You are not required to perform the calculation, you are only required to discuss how you
would come to your conclusions.
Describe the relationship of risk to return for the three investments. Are all three investments on
the “efficient frontier” for the risk/return trade-off? Justify your reasoning.
Solution
I would first calculate the per year before tax return generated by each of the three investments,
the first alternative provides a return of 15%,the second alternative provides a return of 14% and
the third alternative provides a substantial rate of return of almost ten times. Then I would find
the after tax return for each of the alternative, on the second alternative and the third one there
are capital gains tax and also there is income tax return on the first and the second alternatives,
this taxes would led to lowest after tax return for the second alternative, and the maximum after
tax return for the third alternative. Thus we compare the after tax returns.
When the Risk is considered the picture is entirely different, the first alternative has some risk of
default by borrowers but the mortgage is secured by building makes the risk very low, the second
alternative has some risk of default and the interest rate risk. The risk involved in the third
investment is substantial there is a 60% chance of the alternative being a failure with payoff of
just 20% of the invested amount. Considering risk wise the first alternative seems to have least
risk while the third alternative has the most risk.
When combining the after tax return and risk prospective into one:
Highest
Medium
Lowest
After tax return
alternative 3

3. alternative 1
alternative 2
Risk
alternative 3
alternative 2
alternative 1
Seeing from above analysis in the table we see that comparing the Return/risk for each
alternative we see that alternative 1 is most suitable with Medium return and lowest risk.
The risk returns trade-off for the fourth investment and the risk-free investments should be
compared with the above three investment's risk return trade off, the investment with the best
return to risk payoff should be given final consideration.
“efficient frontier” is the set of portfolios where the return is the maximum for a given amount of
risk given a portfolio of investments. It’s possible to construct a portfolio of diverse investments
that can replicate the risk of any of the above alternative investments and then maximize the
return for a given set of weights of investments in the portfolio, therefore its always possible to
construct a portfolio which maximizes a return for a given amount of risk(risk of each alternative
here), the above alternative investments need not lie on the “efficient frontier” for the risk/return
trade-off because it’s always possible to have a portfolio that matches with the risk of the given
alternatives and that provides a larger return than each of the alternatives.
Highest
Medium
Lowest
After tax return
alternative 3
alternative 1
alternative 2
Risk
alternative 3
alternative 2
alternative 1