INDIAN INSTITUTE OF MANAGEMENT BANGALORE
Spreadsheet Models for Business Decision Problems
Assignment 2
(Due 10:30 pm, September 22, 2019)
The year is 2019. The date: January 1. Your daughter is 7 years old now. You wish to fund
her college education ten years from now. You estimate that you will need Rs 40 lakhs
each year for the next four years starting from the year 2029. Your plan is to sell the
ancestral property that you inherited and invest it in the following set of bond options:
Bond 1: 20 year, 10% coupon rate, Face value = Rs. 10000.
Bond 2: 25 year, 7% coupon rate, Face value = Rs. 10000.
Bond 3: 30 year, 6% coupon rate, Face value = Rs. 10000.
Bond 4: 5 year, 10% coupon rate, Face value = Rs. 10000.
Bond 5: 18-yr, 12% coupon rate, with a face value of Rs 10,000.
Bond 6: 30-yr, 11% coupon rate, with a face value of Rs 5,000.
Assume that all the bonds were issued in year 2018. Hence, this is the 2nd year in the life
of the bonds. Assume the current interest rate to be 7%. [Note: You will need to obtain the
price of each bond in 2019.] You expect the annual change in interest rates to be volatile,
with a mean change of zero and a standard deviation of 2.0%. Assume these changes to be
normally distributed. [Note: You may truncate the distribution at 0% on the lower side and
50% on the upper side.]
Clearly, you would like to set aside some of the funds you have now, to plan for your
daughter’s college education. One factor that you might wish to consider is to accomplish
your objective with the least amount of funds. At the same time, you would like to ensure
that the chance of a shortfall exceeding Rs 20 lakhs in year 2032 does not exceed 5%.
[Note: You can measure this shortfall in 2032 or use an appropriately discounted amount
in 2019. Observe as well that the greater the funds that you allocate, lesser is the chance
that the shortfall might exceed Rs 20 lakhs in 2032 – therefore a tradeoff between
allocation vs potential shortfall.] Keeping this in mind, what set of bonds would you
recommend purchasing (selling) and in what quantities? [Note: you have the option of
‘shorting’ bonds as well. Here, instead of purchasing, you first ‘borrow’ bonds, then sell
them immediately, but pay the ‘lender’ as per the payment schedule.]
Another factor that might wish to consider is that you would like the amount of shortfall in
the worst case (defined as the 5th percentile..) be as small as possible. At the same time,
you would not like to set aside more than Rs 75 lakhs for your daughter’s education.
[Observe again that the greater the funds that you allocate, smaller might be amount of
shortfall in the worst case. Clearly, this can get very expensive. The idea then is to minimize
the risk of shortfall using only the money you have now.]
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Considering all the factors highlighted above, how much of your personal wealth would
you like to set aside now to fund your daughter’s education? What set of bonds would you
recommend purchasing (selling) and in what quantities? Make specific recommendations
backed by analysis.
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