STAT 2032/6046: Financial Mathematics assignment 代写
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STAT 2032/6046: Financial Mathematics assignment 代写
STAT 2032/6046: Financial Mathematics Page | 1
THE AUSTRALIAN NATIONAL UNIVERSITY
RESEARCH SCHOOL OF FINANCE, ACTUARIAL STUDIES
AND STATISTICS
FINANCIAL MATHEMATICS (STAT2032 / STAT6046)
SEMESTER 2, 2017
ASSIGNMENT
Due Date: Thursday 20 October 2017 by 4 PM
Total Marks = 40
All students must hand in an assignment of their own. Ensure you also complete and
attach a cover sheet with your assignment. You must complete the assignment using a
spreadsheet. Assignments should be submitted using wattle and should have the answer
and workings set out in a way, which is easy to follow. For your assignment submission
make sure you add a worksheet to your excel file which has all the answers summarized
and workings must be shown on separate worksheets.
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The Scenario
You are a financial planner who is investigating the options for a 45-year old man who
wishes to have enough money to retire by the time he is 65. The man has just turned 45
and has received a sizable inheritance of $150,000. He has approached you to understand
his financial situation and make an informed decision regarding his investment options
for his financial future. His current financial arrangements are as follows:
• His salary has just been increased to $120,000 p.a., which is taxed at a rate of 33%
before being paid to him. This is currently being paid on a monthly basis at the
start of each month.
• Any salary over $200,000 p.a. will be taxed at 40% (i.e. the first $200,000 p.a. of
salary is taxed at 33%, the amount over $200,000 p.a. is taxed at 40% - tax is paid
at a constant rate each month during each year assuming that the monthly salary
is to be earned over the whole year).
• He is paying off a mortgage on the property he lives in. The payments are currently
$3,000 at the end of each month, which is enough to have the property paid off
exactly in 7 years at the current interest rate of 4% p.a. effective.
• Currently each month, $2,500 of his net salary is being used in expenses and any
additional amount is being invested in a bank account earning 2.5% p.a.
compounded monthly. These payments are being made on the same day the net
salary is received.
• The current bank account balance (before receiving the inheritance) can be
assumed to be zero.
• He expects his expenses to increase by 0.6% each month.
• He expects his salary to increase at a rate of 5% p.a. going forward. This increase
is processed on a yearly basis, with the next increase to occur after 12 further
salary payments at the recently increased rate.
• Interest income in the bank account is taxed at a concessional rate of 15%
immediately on the interest income earned each month.
• He intends to live in his home when he is retired and live off the proceeds of his
bank account in retirement.
• Initially, the man wants to deposit the inheritance in his bank account.
a) Calculate the expected amount the man will have in his bank account at age
65 under the basis above. Assume all interest rates remain constant.
(12 Marks)
STAT 2032/6046: Financial Mathematics assignment 代写
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The first thing you notice about this man’s financial affairs is that it would most likely be
beneficial for him to pay off the mortgage as quickly as possible. This would involve using
the inheritance immediately and making a lump sum contribution to the home loan, and
then continuing the $3,000 per month repayments until the loan is paid off. Any
additional amount of salary not used is credited to the bank account.
b) Calculate how much more the man will have at age 65 if he takes this
approach.
(7 Marks)
The client mentions to you he is extremely risk averse and does not want to invest in
anything where the cash-flows aren’t known in advance. Based on this you decide to only
recommend fixed interest securities, with the intention of investigating the impact of
investing the inheritance in either of these securities.
Two options which you are considering are as follows:
Bond A – A zero coupon bond redeemable in 20 years with a gross yield of 6.0% p.a.
effective.
Bond B – Pays half yearly coupons of 6.0% p.a. Redemption is at the decision of the issuer
at the following redemption values:
• 1.2 times the face value on any coupon date in the 11 th year through to the 13 th
year from now
• 1.3 times the face value on any coupon date in the 14 th year through to the 15 th
year from now
This bond has a minimum gross yield of 7.5% p.a. effective.
c) Assuming the man invests in either Bond A or Bond B (but not both at the
same time); calculate the nominal amount of each bond which can be
purchased using the inheritance amount of $150,000.
(5 marks)
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Should the client decide to invest in one of the bonds above, you decide to recommend
that the mortgage continue to be paid off with the $3,000 per month for 7 years. The client
is also subject to a tax of 20% on coupons and capital gains. The tax is payable
immediately it is incurred, with coupons to be invested in the bank account when they
are received. The gross yields of the bonds are unchanged.
d) For both bond purchase options, calculate how much money the man will
have in the bank account at age 65. Assume that Bond B is redeemed at the
end of the 15 th year.
(14 marks)
e) Which of the four alternatives discussed above should the man choose such
that he has the largest bank balance at the age of 65? Give a short
explanation for your answer.
(2 marks)
END OF ASSIGNMENT
STAT 2032/6046: Financial Mathematics assignment 代写
