Institute of Actuaries of India 2008 Subject CT1 – Financial Mathematics - Question Paper

(iii) List 4 limitations of Redington’s immunization theory to apply in practice.
(3)
(6)
(4)
[13]
Q. 8) An investor purchases an ordinary share of a company at the price of Rs.100. The
company pays annual dividends. The next dividend is expected to be of Rs.6 per share
and is due in exactly 1 year’s time. It is expected that following dividends will grow
at rate of 8% per annum and that inflation will be 5% per annum. The investor is
expected to sell the security just after receiving fifth dividend at Rs.150.
compute the expected effective real rate of return per annum for the investor.
[9]
Q. 9) Rs.10, 000 is invested for 10 years. In any year the yield on the investment will be 5%
with probability 0.4, 7% with probability 0.2 and 9% with probability 0.4 and is
independent of the yield in any other year.
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(i) compute the mean accumulation at the end of 10 years.
(ii) compute the standard deviation of the accumulation at the end of 10 years.
(iii) Without carrying out any further calculations, discuss how your answers to (i) and
(ii) would change (if at all) if:
the yields had been 6%, 7% and 8% instead of 5%, 7% and 9% per annum,
respectively;
(2)
(5)
(2)
[9]
Q. 10) A housing finance company loans Rs. 1,500,000 to an individual. The loan is to be
repaid by level monthly installments in arrears over a period of 20 years. After 10 years,
the amount of level installment increases by 20% of that in 1st 10 years. The
installments are such that the borrower pays interest at an interest rate of 12% per annum
convertible quarterly on the loan.
(i) compute the level monthly installment payable in 1st 10 years and that in last 10
years.
(ii) compute the total capital repayment and total interest payment that will be made
from the monthly installments paid during the period from eleventh years to 15th
years.
(4)
(6)
[10]
Q. 11) (i) State what is meant by a “forward contract”. Your ans should include
reference to the terms “short forward position” and “long forward position”.
(ii) An investor bought a 5-year forward contract on one June 2004 to buy Rs.400
nominal of a stock that pays coupons of five % pa payable half yearly on 31 March,
30 September. The stock is also expected to pay out a lump sum of Rs.50% of
nominal value on one June 2008. The stock is expected to yield 5.5% pa effective
if purchased on one June 2004 and held forever.
compute the forward price for the contract, provided that the risk free rate of interest
is 6% per annum.
(3)
(5)
[8]
Q. 12) (i) discuss what is meant by the subsequent terms:
(a) formula of value
(b) Discounted payback period from an investment project
(ii) A consortium of investors is considering starting a major sport venture of hosting
twenty-twenty cricket league in India where players from various cricket
playing nations will participate through 6 teams representing big cities of India.
The venture is expected to begin on one July 2008. The consortium estimates that the
subsequent cash flows will be generated by the event (all figures in Rs. Crores):
(1.5)
(1.5)
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Costs
Initial Setup costs and initial costs of enrolling the players:
Rs. 390 crore on one July 2008
Cost of building infrastructure:
To be incurred continuously at the rate of 20 crore per month for
next six months starting from 1July 2008
Running costs of the event:
To be incurred at the end of the month of Rs. one crore per month for
5 years starting on one January 2009 increasing every month by
0.5% per month.
Revenue
Sale of television rights:
To be received continuously at a rate of 25 crore per month for 6
months starting on one July 2008.
Other revenue from sale of tickets, merchandise, marketing rights etc.:
presumed to be received in the every month from January 2009 to
December 2013 at the end of month. The revenue from this source
is expected to begin at Rs. four crore per month and increase every
month by 1% per month.
Revenue from sale of venture:
This will be received on one January 2014, the expected time to sell
the venture.
The project will be regarded as viable if it provides a positive net current value at a
rate of interest of 18% per annum convertible monthly. Determine how much sales
proceeds would have to be achieved from selling the venture for the project to be
considered viable.
(11)
[14]

Earning:   Approval pending.