Institute of Actuaries of India 2005 Subject CT1-Financial Mathematics Core Technical - Question Paper

3.5% per annum effective and a standard deviation of 3% per annum effective. (1 + it)
is independently and lognormally distributed.
(i) Deriving all necessary formulae, compute the mean and standard deviation of
the accumulation of the premiums over the five-year period. [9]
(ii) A director of the company suggests that investing all the premiums in the
assets with an uncertain return would be preferable because the expected
accumulation of the premiums would be greater than the payments due to the
policyholders.
discuss why this still may be a more risky investment policy. [2][Total 11]

9 (i) discuss what is meant by the expectations theory for the shape of the yield
curve. [2]
(ii) Short-term, one-year annual effective interest rates are currently 8%; they are
expected to be 7% in 1 years time, 6% in 2 years time and 5% in three
years time.
(a) compute the gross redemption yields (spot rates of interest) from
1-year, 2-year, 3-year and 4-year zero coupon bonds assuming the
expectations theory explanation of the yield curve holds.
(b) The price of a coupon paying bond is computed by discounting
individual payments from the bond at the zero-coupon bond yields
in (a).
compute the gross redemption yield of a bond that is redeemed at par
in exactly 4 years and pays a coupon of five per annum annually in
arrear.
(c) A two-year forward contract has just been issued on a share with a
price of 400p. A dividend of 4p is expected in exactly 1 year.
compute the forward price using the above spot rates of interest,
assuming no arbitrage. [12][Total 14]

10.An investor purchased a bond with exactly 15 years to redemption. The bond,
redeemable at par, has a gross redemption yield of 5% per annum effective. It pays
coupons of 4% per annum, half yearly in arrear. The investor pays tax at 25% on the
coupons only.
(i) compute the price paid for the bond. [3]
(ii) After exactly 8 years, immediately after the payment of the coupon then
due, this investor sells the bond to a different investor who pays income tax at a
rate of 25% and capital gains tax at a rate of 40%. The bond is purchased by
the 2nd investor to give a net return of 6% per annum effective.
(a) compute the price paid by the 2nd investor.
(b) Calculate, to 1 decimal place, the annual effective rate of return
earned by the 1st investor during the period for which the bond was
held. [10][Total 13]

11 (i) discuss what is meant by the subsequent terms:
(a) formula of value
(b) discounted payback period from an investment project [4]
(ii) An insurance company is considering setting up a branch in a country in
which it has previously not operated. The company is aware that access to
capital may become difficult in twelve years time. It therefore has two
decision criteria. The cashflows from the project must give an internal rate
of return greater than 9% per annum effective and the discounted payback
period at a rate of interest of 7% per annum effective must be less than twelve
years.
The subsequent cashflows are generated in the development and operation of
the branch.
Cash Outflows
ranging from the current time and the opening of the branch in 3 years time the
insurance company will spend £1.5m per annum on research, development and
the marketing of products. This outlay is presumed to be a constant continuous
payment stream. The rent on the branch building will be £0.3m per annum
paid quarterly in advance for twelve years starting in 3 years time. Staff
costs are presumed to be £1m in the 1st year, £1.05m in the 2nd year, rising
by 5% per annum every year thereafter. Staff costs are presumed to be incurred
at the beginning of every year starting in 3 years time and presumed to be
incurred for 12 years.
Cash Inflows
The company expects the sale of products to produce a net income at a rate of
£1m per annum for the 1st 3 years after the branch opens rising to £1.9m
per annum in the next 3 years and to £2.5m for the subsequent 6 years.
This net income is presumed to be received continuously throughout every year.
The company expects to be able to sell the branch operation 15 years from the
current time for £8m.
Determine which, if any, of the decision criteria the project fulfils.[17][Total 21]

Earning:   Approval pending.