EFN406 Assignment: Financial Mathematics and Security Valuation 2019

This document provides a comprehensive solution to the EFN406 Managerial Finance assignment, focusing on financial mathematics and security valuation. The assignment covers a range of topics including loan calculations, investment analysis, bond valuation, and share valuation. Detailed solutions are provided for each of the ten questions, including manual calculations and Excel-based solutions, as required by the assignment brief. The solutions cover present value and future value calculations, repayment schedules, and the application of financial concepts to real-world scenarios. The document addresses topics like calculating loan installments, investment returns, bond yields, share prices, and the internal rate of return (IRR) of insurance premiums. The solutions are presented with clear explanations and workings, ensuring a thorough understanding of the financial concepts involved. This resource is designed to help students studying managerial finance to understand and solve complex financial problems.

Ques 1
I. The amount of deposit that Scott and Helen have already saved is $ 50,000 and the cpst
of the house is $600,000, thus, they would require a loan of $ 550,000.
Instalment for a loan of $550,000 for a period of 25 years and at a rate of interest of 6%, would be
$3,544.
ii. Repayment schedule is provided in the excle file of the solution
iii. If after 10 years, the bank reduces the rate of interest to 4.8%, and Scott and Helen wants to
repay the loan in 10 years, the revised installment, that they need to pay shall be $3,571.
Ques 2:
(i)
In case Jim makes the first deposit of $20,000 today and further invests $5,000 p.a for next 8 years
and $ 10,000 for 8 more years
The amount available with Jan at her 17th birthday, given the rate of interest of 5%p.a. would be
$170,042.
(ii)
If Jan intends to withdraw the amount in equal installments for 5 years, after her 17th birthday, she
would be able to make withdrawls of $3,055 per month.
The schedule is given in the excel file.
Ques 3:
(i)
The annual return on S&P/ASX 200 is2.82% (negative) , whereas the annual return provided by
accumulation Index is 6.43%
Thus, The difference between the annual return for the two indices, viz., S&P/ASX 200 and
accumulation index is 9.25%.
(ii)
For the given returns, for 5 years, the geometric mean is 2.8% and arithmetic mean is 2.86%
Ques 4:
The future value of the amount invested by Fran for 15 years would be $ 800,943.51 at the end of 15
years -and Fran would be able to get another $200,000 as a result of shifting to a small size
apartment from his current house. Thus, Fran would have total 1,000,943.51 to survive on.
Since, Fran wants to leave the capital amount for his legal heirs, and he intends to survive on the
interest that he would earn on this capital amount. Thus, amount that he would be having to spend
is $ 40,037.34 per annum.

Ques 5:
(a)
The bond in discussion has yield of 2% p.a and the time to maturity is 180 days, thus interest for 180
days would be 1%.
Thus, issue price of bond, based on interest of 1% would be $ 9900990.099.
(b)
The bond in discussion has yield of 2% p.a and the time to maturity is 120 days, thus interest for 120
days would be 0.67%
Thus, issue price of bond, based on interest of 0.67% would be $ 9933774.83.
Holding period yield on the bond would be 0.67% and the annual nominal return on the bond shall
be 2%.
Ques 6:
The coupon rate of bond is 6% and the yield of the bond is 3%, using these numbers, the value of a
$100 face value bond would be $108.546.
After 12 months, based on revised yield, the value of the bond shall be $108.184
Ques7:
Price of the share is the present value of the dividends that the company intends to pay for lifetime.
In the given case, dividends for next 13 years would grow at different and post that it is expected to
grow at a constant rate of 1% p.a.
The present value of these dividend streams including the residual value is $ 136.546.
Thus, the price of share of polycorp is $ 136.546
Ques 8:
(a)
Given that the current earnings of the company are $ 4.2 per share and there is expected to be no
growth in the earnings.
Thus value of share would be 52.5, i.e. Earnings/required rate of return.
(b)
Dividend at the end of 6th year is expected to be $8, thus price of share then would be $160
And the present value of such $160, is $93.358, i.e. the value of the share today.

Ques 9:
Annual premium for insurance is given to be $ 20,000 and a discount of 5% is available if the
company pays the entire amount upfront.
The alternate option with the company is to pay the amount on 12 equal instalments of $ 2,000 per
month.
The IRR of the case, involving payment in 12 months vs paying upfront is 45.49%
Ques 10:
In the first alternate, where it is expected to receive $10,000 every 2 years until perpetuity, the
present value of income stream is $ 82,101.86
Whereas in the alternate 2, i.e. receiving an amount of $2,500 quarterly for next 10 years, the
present value of the income stream is $.74,789.61
Since the present value of income stream is higher in option-1, it is preferable to choose option-1
against option 2.