KOI FIN700: Financial Management Assignment - Time Value of Money

This document presents a comprehensive solution to a financial management assignment (KOI FIN700), addressing key concepts such as the time value of money, deferred annuities, and loan repayments. The solution begins with a retirement planning scenario, calculating the required contributions to reach a retirement goal, and determining the subsequent monthly pension. It then proceeds to analyze a home loan, calculating the effective annual interest rate, the monthly repayment amount, and exploring alternative repayment schedules. The assignment utilizes formulas for present value and future value of annuities to solve for unknown variables such as monthly payments and loan terms. The solution provides step-by-step calculations and explanations, demonstrating a clear understanding of financial management principles. This assignment covers topics including calculating future values, present values, and the effective annual rate of interest. It also analyzes different loan repayment scenarios.

KOI
FIN700 – Financial Management
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in the Subject Outline. This mark will be converted to a score out of 30%.
QUESTION 2. [(4 + 4) + (2 + 2 + 3 + 3) = 18 Marks]
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a) This question relates to the time value of money and deferred annuities.
Joan Daly is age 38 today and plane to retire on her 600h birthday. With future
inflation, Joan estimates that she will require around $1,800,000 at age 60 to
ensure that he will have a comfortable life in retirement. She is a single
professional and believes that she can contribute $3,600 at the end of each
month, starting in one months’ time and finishing on her 60th birthday.
i) If the fund to which she contributes earns 5.4% per annum, compounded
monthly (after tax), how much will he have at age 60? Will she have
achieved her targeted sum? What is the surplus or the shortfall?
Fund at Age 60 $1,800,000.00
Number of Years to Age 60 22 years
PMT $3,600.00
i(12) 5.40%
Monthly effective rate (j) =5.40%/12= 0.45%
Using Formula
Future Value of Annuity @i =PMT *{((1+j) n-1))/j}
Then
FV at age 60 = 3600*{((1+0.45%)22*12-1))/0.45%}
=$1,817,426
Since 1,817,426 >1,800,000, Joan will have achieved her targeted sum at age
60. She will also have a surplus
Surplus= Target-Future Value
= 1,817,426-1,800,000
=$17,426
ii) Using the entire fund balance, Joan then wishes to commence a monthly
pension payable by the fund starting one month after her 60th birthday,
and ending on her 85th birthday, after which she expects that the fund will
be fully expended. If the fund continues to earn the above return of 5.4%
per annum, compounded monthly, how much monthly pension will Joan
receive, if the fund balance reduces to zero as planned after the last
pension payment on her 85th birthday?
Fund at Age 60 $1,817,426.13
Fund at Age 85 $0
Number of Years to Age 85 25 years
i(12) 5.40%
Monthly effective rate j =5.40%/12= 0.45%
2

Find PMT?
We can solve for PMT using Formula below:-
Present Value of Annuity @i =PMT *{(1-(1+j)-n)/j}
Then
PMT = Present Value of Annuity/{(1-(1+i)-n)/i}
PMT=1,817,426.13/{(1-(1+0.45%)-25*12)/0.45%}
PMT=$11,052.31
Joan will receive a monthly pension of $11,052.31
QUESTION 2 continued.
b) This question relates to loan repayments and loan terms.
Jack and Jill Jacobs wish to borrow $700,000 to buy a home. The loan from the
Highway Bank requires equal monthly repayments over 20 years, and carries.an
interest rate of 4.2% per annum, compounded monthly. The first repayment is
due at the end of one month after the loan proceeds are received.
You are required to calculate:
i) the effective annual interest rate on the above loan (show as a
percentage, correct to 3 decimal places).
Using formula below, the effective annual rate (i) can be solved as
EAR (i) = (1 + i( n)
n )n - 1
Where
i(n) is the Nominal rate and n is the compounding period
In this scenario, we solve for EAR (i) as follows
EAR (i) =( 1+i(n)/n)n-1
=( 1+i(12)/12)12-1
=( 1+4.2%/12)12-1
=4.282%
Therefore, Effective annual rate is 4.282%
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ii) the amount of the monthly repayment (consisting of interest and principal
repayment components) if the same amount is to be paid every month
over the 20 year period of the loan.
PV $700,000
Number of Years 20 years
i(12) 4.2%
j =4.2%/12= 0.35%
Find Monthly PMT?
Solve PMT Using Formula below
Present Value of Annuity @i =PMT *{(1-(1+i)-n)/i}
PMT= Present Value /{(1-(1+i)-n)/i}
PMT=700,000/{(1-(1+0.35%)-20*12)/0.35%}
PMT=$4,316
QUESTION 2 continued.
iii) the amount of $X, if - instead of the above – the Highway Bank agrees
that Jack and Jill will repay the loan by paying the bank $3,500 per
month for the first 12 months, then $3,800 a month for the next 12
months, and after that $X per month for the balance of the 20 year term.
PV $700,000
Number of Years 20 years
i(12) 4.2%
Monthly effective rate (j) =4.2%/12= 0.35%
Annual effective rate (i) =4.282% ( see part b(i))
PMT1( t= 0-12 ) $3500
PMT2( t=12-24) $3800
PMT3( t=24-216) ?
Using Formula below and time value of money, we can solve for X
Present Value =PMT *{(1-(1+i)-n)/i}
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iv)
Then
700,000= 3500*( 1−(1+ J ¿¿ ¿−12)
J )+ 3800*( 1−(1+J ¿¿ ¿−12)
J )*(1+i)−1+PMT3*(
1−(1+J ¿¿ ¿−18∗12)
J )*(1+i)−2
700,000=41,059.90+42,748.90+ X*( 1−(1+J ¿¿ ¿−216)
J )*(1+i)−2
Therefore X is $4,426.46
v) How long (in years and months) would it take to repay the loan if,
alternatively, Jack and Jill decide to repay $4,500 per month, with the first
repayment again being at the end of the first month after taking the loan,
and continuing until the loan was repaid. [HINT: The final repayment is
likely to be less than $4,500, and will be paid one month after the final full
instalment of $4,500 is paid.)
Present Value $700,000
i(12) 4.2%
j =4.2%/12= 0.35%
I =4.282% ( see part b(i))
PMT $4500
We can Solve n using Formula
Present Value of Annuity @i =PMT *{(1-(1+i)-n)/i}
Then
700,000 =4,500*{(1-(1+0.35%)-n*12)/0.35%}
Solve, n = 18.753 years
i.e 18 years 9.032 months
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$3500 $3800 PMT= ?
T= 24T=12T=0 T= 240

Since there is a final small payment, the n is rounded down to
= 18 years 10 months
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