8/11/2019 Loan Valuation Assignment

1/3

Viraj Shah3462191

ACTL 2111

Summary ReportFor this assessment task, we were assigned a loan valuation question that corresponded to

a similar looking real life case scenario. The context of the assessment task emphasized on a just turned 50 year old man that took the option of a reverse mortgage loan. The task wasdistributed among seven questions with each question depending on the previous one.

The first question was asked to calculate the accumulation value of Marweyis savingsaccount after two months which had an initial amount of $30,500. The interest was paid at3% p.a. (convertible quarterly, credited monthly). In my opinion this was a basic questionaimed at us getting started smoothly so that the later parts can become less difficult. Thisquestion was done in the 1 st worksheet of the excel file. To account for quarterly frequency,the annual rate was converted to effective rate in order to find the actual interest paymentsthat were credited monthly. After setting up initial parameters, various basic arithmeticexcel functions were used. The results of question 1 can be seen in the diagram:

Furthermore, it was also asked to provide a schedule on how Marweyi's salary will increasethrough time until he goes into retirement. The last income value before retirement is

depicted below:-

The 3% depicts the annual rise from the previous years salary due to inflation.

Question 2 asked us to simulate the nominal fortnightly mortgage rates corresponding tothe repayment period until retirement. I was a bit clueless in the beginning since I hadnthad practice in modelling and generating random numbers that followed a normaldistribution as this was important to calculate the Wiener increment that played asignificant role in calculating the corresponding interest rates. Luckily, the formula was

already given in the question and it only required to copy that onto the excel spreadsheet.The formula of datedif() was used to calculate the number of fortnights between Marweyis50 th birthday and 65 th birthday (after which he goes into retirement). Furthermore, it wasalso necessary that the random generated rate stayed between 5% and 9% in order tofollow the mortgage interest rate collar as described in the question. The if formula wasused and nested twice in order to restrict the rate between 5% and 9%. The correspondingeffective fortnightly rate was found just by basically dividing the annual rate by 26. Since therates were randomly generated, pressing the F9 key automatically refreshed and randomlygenerated new rates. Some of the output is depicted below:-

Date Opening Balance Interest Credited Closing Balance1/04/2014 $30,500.00 $0.00 $30,500.001/05/2014 $30,500.00 $76.25 $30,576.251/06/2014 $30,576.25 $76.25 $30,652.50

1/1/2029-31/03/2029 $3,894.92 3%

Fortnight # Wiener Increment Interest rate (p.a.) Effective fortnightly rate1 - 5.60% 0.215%

2 -0.018451 5.57% 0.214%3 -0.003979 5.56% 0.214%4 0.052548 5.66% 0.218%5 0.046686 5.75% 0.221%6 -0.053807 5.65% 0.217%7 0.006749 5.66% 0.218%

8/11/2019 Loan Valuation Assignment

2/3

Viraj Shah3462191

ACTL 2111

Question 3 and question 4 were, in my opinion, the most difficult sets of questions in thetask. These two questions required advanced MS Excel skills in order for them to functionperfectly. Question 3 was about developing a mortgage calculator on a spreadsheet showingthe fortnightly repayments from inception of the loan. It should also include all components

of a loan schedule such as the simulated mortgage rates together with the correspondinginterest payments, etc. Question 4 was a more generalised version of question 3 in that thecalculator developed should be compatible with various payment frequencies such as daily,weekly, monthly, etc. This was a pretty difficult thing to implement since every frequencyhad its own constant parameters e.g. speed of mean reversion of interest rate process, long-term mean rate, volatility etc. To account for all seven scenarios to give an exact outputwithin a cell was difficult. A series of if formulas were used and they were also nestedmultiple times in order to incorporate all the frequencies. The constant parameters tablewas copied straight from the assessment task which came in handy. To calculate payment,pmt formula wa s used with a variable rate that was calculated in the accompanying cell.This question would have been much easier to do with the help of VBA instead of usingexcel functions. Some of the snapshots of these questions worksheet are portrayed below: -

Question 5 and question 6 were relatively easy compared to the previous questions.Question 5 asked to basically calculate the outstanding balance at Marweyis deathassuming he dies at age 85 and stops payments after retiring. This was basicallycompounding the market value of the house at age 65 by the specified interest rate i.e. 2%for 20 more years. However, it was important to set the frequency of the payment to 26 per

year since this was the original tenure and also the outstanding balance in this worksheetcorresponded to the cell reference in the previous sheet. The result summary is shownbelow:-

Pressing the F9 key refreshed the value of the outstanding balance at death although itmostly stayed between $430,000 and $450,000.Question 6 was the one that asked to account for the reverse mortgage aspect of theassessment task. It incorporated the appreciation of the house with time. It asked to

Market Value of House $450,000.00Initial Deposit $30,652.50Loan Principle $419,347.50Loan Term (years) 30Repayment Frequency (in a year) (dropdown) 26Number of repayments 780

Interest rate(p.a.) Restricted rate (p.a.) Effective Interest Rate Payment Interest Principal Paid Outstanding Balancing$419,347.50

0.056 5.600% 0.21538% $1,110.56 $903.21 $207.35 $419,140.150.055894935 5.589% 0.21498% $1,109.28 $901.07 $208.21 $418,931.930.055008731 5.501% 0.21157% $1,098.52 $886.34 $212.18 $418,719.750.054211735 5.421% 0.20851% $1,088.89 $873.06 $215.83 $418,503.920.053638786 5.364% 0.20630% $1,082.00 $863.39 $218.61 $418,285.31

Question 5Outstanding Balance at retirement(note- the frequency in prev. sheet should be set at26) $294,856.02Interest Rate (p.a., effective) 2%expected lifetime after retirement (years) 20

Outstanding balance at death 438140.5304

8/11/2019 Loan Valuation Assignment

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Viraj Shah3462191

ACTL 2111

calculate the expected home value at the end of year of Marweyi's death, the amount ofmoney that will be paid to the bank and also the excess (if remaining) that would be paid toMarweyis beneficiaries. The annual effective appreciation rate was converted to fortnightlyeffective rate. Furthermore, it was assumed that the appreciation rate was applied to

market value of the house after it got deducted by Marweyis withdrawals. The results aresummarised below:-

Overall, in my opinion, this assessment task was very well designed as it relied on thetechnical skills required for various calculations and also how the various data arerepresented and interpreted. This could give insight to what various financial careersactually involve.

Initial Withdrawal $250Annual Increase $10

Appreciation rate (p.a., effective) 1.50%Effective Fortnightly rate 0.057%Total fortnights between 1/06/2014and 31/03/2029 387Market Value of house at retirement $561,615.78

Market Value at death $604,789.72Outstanding balance at death $435,075.84Benefit paid to beneficiaries $169,713.88