SMM092: Modelling Practice (CP2)

Assessment 1 (March 2024)

Time allowed: 3 hours

Background

The University of the Humanities of Actuaria (UHA) offers three-year undergraduate  degree programmes starting in September every year. One of the degrees courses on offer is the BA in Politics. Students wishing to be admitted to the BA in Politics must  apply directly to UHA unless they are studying on a recognised Foundation Year programme, in which case their application is submitted along with those of all the other students in their cohort in a single batch.

The University has had problems in the past when the lecture theatres reserved for the new September intake have turned out to be either too big or too small.  The dean of the school is asking your expert modelling services to improve its planning this year in order to avoid problems of this kind.

Admission Routes

There are two main admission routes possible for applicants to register to the course:

• Direct applications to UHA:

Direct applications to UHA for the next academic year are accepted starting from November of the current year until next August.

During this open application period the record of the current total number of “live" applications is updated after each review by the admissions officer.

All applications are considered to be live unless they have been withdrawn.

• Indirect applications through Foundation Year Providers (FYP) :

In addition to direct applications, the UHA receives applications from students  on Foundation programmes. These applications are submitted in a block for all interested students in a given cohort by the foundation year provider (FYP) .

Applications Data

The Programme’s Admissions team was asked to look through the archives to work out how many of the applications received by a given date resulted in students being admitted to the programme the following September. The person delegated to this task is a new member of the team who was in charge of handling the admissions data.

Making use of the admissions office entry logs, he has managed to compile the data on short notice for the past three application years 2020/21 to 2022/23 and for the current year 2023/24.

Tables A1 to A4 contain the admissions officer (AO) records’ entry dates and the corresponding total live applications for all 4 years. Further, there are shown the current withdrawal rates , expressed as a percentage of the live applications at the previous entry date. Namely , the total number of applications at any given date is made up by the current live applications and the total number of previous withdrawals. The rate of withdrawals proved to be fairly random ranging between 0% to 4% .

The AO has reviewed the applications once a week (sometimes even in the weekends) during the application period, which is made up by 38 weeks in total , starting from mid-November of each year. However, there’s roughly a 3-weeks break after week 5 for the holiday season and for the start of the new year (see Table 1) .

In addition, he has provided Tables B1 to B3 that show, at five key stages of each year (i.e. at certain weeks) , the number of direct applications which had been received by that date , and also record how many of those applications resulted in the student being admitted to the BA in Politics in September.

Further, he has supplied figures for the last three years for the three principal FYPs, which are the Foundation of Actuarian Education (FActEd), University Education For All (UEFA) and edYOUcate (edY) . This year a fourth FYP, International Educative Partners (IEP), has opened a branch in Actuaria and some applications have been received from them as well.

Tables C1 to C3 indicate the number of students taking the Foundation Year who applied to UHA for the BA in Politics and the number who were admitted on to the degree. Table C4 shows the current number of applicants for the September 2024 entry.

Overseas Course Promotion

In an attempt to increase the number of applicants, the Course Director for the BA in Politics intends to embark on a course promotion programme to advertise the course to potential students from abroad. He has identified the opportunity to go on a tour in the target overseas countries in March 2024 , giving talks in schools and making presentations to larger groups of young people. The cost of the trip is estimated to be £ 10,000, charged to the programme budget.

Students from these target overseas countries , who are admitted to the BA in Politics , pay fees of £ 15 ,000 per year.  In line with past progression records , students from these countries are expected to have a 75% probability of passing the first year of the  degree, and 85% of those who get through the first year are likely to go on to pass the second year and complete the third year as well (see Table 2) .

Only 60% of the fees paid by first-year students are kept by the programme; this percentage is 70% and 80% for second- and third-year students , respectively (see Table 3) .

Requirements

1.   Read the background document, which describes the situation being modelled , and examine the corresponding Excel file that contains the raw data and the parameters relating to the calculations you will be asked to perform.

2.   Construct a spreadsheet model which produces the following calculations and charts.  You should ensure that your spreadsheet contains appropriate self-checks and that you conduct robust reasonableness tests where possible.

iii.      Apply the results from part ii. to the entire 38-week period in tables A1-A3 to estimate the weekly total number of applications by also allowing for the cumulative withdrawals. Finally, based on the first

iv.      The Head of Admissions believes that candidates who apply early in the applications process are more likely to be admitted than candidates who apply later on.

Hence, based on the given past three years of conversions data (Tables B1-B3) and the total applicants from part iii. , estimate the probability of being admitted at each of the five key stages (i.e. weeks) of the application period.                        [3]

v.       Illustrate your findings in part iv. by means of a suitable graph.                     [2]

vi.      Predict how many direct applicants will be admitted to the BA in Politics at the five key stages of the admissions period in 2023/24 .              [2]

vii.      Predict how many applicants who are currently on Foundation Year programmes will be admitted to the BA in Politics in September 2024.          [2]

viii.      Produce suitable illustrations to show the trend in:

(a)       the total number of students admitted,                                                            [1]

(b)       the proportion of students admitted who have come through a Foundation Year programme.                                     [2]

ix.      Assuming a discount rate of 6% per annum, calculate the net present value (NPV) to the programme of  1additional student admitted in 2024/25.                                                                                                                                            [2]

If 10% of the total student fees revenue (i.e. over the entire three-year term) of each extra student recruited is allocated to cover the cost of the trip , use the above NPV calculations to work out how many additional students the Course Director would have to recruit to make a profit on the recruitment tour.                                                                             [2]

Marks available for spreadsheet model and checks:

Accurate completion of above modelling steps [30]

Demonstration of good modelling technique and practice [7]

Checks [8]

[Sub total 45]

Fill in the Audit Trail template worksheet (appended to the Excel data file) for your spreadsheet model which includes the following aspects:

•   task description and purpose of the model

•   data and assumptions used

•   methodology, i.e. description of how each calculation stage in the model has been produced

•   explanation of the checks performed

You should ensure that your audit trail is suitable for both a senior

actuary, who has been asked to approve your work, and a fellow student, who has been asked to peer review and correct your model, or to continue work on it, or to use it again for a similar purpose in the future.

Marks available for audit trail:

Audit approach

Fellow student can review and check methods used in the model [8]

Senior actuary can scrutinise and understand what has been done [8]

Written in clear English                                                                                                  [4]

Written in a logical order [3]

Audit content

All steps clearly explained [7]

Clear signposting throughout [5]

Statement of assumptions made [5]

All model steps accurately covered [15]

[Sub total 55]

[Total 100]