University Project: Life Insurance and Retirement Valuation Analysis

This assignment delves into the intricacies of life insurance and retirement valuation, focusing on the application of the Projected Unit Credit (PUC) and Entry Age Normal (EAN) methods. It involves creating assumptions for both methods within a defined-benefit pension scheme, considering factors like employee age, salary, and contribution rates. The project requires building Excel models to determine initial contribution rates and assess the scheme's funding position over a 15-year period under various scenarios, including changes in contribution calculation methods, scheme closures, and large-scale redundancies. Furthermore, the assignment explores the impact of different scenarios on the scheme's progression. The student also identifies potential factors influencing the scheme's progress and contribution requirements, such as demographic shifts, economic conditions, and policy adjustments, culminating in a business memo to the Board of Trustees outlining funding speeds and strategies for managing conflicts among stakeholders.

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Name:
Course
Professor’s name
University name
City, State
Date of submission

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1) Determine an initial contribution rate for each Grade using the PUC Method
and the EAN method
a) Create a set of assumptions for both the EAN and PUC method and
assumptions for meant for each of the methods
1. The actuarial methods and assumptions to this two agree on a defined –benefit,
price and salary. The plans of the dependent dominate the occupational provision
retirement and therefore the actual involvement in actuarial costing.
2. The methods and actuarial provisions vary from country to country and sometimes
may depend of the method used for financing and implementation of the
arrangement benefit and the pension scheme size.
3. In most places the use of the two methods has increased due to the size and the
magnitude of the defined contribution plans (Arnold, et al, 2019).
4. In defined contribution such as this, the arrangements reflects more on the
involvement of actuarial valuations on the normal life insurance savings and in
many cases the methods used may be implemented using insurance contracts.
5. The two methods have mostly been used due to the defined contribution plans
6. Taxation treatment in the retirement scheme has played a major role in accounting
for the benefits in the two methods.
Assumptions meant for the PUC Method
This actuary method assumption is an estimate of uncertain model in variable input normally
used in for the purposes of calculating benefits and premiums. It is an evaluation risk method
of probabilities and has broad applications which include computer programming, economics,
insurance industry and even the fiancé industry. The actuarial method assumption may

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include predicting the person’s age, health conditions, gender and even their possible
lifespan. Large statistical data that is creatable to the uncertain variables and that may lead to
a predictive variable (Ayuso, Bravo, and Holzmann, 2016).
This method is an estimate and a forecast on an uncertain variable used for the sole purpose
of calculating insurance premiums and benefits.
It may involve statistical data or mathematical models designed to evaluate the risk of a
particular risk event of pension and retirement benefits.
There are broad applications of actuarial assumptions including in the field of insurance,
computer programming and finance.
Assumptions of the EAN method
1. It is designed to calculate the projection, forecast and expectancy of a person seeking
the benefit of pension’s schemes.
2. Focuses on the projected premiums in the RNA and potential payouts for insurance
benefits and pension plans.
3. It include analysis of retirement contribution rates, mortality rates, and survivorship
and disability rates (Beetsma et al, 2019).
4. This method is an estimate and a forecast on an uncertain variable used for the sole
purpose of calculating insurance premiums and benefits.
b) Develop a flowchart that shows the calculation logic for the determination of
the initial contribution rate using the PUC method.

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Age at the start of the year Number of
employees
Average salary Grade
30 210 78,000 B
30 20 100,000 A
40 220 87,000 B
40 15 150,000 A
45 240 95,000 B
45 30 175,000 A
50 180 103,000 B
50 25 185,000 A
55 50 103,000 B
55 10 250,000 A

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c) Write your model in excel for both methods and both Grades
Normal insurance calculation using the Projected Unit Credit (PUC) Method
Age at
the start
of the
year
Number of
employees
Average
salary
Grade PUC
Method
( Based on
the Salary
assumption)
Bx=k( 1+s)
^r-1-
xSx( x-e)
30 210 78,000 B 78,000
30 20 100,000 A 100,000
40 220 87,000 B 87,000
40 15 150,000 A 150,000
45 240 95,000 B 95,000
45 30 175,000 A 175,000
50 180 103,000 B 103,000
50 25 185,000 A 185,000
55 50 103,000 B 103,000
55 10 250,000 A 250,000
Where : r= the normal retirement age of the employees

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e= entry age of the employees
x= age at the valuation time using PUC
k= normal benefits percentage
s= proportionate salary increment per person
Normal insurance calculation using the Projected Unit Credit (PUC) Method
Age
at
the
start
of
the
year
Number of
employees
Average
salary
Grad
e
EAN
Method
( PVFB
)
NC=PVFB/
Annuity
from
fromval-dt
retirement
age
AL=NC*Annuity
from entry- age to
retirement
30 210 78,000 B 78,000 175,000 175,000 215,000
30 20 100,000 A 100,000 215,000 250,000 275,000
40 220 87,000 B 87,000 275,000 300,000 -
40 15 150,000 A 150,000 175,000 175,000 175,000
45 240 95,000 B 95,000 250,000 250,000 250,000
45 30 175,000 A 175,000 300,000 300,000 300,000
50 180 103,000 B 103,000 250,000 175,000 175,000
50 25 185,000 A 185,000 300,000 250,000 250,000
55 50 103,000 B 103,000 250,000 300,000 300,000

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55 10 250,000 A 250,000 220,000 450,000 -
Where: r= the normal retirement age of the employees
e= entry age of the employees
x= age at the valuation time using PUC
k= normal benefits percentage
s= proportionate salary increment per person
2. Determine the scheme’s funding position (for accrued past service benefits) in 15 years’
time, using your original assumptions and under each of the following scenarios
a. Contributions are calculated each year using PUC method determined at commencement
and updated every three years
Age at
the start
of the
year
Number of
employees
Average
salary
Grade PUC
Method
( Based on
the Salary
assumption)
Bx=k( 1+s)
Year 1 Year 2 Year 3

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^r-1-
xSx( x-e)
30 210 78,000 B 125,000 125,00
0
175,000 215,000
30 20 100,000 A 175,000 175,00
0
215,000 250,000
40 220 87,000 B 215,000 250,00
0
275,000 300,000
40 15 150,000 A 275,000 300,00
0
- 175,000
45 240 95,000 B 175,000 175,00
0
175,000 250,000
45 30 175,000 A 250,000 250,00
0
250,000 300,000
50 180 103,000 B 300,000 300,00
0
300,000 175,000
50 25 185,000 A 250,000 175,00
0
175,000 250,000
55 50 103,000 B 300,000 250,00
0
250,000 300,000
55 10 250,000 A 250,000 300,00
0
300,000 450,000

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b. Contributions are calculated each year using the EAN contribution rates determined at
commencement.
Ag
e
at
the
sta
rt
of
the
yea
r
Number
of
employe
es
Avera
ge
salary
Gra
de
EAN
Meth
od
( PVF
B)
NC=PVF
B/
Annuity
from
fromval-
dt
retireme
nt age
AL=NC*Ann
uity from
entry- age to
retirement
Year
1
Year
2
Year
3
30 210 78,00
0
B - 125,000 125,000 175,0
00
215,0
00
175,0
00
30 20 100,0
00
A 0 175,000 175,000 215,0
00
250,0
00
215,0
00
40 220 87,00
0
B 0 215,000 250,000 275,0
00
300,0
00
275,0
00
40 15 150,0
00
A 0 275,000 300,000 - 175,0
00
-
45 240 95,00
0
B 0 175,000 175,000 175,0
00
250,0
00
175,0
00
45 30 175,0
00
A 0 250,000 250,000 250,0
00
300,0
00
250,0
00
50 180 103,0 B 0 300,000 300,000 300,0 175,0 300,0

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00 00 00 00
50 25 185,0
00
A 0 250,000 175,000 175,0
00
250,0
00
175,0
00
55 50 103,0
00
B 0 300,000 250,000 250,0
00
300,0
00
250,0
00
55 10 250,0
00
A 0 250,000 300,000 300,0
00
450,0
00
300,0
00
c. The scheme closed to new entrants three years after it was launched, and assuming
contributions use the EAN method.
Ag
e at
the
star
t of
the
yea
r
Number
of
employe
es
Avera
ge
salary
Grad
e
EAN
Metho
d
( PVF
B)
NC=PVF
B/
Annuity
from
fromval-
dt
retiremen
t age
AL=NC*Ann
uity from
entry- age to
retirement
Year 1 Year 2 Yea
r 3
30 210 78,000 B 125,000 175,0
00
215,0
00
30 20 100,00
0
A 175,000 215,0
00
250,0
00
40 220 87,000 B 250,000 275,0 300,0

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00 00
40 15 150,00
0
A 300,000 - 175,0
00
45 240 95,000 B 175,000 175,0
00
250,0
00
45 30 175,00
0
A 250,000 250,0
00
300,0
00
50 180 103,00
0
B 300,000 300,0
00
175,0
00
50 25 185,00
0
A 175,000 175,0
00
250,0
00
55 50 103,00
0
B 250,000 250,0
00
300,0
00
55 10 250,00
0
A 300,000 300,0
00
450,0
00
d) A large-scale redundancy occurred at the start of year 10, also assuming
contributions use the EAN method
Ag
e at
the
sta
rt
Numbe
r of
employ
ees
Avera
ge
salary
Gra
de
EAN
Meth
od
( PVF
B)
NC=PV
FB/
Annuity
from
fromval-
AL=NC*An
nuity from
entry- age to
retirement
Year
1
Year
2
Year
3

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of
the
yea
r
dt
retireme
nt age
30 210 78,000 B 175,000 125,0
00
175,0
00
215,0
00
30 20 100,00
0
A 215,000 175,0
00
215,0
00
250,0
00
40 220 87,000 B 275,000 250,0
00
275,0
00
300,0
00
40 15 150,00
0
A - 300,0
00
- 175,0
00
45 240 95,000 B 175,000 175,0
00
175,0
00
250,0
00
45 30 175,00
0
A 250,000 250,0
00
250,0
00
300,0
00
50 180 103,00
0
B 300,000 300,0
00
300,0
00
175,0
00
50 25 185,00
0
A 175,000 175,0
00
175,0
00
250,0
00
55 50 103,00
0
B 250,000 250,0
00
250,0
00
300,0
00
55 10 250,00
0
A 300,000 300,0
00
300,0
00
450,0
00

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3) Identify 10 other scenarios that might affect the progression of the scheme and
contributions required.
While ensuring that policies set for contribution of pension funds, different demographics and
factors have been factored in. this is to make it easier to cater for policies that are both
sustainable and accessible to the employees. There have been different factors that are
affecting the contribution, growth and progress of a pension scheme.
1. The first challenge is the considerable challenges in timing and demographic ageing
of employees. Most of the workforces are made of different demographics from
gender and age. In Europe for example, the workforce remains to be of the old and
therefore category B of the workforce who are paid much higher wages and a
considerable higher contribution to pension schemes.
2. The second challenge is the design of the pension scheme. Faced by an increase in the
dependency ration and old age, pension schemes have faced challenges in the
sustainability and growth and this has led to change in policy to ensure that there is
fairness within generations and between genders that is male and females. Reforms
should be brought to ensure sustainability especially in public pension funds
(Cowling, et al, 2019).
3. Recognition of adaptive measures to sustainability of the pension funds is also another
factor affecting pension funds. Changes in pension schemes will tend to make more
benefits in labor development and in the financial markets. There are important risks
relating to employment rates and budgetary considerations.
4. Lower prospective growth and sustainability concerns have been increased by the
crisis. The debt crisis have affected most of the employees and in today’s world, the

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pensioners have been largely protected against such losses but the scheme may be
affected by large portions of unemployment in the economy and lower contributions.
This are all crisis that highly affect the active population who are mainly in
employment.
5. Market exposure is also a crisis that is designed to be in risk sharing. The pension
funds must be protected from great risks.
6. Sustainability and adequacy are two sides of the same coin. This means that
employees have to work more to ensure that both factors are met. The challenges in
this is that pension funds are affected due to economic crisis and changes in working
age demographics. Pension schemes have seen less contributions amid economic
crisis and unemployment rate soaring.
7. Transparency of information are essential in ensuring that there is public trust in
pension funds. To ensure this happens, pension schemes must ensure that their
financials are highly public.
8. The main challenge facing growth and development of pension funds are employment
rates demographics. As more and younger people lack employment, 40% of
employees in Europe are above the age of 60 while less women are in employment
also (Hitchcox, et al, 2018).
9. Policy in pension funds needs to ensure that retirement benefits are at present and in
the future. To take into account a specific country, policies need to ensure that the
pensioners have pre-retirement income as well as the pension benefits.
10. Lastly, Pension schemes have seen less contributions amid economic crisis and
unemployment rate soaring.

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4. Write a business memo to the Board of Trustees outlining different speeds of
funding and explain how conflicts between different stakeholders may be
managed.
DATE: 14TH FEB, 2020
TO: The Board of Trustees
FROM: Emmaus Sanders Pensioners
SUBJECT: Managing Conflicts between Different Stakeholders in Speeds of Funding
I am writing to explain how conflict between different stakeholders can be managed and
avoided in a public domain. Whereas the most conspicuous and dominant theoretical
perspective in corporate governance of pension schemes, there is a conflict between
executives of pension funds and shareholders. In practice, the pension executives must
adjudicate frequently between multiple principle demands and the conflict of interest.
The solution is to examine how a firm will be compensated in their defined benefit (DB)
pension plans of participating employees. The management must ensure that policies are well
set such that they transparency is maintained in the system. Participating employees must
ensure that they forgo some of their salaries in order to ensure that they have adequate post
retirement earnings. The employees in different firms rely on pension fund employees to
properly manage and fund assets for future payouts.
Effective corporate structures should be set to ensure that every role is given to a specific
member of the executive such as Auditing, Finance, and Governance etc(Holzmann, et al,
2019).

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Whether the executive do so, I presume is determined by separating and parting the powers
between the employees interest and the shareholders interest. Earning management in pension
funds should also be introduced to the executive such as returns on assets and retirement
plans.
The debt crisis have affected most of the employees and in today’s world, the pensioners
have been largely protected against such losses but the scheme may be affected by large
portions of unemployment in the economy and lower contributions.
Yours Faithfully
Daniel
CEO-Emmaus Sanders Pensioners.
5) Write a two-page magazine-style article explaining aspects of the scheme relevant to
the Grade B employees in preparation for the launch.

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Grade A employees are better remunerated
and salaried and have a better pension
scheme. They seem to the management or
at least more experience than Grade B
employees. They are better paid and are
fewer in the firm.
Grade B employees seem to be of lower
training or are second to grade A
employees. It could be that grade B
employees are locals while grade A
employees are expatriates or management
based employees (Platanakis, and
Sutcliffe, 2017).
The aspects of the scheme relevant to
grade B employee is that it is a greater
pool of fund receiving less fund but from
many employees. It is a lower scheme than
grade A scheme and may have even a
higher and better rates than the other
schemes.
The solution is to examine how a firm will
be compensated in their defined benefit
(DB) pension plans of participating
employees. The management must ensure
that policies are well set such that they
transparency is maintained in the system.

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The pension scheme may include
predicting the persons age, health
conditions, gender and even their possible
lifespan. Large statistical data that is
creatable to the uncertain variables and
that may lead to a predictive variable
(Schutte, 2018).
This method is an estimate and a forecast
on an uncertain variable used for the sole
purpose of calculating insurance premiums
and benefits.

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References
Arnold, S., del Carmen Boado-Penas, M. and Song, Z., 2019. Minimum Pension and
Longevity Risk: a Solution for Notional Defined Contribution Pension Schemes.
Ayuso, M., Bravo, J.M. and Holzmann, R., 2016. On the heterogeneity in longevity among
socioeconomic groups: Scope, trends, and implications for earnings-related pension schemes.
Barrientos, A., 2018. Pension Reform in Latin America. Routledge.
Beetsma, R.M., Chen, D. and van Wijnbergen, S., 2019. Unhedgeable Inflation Risk within
Pension Schemes.
Cowling, C.A., Fisher, H.J., Powe, K.J., Sheth, J.P. and Wright, M.W., 2019. Funding
defined benefit pension schemes: An integrated risk management approach. British Actuarial
Journal, 24.
Hitchcox, A.N., Patel, C., Ramsey, C.J., Studd, E.L., Ma, L.T., Elliott, M.B. and Keogh,
T.W., 2018. Integrated risk management for defined benefit pension schemes: a practical
guide. British Actuarial Journal, 23.
Holzmann, R., Palmer, E., Palacios, R. and Sacchi, S. eds., 2019. Progress and Challenges of
Nonfinancial Defined Contribution Pension Schemes: Volume 1. Addressing Marginalization,
Polarization, and the Labor Market. The World Bank.
Platanakis, E. and Sutcliffe, C., 2017. Asset–liability modelling and pension schemes: the
application of robust optimization to USS. The European Journal of Finance, 23(4), pp.324-
352.
Schutte, H., 2018. Feasibility test for Defined Contribution pension schemes.

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