Each year, many companies in the Netherlands have to decide on the amount of money they set
Question:
Each year, many companies in the Netherlands have to decide on the amount of money they set aside and reserve to fund their pension plans.
Consider the case of ASML, which makes these decisions based on an 8-year rolling horizon. Specifically, ASML’s internal regulations state that the amount they should set aside in a year has to be such that, if that amount was set aside in each of the next 8 years, there will only be a 1 in 8 chance that its pension fund will fall short after 8 years. (last year, for example, ASML set aside €32 mln).
ASML’s pension fund distinguishes between two classes of retirees: classified and non-classified. Currently, the fund provides pension benefits for 5,000 classified retirees and 2,500 non-classified retirees. However, the number of classified retirees will change every year, and ASML believes the annual change in classified retirees will follow a normal distribution with a mean of 3% and a standard deviation of 1.5%. Similarly, ASML believes that the change from year to year for non-classified retirees will follow a normal distribution with a mean of 2% and a standard deviation of 1%.
On average, ASML pays its classified retirees an annual pension of €60,000 and its non-classified retirees an annual pension of €30,000. However, these pensions are indexed to inflation, which ASML expects will follow a triangular distribution that ranges between 1% and 6%, with a most likely value of 2.5%.
Currently, ASML’s pension fund has €2.3 bln in reserves. Investments with this fund yield an annual return that is normally distributed with a mean of 12% and a standard deviation of 3%.
Create a spreadsheet model for this problem and use monte-carlo simulation to determine the amount of money ASML should set aside this year to fund their pension plan.
a) What is your recommendation?
b) Suppose now that regulation changes would require that there can only be a 5% chance that its pension fund will fall short after 8 years? How will that change your recommendation?
c) Suppose now that ASML recognizes there is a positive correlation between the annual inflation and the annual returns? Assume their correlation coefficient equals 0.3. How does this impact your recommendation?
Business Statistics a decision making approach
ISBN: 978-0133021844
9th edition
Authors: David F. Groebner, Patrick W. Shannon, Phillip C. Fry