Question

Can someone please explain this on a step by step way so I can understand it thank you!

Q3.1 You have been hired to run the pension fund for a small company with five employees. You estimate, based upon their ages and retirement schedules, that your liabilities under the plan will be as follows: Years 6-10 11-20 21-25 Expected cash payments £100,000 £250,000 E100,000 You currently have £500,000 in investments in the plan. You want to fully fund all your above-listed liabilities by the end of year 5. How much would you have to set aside each year for the next five years to ensure this, if your opportunity cost is 8%? (15 marks)

Answer 1

NOTE: The underlying logic behind this problem is that the annual amount to be set aside beginning one year from now and continuing up to the end of Year 5 and the initial 500000 pound, should have a combined future value (at end of Year 5) equal to the sum of the discounted values at t=5 years, of all pension liabilities. This is under the assumption that all liabilities are due at the end of the year. This implies that the first set of liabilities of 100000 pound between year 6 and year 10 needs to be discounted to end of year 5, the next set of liabilities of 250000 pound between year 11 and year 20 needs to be discounted to end of year5 and so on. The combined value of all these discounted values should be equal to the sum of the initial investment's future value and annual deposits future value at the end of year 5.

Combined Discounted Value of All Pension Liabilities = 100000 x (1/0.08) x [1-{1/(1.08)^(5)}] + 250000 x (1/.08) x [1-{1/(1.08)^(10)}] x [1/(1.08)^(5)] + 100000 x (1/0.08) x [1-{1/(1.08)^(5)}] x [1/(1.08)^(15)] = 1666830.03837 pound

Future Value of Initial Investment at end of Year 5 = 500000 x (1.08)^(5) = 734664.0384 pound

Let the annual deposits be K pound per annum

Therefore, K x (1.08)^(4) + K x (1.08)^(3) + K x (1.08)^(2) + K x (1.08) + K = 1666830.03837 - 734664.0384

K x 5.8666 = 932166

K = 158893.7374 pound or 158893.74 pound approximately which is close to the quoted answer of 158893.8326