# CF excercise question

A pension fund manager knows that the following liabilities must be satisfied: Year from now: Y1 Y 2 Y3 Y4 Liability (in million): 2.0 3.0 5.4 5.8 Suppose that the pension fund manager wants to invest a sum of money that will satisfy this liability stream. Assuming that any amount that can be invested today can earn an annual interest rate of 7.6%, how much must be invested today to satisfy this liability stream? -------------------------- I think the question here is not clear enough to decide the solution? I don’t know whether the fund manager must invest an amount at the beginning for entire 4 year or invest each year separately? If investing one time, i don’t know whether the interest flow earned each year is reinvest or not? So i select the biggest liability of four years and define one time investment from the beginning as following: Investment amount = 5.8/7.6%=76.32 million Am i right or wrong? I feel I am getting something seriously wrong, so i need your help for this exercise! If this question is so naive, please feel free to laugh at me because i am actually not native speaker and i often get difficult to understand the questions like this. Thank you so much for your comments.

PV of the Cash flow stream 2.0/1.76 + 3/1.076^2 + 5.4/1.076^3 + 5.8 / 1.076^4 That is the amount that would be needed today to satisfy those liabilities in the future. CP

This is a simple PV question. It is clearly mentioned in the question to calculate how much should be invested TODAY to satisfy the CF stream. PV by definition is the amount that has to be invested today in order to make future payments and exhaust the account with the final withdrawal. PV of above mentioned CF is 13.10 millions First year interest = 13.10X1.076=14.10 payment =2 left = 12.10 Second year interest = 12.10X1.076= 13.02 payment = 3 left = 10.02 Third year interest = 10.02 X1.076 = 10.78 payment = 5.4 left = 5.38 Fourth year interest = 5.38 X 1.076 = 5.8 payment= 5.8 left = 0 Does that seem reasonable to you? In nutshell money left at the end of every year after paying the dues is invested again . thank you

Thanks both of you for your help! Cpk123 gave the right result but actually i still feel some confusion. Boilermaker’s explain seems much clearer now.

Another spin on the problem: You need the investment today (CF0) that would generate the flows CF1 to CF4 described in the problem. This could be assimilated to a NPV question, in which you are looking for your CF0. If you input CF0=0 and CF1 to CF4 as the flows described in the problem, solve for NPV with the rate of 7.6 and you get an NPV of 13.1115 which will actually be your CF0.