Question

Q1. Your firm decides to begin to fund a retirement pension for a new employee. The details of the pension plan are as follows:

1. The employee is 30 years old; the pension fund will begin to make annual payments to the employee 20 years from the date when funding for the pension begins.
2. When payments begin, the employee will receive quarterly payment for 15 years. The first quarterly payment will be $ 20,000, and each succeeding payment will grow by 2.5% (annual rate 10%).
3. Money paid into the funds is assumed to earn constant 12% annual rate of return.
4. The annual contributions your firm makes to the fund will grow at a 3%.

a) As a financial manager, please determine how much you need to deposit now to get this pension plan in motion?  

b) If the return from the funds is lower than 12%, will the retirement pension be under-funded or over-funded? Why?     

Answer 1

Answer a

Quarterly Payment =$20000

Payment growth rate, g = 2.5%

Rate of return, r = 12%

Quarterly, r = 2%/4 =3%

Total no of periods =15*4=60 quarters

For calculation of PV, n=59 as first payment is made at start of quarter.

First payment of Annuity will be 20000*(1+2.5%) =20000*1.025=$20500

Hence PV of the pension fund at the time of start of pension fund will be PV=A*(1-(1+g)^n/(1+r)^n)/(r-g)

=20500*(1-(1+2.5%)^60/(1+3%)^59)/(3%-2.5%)

=20500*(1-(1.025/1.03)^59)/(0.5%)

=20500*(1-0.995^59)/0.005

=20500*(1-0.7504)/0.005

=20500*0.2496/0.005

=$1023225.57

Hence the PV of the fund at start of pension fund=1023225.57+20000 = $1043225.57

Hence FV of the annual payments will be $1043225.57

n= 20 years

r = 12%

g = 3%

Hence FV = A*((1+r)^n-(1+g)^n)/(r-g)

or, 1043225.57 = A*((1+12%)^20-(1+3%)^20)/(12%-3%)

or, 1043225.57 = A*((1.12)^20-(1.03)^20)/(9%)

or, 1043225.57 = A*(9.6463-1.8061)/0.09

or, 1043225.57 = A*7.8402/0.09

or, A=1043225.57 *0.09 / 7.8402

or, A = 11975.53

Hence Amount to be deposited now =$11975.53

Answer b

If return is less than 12%, the FV of fund will be lesser, hence the fund will be under funded