Question

1. Obrien Group wishes to accumulate funds to provide a retirement annuity for its Director of Research, Peter Alexander; Mr. Alexander by contract will retire at the end of exactly 12 years. On retirement, he is entitled to receive an annual end-of-year payment of $42,000 for exactly 20 years. If he dies prior to the end of the 20-year period, the annual payments will pass to his heirs. During the 12-year 'accumulation period', Obrien wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 9 percent interest. Once the 20-year 'distribution period' begins, Obrien plans to move the accumulated monies into an account earning a guaranteed 12 percent per year. At the end of the distribution period the account balance will equal zero. Note the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13.

Required:

1. What is the time value of money? Explain using the above scenario and draw a timeline depicting all the Cash flows associated with Obrien's view of the retirement annuity.
2. How large a sum must Obrien accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?

3. How large must Obrien's equal annual end-of-year deposits into the account be over the 12-year accumulation period to fund fully Mr. Alexander’s retirement annuity.

4. How much should Obrien have to deposit annually during the accumulation period if it could earn 10 per cent rather than 9 per cent during the accumulation period?

5. How much would Obrien have to deposit annually during the accumulation period if Mr. Alexander’s retirement annuity was a perpetuity and all other terms were the same as initially described?

Answer 1

A. The time value of money is a basic financial concept that holds that money in the present is worth more than the same sum of money to be received in the future. This holds true because current money can be invested and earn a return, thus creating a bigger amount of money in the future.

0 yr <---------Investing money every year for 12 years---------->13yr<---- Drawings from pool of money------->32yr

15576 deposited each year for 12 years at 9% = 313,716.63 = Withdrawal of 42000 for next 20 yrs,12% interest  

B. We will use excel functions to calculate the value.

Since we need to find the value of funds which will furnish the 20 yr requirements of O'Brien's retirement

We will use PV function to find the value

Here Rate = 12% (The retirement funds will offer 12% returns)

Time = NPER = 20

Annual Withdrawals = PMT = $42000

FV = 0

Type = 0 (Drawings at the end of the period)

The PV = Value of funds which will furnish the 20 yr requirements of O'Brien's retirement

= PV(12%,20,42000,0,0) = $313,716.63

C. We will find the equal annual deposits using PMT function in excel

Here Rate = 9% (The rate at which accumulation grows is 9%)

NPER = 12 (12 years for accumulation)

PV = 0

FV = 313,716.63 (The value required after 12 years to fund 20 years of retirement)

Type = 0 (Payment at the end)

Annual deposits required = PMT(9%,12,0,313716.63,0)

= - $15,576.24 (the negative sign indicates cash outflow)

D. If the rate is 10%, rest all remain same as above

Annual deposits required = PMT(10%,12,0,313716.63,0) = - $14,670.43 (the negative sign indicates cash outflow)

E. If the retirement annuity is a perpetuity, which means O'Brien or dependents will draw 42000 every year, till an unlimited time

The fund required for this annuity at the retirement = Annual Requirement / Rate of return

= 42000/ 12% = $350,000

Now to calculate annual deposits,

Rate = 9% (The rate at which accumulation grows is 9%)

NPER = 12 (12 years for accumulation)

PV = 0

FV = 350,000 (The value required after 12 years to fund 20 years of retirement)

Type = 0 (Payment at the end)

Annual deposits required = PMT(9%,12,0,350000,0)

= - $17,377.73 (the negative sign indicates cash outflow)