Question

Aisha is a pension fund manager. According to her estimates, retirees will be paid benefits worth $800,000 annually 12 years from now. Given a discount rate of 6 percent, what is the present value of the payments today if these annuity payments start at the beginning of the year rather than at the end of each of the next twelve years?

An example in the book:

PEARSON 4.4 Annuity Due and Perpetuity (continued) Example 4: Annuity Due versus Ordinary Annuity Let's say that you are saving up for retirement and decide to deposit $3,000 each year for the next 20 years into an account which pays a rate of interest of 8% per year. By how much will your accumulated nest egg vary if you make each of the 20 deposits at the beginning of the year, starting right away, rather than at the end of each of the next twenty years PEARSON 4.4 Annuity Due and Perpetuity (continued) Example 4 Answer Given information: PMT - $3,000; n=20; i-8%; P=0; FV-PMT (1+r)-1] FV ordinary annuity - $3,000 ((1.08)20 - 17.08] = $3,000 45.76196 = $137,285.89 FV of annuity due = FV of ordinary annuity *(1+r) FV of annuity due = $137,285.89*(1.08) = $148,268.76 PEARSON 4.4 Annuity Due and Perpetuity (continued) Perpetuity. A Perpetuity is an equal periodic cash flow stream that will never cease. The PV of a perpetuity is calculated by using the following equation: PV-PM

Answer 1

Annuity can be defined as a contract between two parties to make either lump sum payment or a series of payments in consideration to receive regular disbursements either at beginning of the period or at some future interval.

Annuity are of two types:

1. Annuity Regular: Under annuity regular, the first payment or receipt takes place at the end of the first period.
2. Annuity Due or Annuity Immediate: Under annuity due or annuity immediate, the first payment or receipt takes place today or at the beginning of the annuity period.

As per the information provided, the present value of the annuity immediate is calculated by using the steps given below:

Step 1: Compute present value of the annuity as if it were a regular annuity for one year less i.e., for 11 years

= 800,000 X P(11,0.06) = 800,000 x 7.88687 = 6,309,499.67

Here, P stands for Present Value at 6% rate for period of 11 years.

Step 2: Now, add initial amount of benefit to the step 1 value:

=(6.309.499.67-800,000)=7, 109,499.67

Hence, the amount of Present Value of the payments today if these annuity payments starts at the beginning of the year comes out to be $ 7,109,499.67