Question

2. (5 points) Nerwin, Inc. is a furniture manufacturing company with 50 employees. Recently, after a long negotiation with the local labor union, the company decided to initiate a pension plan as a part of its compensation plan. The plan will start on January 1, 2014. Each employee covered by the plan is entitled to a pension payment each year after retirement. On the basis of a discussion with the supervisor of the Personnel Department and an actuary from an insurance company, the controller develops the following information related to the pension plan. Average length of time to retirement Expected life duration after retirement Total pension payment expected each year after retirement for all employees. Payment made at the end of the year. Amount includes all employees. 10 years 15 years $300,000 per year The interest rate to be used is 7%. Required: Calculate the present value of this deferred annuity (at January 1, 2014).

Answer 1

Basically, for this pension plan, the company must be able to pay $300,000 every year at the end of the year for a total of 15 years (This payment shall start after 10 years)

Now, let us consider the time reference as that at the end of 10 years from now. Here, the first payment of $ 300,000 is at the end of one year and the 15th payment is at the end of 15 years

The present value of all these amounts at this time reference (PV₁₀) is given by

PV₁₀ = 300,000/(1+0.07) + 300,000/(1+0.07)² + ......+ 300,000/ (1+ 0.07)¹⁵

Applying the sum of GP formula ,

PV₁₀ = 300000/1.07 * (1-(1/1.07)¹⁵) / (1- (1/1.07))

= 300000/0.07 * (1- (1/1.07)¹⁵)

= 2,732,374.20

Hence , the present value of this annuity happening after 10 years (deferred annuity) is given by

PV₀ = PV₁₀ / (1+0.07)¹⁰

= 2732374.2 / 1.07¹⁰

  = $1,389,000.49