Question

Nasty Industries is closing down an outmoded factory and throwing all of its workers out on the street. Nasty’s CEO is enraged to learn that the firm must continue to pay for workers’ health insurance for 4 years. The cost per worker next year will be $2400 per year, but the inflation rate is 4%, and health costs have been increasing at 3 percentage points faster than inflation. What is the present value of the obligation? The nominal discount rate is 10% and company does not pay taxes.

Answer 1

The real discount rate is calculated as follows : -

(1 + nominal discount rate) Real discount rate = 1 (1 + inflation rate)

Real discount rate = (1 + 0.10) (1 +0.04)

Real discount rate = 5.77%

The health care costs increases at 3 percentage points faster than inflation.

3 Growth rate of health care costs = 0.04 + 0.04

Growth rate of health care costs = 4.12%

The present value of the obligation is calculated using the present value of growing annuity equation

Present value of growing annuity=C Ir-gr

Present value of obligation = $2400 west obligation - 59400_ 1 0.0577 -0.0412 _ 1 0.0577 -0.0412 (1+0.0412) (1 + 0.0577)

Present value of the obligation = $ 8,866.11