Suppose a worker with an annual discount rate of 10 percent currently resides in Pennsylvania and is deciding whether to remain there or to move to Illinois. There are three work periods left in the life cycle. If the worker remains in Pennsylvania, he will earn $20,000 per year in each of the three periods. If the worker moves to Illinois, he will earn $22,000 in each of the three periods. What is the highest cost of migration that a worker is willing to incur and still make the move?

$4,973.70

Explanation:

Using ordinary annuity formula, we have

PV of Pennsylvania income = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………. (1)

Where;

P = yearly income = $20,000

r = interest rate = 10% = 0.10

n = number of years = 3

Substitute the values into equation (1) to have:

PV of Pennsylvania income = $20,000 × [{1 - [1 ÷ (1+0.1)]^3} ÷ 0.1] = $49,737.04  

PV of Illinois income = P × [{1 - [1 ÷ (1+r)]^n} ÷ r]   (2)

Where;

P = yearly income = $22,000

r = interest rate = 10% = 0.10

n = number of years = 3

Substitute the values into equation (2) to have:

PV of Illinois income = $22,000 × [{1 - [1 ÷ (1+0.1)]^3} ÷ 0.1] = $54,710.74  

Highest cost of migration = PV of Illinois income - PV of Pennsylvania income = $54,710.74 - $49,737.04   = $4,973.70

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