Question

1.  Suppose someone offered to give you $1,000,000 five years in the future and the anticipated interest rate is 5 percent. How much is the present value of this offer?

2. Pat is debating whether to take a job as a professional therapist or a florist. She will earn $40,000 a year as a therapist or $30,000 a year as a florist. If Pat chooses to be a therapist, what is the opportunity cost?

Answer 1

(1) You will get $1,000,000 in five years and the interest rate is 5%

Present value formula:

PV = FV /(1 + i)ⁿ.

Where PV is present value; FV is future value; i is interest rate; n is number of years.

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PV = FV /(1 + i)ⁿ.

Put FV = $1,000,000; i = 5% = 0.05 and n = 5

=> PV = $1,000,000 / (1 + 0.05)⁵.

=> PV = $1,000,000 / (1.05) ⁵.

=> PV = $783526.1665

=>PV = $783526. 17

The present value of this offer is $783526.17

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(2) Pat has an option to choose a job either therapist or a florist.

She will earn $40,000 a year as a therapist or $30,000 a year as a florist.

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Opportunity cost is the forgone value of next best alternative (or it is the value of thing you give up in order to choose other thing)

In order to choose therapist job, Pat has to give up florist job.

Hence, the opportunity cost of choosing therapist job is $30,000 (i.e., the value of florist job)