The Dean considers Professor X to be totally incompetent thinking to firm him. U

Question

The Dean considers Professor X to be totally incompetent thinking to firm him. Unfortunately (from the Dean’s perspective) under the terms of Professor X’s contracts, the professor cannot be dismissed for 5 years.  If Professor X’s salary will be $100,000 each year (paid at the end of each year), how much will it cost the Dean to buy up the contract if the Dean believes Professor X will quit in exchange for 40% of the present value of his salary?  The discount rate is 8%.

____

$159,708

$200,000

$170,895

$399,270

Explanation / Answer

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=$100,000[1-(1.08)^-5]/0.08

=$100,000*3.992710037

=$399271.0037(Approx)

Hence cost to Dean=$399271.0037*40%

which is equal to

=$159708(Approx).

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