Question

Dave Cooke hits the $160,000 jackpot at the Palms Casino in Las Vegas. The casino gives him two options for collecting his​ winnings:

Option A​:	Cooke can take all of his winnings today. They will be taxed by the federal government at 20​%.
Option B​:	Cooke can receive his winnings on an installment plan. He would receive 2020 equal payments of $10,000 beginning today. Each payment will be taxed at a rate of 10​%.

​(Assume that taxes are taken out at the time of payment under both​ options.)

Requirement: Given an interest rate of 11​%, compounded​ annually, which option should Cooke ​choose?

Begin by computing the present value of option A.

The present value of Option A is $

????

Now compute the present value of option B.

The present value of Option B is $

????

Cooke should choose ______.

A. Option A

B. Option B

Answer 1

Present Value of Option A = Amount Received * (1- Tax rate) = $160,000*80% = $128,000

Option B

PMT = Amount Received * (1- Tax rate) = 10000*90% = $9000

Int Rate (r) = 11%

Time Period (n) = 20 years

Present Value of Option B = PMT * ((1+r)^n -1)/r = 9000 *( (1.11)^20 -1).11 = $ 577,825.49

Hence, Cooke should choose Option B.