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As a result of a slowdown in operations, Tradewind Stores is offering employees who have been terminated a severance package of $104,000 cash paid today; $104,000 to be paid in one year; and an annuity of $37,000 to be paid each year for 9 years. Required: What is the present value of the package assuming an interest rate of 9 percent? (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) Note: Use appropriate factor(s) from the tables provided. Round the final answer to nearest whole dollar.

Question

As a result of a slowdown in operations, Tradewind Stores is offering employees who have been terminated a severance package of 104,000cashpaidtoday;104,000 cash paid today; 104,000 to be paid in one year; and an annuity of $37,000 to be paid each year for 9 years.

Required: What is the present value of the package assuming an interest rate of 9 percent? (Future Value of 1,PresentValueof1, Present Value of 1, Future Value Annuity of 1,PresentValueAnnuityof1, Present Value Annuity of 1.)

Note: Use appropriate factor(s) from the tables provided. Round the final answer to nearest whole dollar.

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Solution

To calculate the present value of the severance package, we need to discount each component of the package to its present value using the given interest rate of 9 percent.

  1. The first component is 104,000cashpaidtoday.Sinceitspaidtoday,itspresentvalueissimply104,000 cash paid today. Since it's paid today, its present value is simply 104,000.

  2. The second component is 104,000tobepaidinoneyear.Tofinditspresentvalue,weusetheformulaforthepresentvalueofasinglesum:PV=FV/(1+r)n,whereFVisthefuturevalue,ristheinterestrate,andnisthenumberofperiods.Inthiscase,FV=104,000 to be paid in one year. To find its present value, we use the formula for the present value of a single sum: PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of periods. In this case, FV = 104,000, r = 9% or 0.09, and n = 1. So, PV = 104,000/(1+0.09)1=104,000 / (1 + 0.09)^1 = 95,412.84.

  3. The third component is an annuity of 37,000tobepaideachyearfor9years.Tofinditspresentvalue,weusetheformulaforthepresentvalueofanannuity:PV=PMT[(1(1+r)n)/r],wherePMTistheannuitypayment,ristheinterestrate,andnisthenumberofperiods.Inthiscase,PMT=37,000 to be paid each year for 9 years. To find its present value, we use the formula for the present value of an annuity: PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annuity payment, r is the interest rate, and n is the number of periods. In this case, PMT = 37,000, r = 9% or 0.09, and n = 9. So, PV = 37,000[(1(1+0.09)9)/0.09]=37,000 * [(1 - (1 + 0.09)^-9) / 0.09] = 209,536.16.

Adding up the present values of the three components, we get the total present value of the severance package: 104,000+104,000 + 95,412.84 + 209,536.16=209,536.16 = 408,949.

So, the present value of the package, rounded to the nearest whole dollar, is $408,949.

This problem has been solved

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