Question

You are the recipient of a gift that will pay you $25,000 one year from now and every year thereafter for the following 24 years. The payments will increase in value by 2.5 percent each year. If the appropriate discount rate is 8.5 percent, what is the present value of this gift? STEPS FOR BAII PLUS CALCULATOR PLEASE!

Answer 1

Calculation of Present Value of Growing Annuity With the Use of Financial Calculator:

Step 1: Calculate I/Y (Rate)

The value of I/Y can be calculated as below:

I/Y = (Discount Rate - Growth Rate)/(1+Growth Rate) = (8.5%-2.5%)/(1+2.5%) = 0.058537

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Step 2: Calculate Amount of PMT (Payment)

The value of PMT is arrived as below:

PMT = Amount of First Payment/(1+Growth Rate) = 25,000/(1+2.5%) = $24,390.24

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Step 3: Calculate PV (Present Value) of Gift with the Use of PV Function

The following values will have to be used in the PV (Present Value) function of the financial calculator:

I/Y = 0.058537, N = 25, PMT = $24,390.24 and FV = 0 (FV indicates Future Value which is 0 in this question]

Present Value of Gift (PV) = PV(I/Y,N,PMT,FV) = PV(0.058537,25,24390.24,0) = $316,172

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Calculation of Present Value of Growing Annuity With the Use of Formula:

The present value of a growing annuity can be calculated with the use of following formula:

Present Value of a Growing Annuity = Value of First Payment Payment/(Discount Rate - Growth Rate)*[1-((1+Growth Rate)/(1+Discount Rate))^Period]

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Here, Value of First Payment Payment = $25,000, Discount Rate = 8.5%, Growth Rate = 2.5% and Period = 25

Substituting these values in the above formula, we get,

Present Value of Gift = 25,000/(8.5%-2.5%)*[1-((1+2.5%)/(1+8.5%))^25] = $316,172