Question

(2) Your wealthy Aunt offers you a graduation gift. She will give you a $10,000 lump sum payment or 1,100/year for the next 10 years. This is essentially a risk free gift from your standpoint. The risk free rate currently sites at 2.5%. Which will you take? Why? Please use the financial principles from the chapter to make this decision. show your work.

Answer 1

Lumpsum amount received today = $10000

Annual payment for next 10 years = $1100 per year, Risk free rate = 2.5%

As the lumpsum payment is received today and annual payments are spread over next 10 years.,Hence we can only compare two options by finding their equivalent values at particular time period. This can done by comparing present value of annual payment with lumpsum.

Since this is a risk free gift we will use risk free rate to discount annual payment for 10 years to find present value of annual payment of $1100

If Lumpsum amount is greater than present value of annual payments then lumpsum amount option should be chosen. On the other hand if present value of annual payments is greater than lumpsum amount, then annual payments should be chosen

To find present value of annual payments, we will pv function in excel

Formula to be used in excel: =pv(rate,nper,-pmt)

Using pv function in excel, we get present value of annual payments = $9627.27

As lumpsum amount is greater than present value of annual payments, hence lumpsum amount should be chosen

Hence we will take lumpsum payment as a gift.