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Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $2,750 today. If you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today.
1) At an interest rate of 6% per year, the winner would be better off accepting the ________ (lump sum or payments over time), since it has the greater present value.
2) At an interest rate of 9% per year, the winner would be better off accepting ________ (lump sum or payments over time), since it has the greater present value.

Respuesta :

Shahzaibfaraz

Answer:

1) the payment over time ( $2833.39 )

2) the payment over time ( $2759.11 )

Explanation:

We get the lump sum today of $2750 which is exactly the value of this amount today and there is no need to discount this amount. We will compare this amount with the present value of the cash flows we will receive over time. If the present value of over time cash flows is more than lump sum payment, we will  choose over time cash flows and vice versa.

1) The present at 6% for over time cash flows is,

  • PV = 1000 + 1000/1.06 + 1000/1.06^2 = $2833.392
  • As 2833.392 is more than 2750, we will choose payment over time.

2) The present at 9% for over time cash flows is,

  • PV = 1000 + 1000/1.09 + 1000/1.09^2 = $2759.11
  • As 2759.11 is more than 2750, we will choose payment over time.

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