Suppose you have won $1,000,000 in a lottery. Your prize money is paid to you in

Question

Suppose you have won $1,000,000 in a lottery. Your prize money is paid to you in five equal annual installments of $200,000 the first of which is paid right away on the spot. The other four payments are made in the next four years.The lottery organization offers you the option of receiving $800,000 in cash on the spot instead of the five installments. Would you take the lesser amount in cash or would you go for the five installments? Demonstrate.
Note: Assume the interest rate on risk-free deposits is 5% while one could (potentially) get higher returns on riskier investments such as stocks.  

Be sure to show/explain your work PLEASE

Explanation / Answer

The present worth of $800,000 in cash is $800,000. If we are to accept the original cash stream where we are paid five equal annual installments of $200,000, its present value must be greater than $800,000.

We know that Present value = cash flow 1*(1 + rate)^-1 + cash flow 2*(1 + rate)^-2 + ... + cash flow n*(1 + rate)^-n

PV of prize money = $200,000 + $200,000*(1+5%)^-1 + $200,000*(1+5%)^-2 + $200,000*(1+5%)^-3 + $200,000*(1+5%)^-4

= $909,190.10

Since the present worth of the prize money received in installments is higher, we should not accept $800,000 in cash.

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