John wins the lottery and has the following three payout options for after-tax prize money:
1) $150,000 per year at the end of each of the next six years
2) $300,000 (lump sum) now
3) $500,000 (lump sum) six years from now
The required rate of return is 9%. What is the present value if he selects the first option? Round to nearest whole dollar.
Present value of annuity of $1:
$$\begin{array} { | r | r | r | r | }
\hline & 8 \% & 9 \% & 10 \% \
\hline 1 & 0.926 & 0.917 & 0.909 \
\hline 2 & 1.783 & 1.759 & 1.736 \
\hline 3 & 2.577 & 2.531 & 2.487 \
\hline 4 & 3.312 & 3.24 & 3.17 \
\hline 5 & 3.993 & 3.89 & 3.791 \
\hline 6 & 4.623 & 4.486 & 4.355 \
\hline 7 & 5.206 & 5.033 & 4.868 \
\hline
\end{array}$$ Present value of $1:
$$\begin{array} { | r | r | r | r | }
\hline & 8 \% & 9 \% & 10 \% \
\hline 1 & 0.926 & 0.917 & 0.909 \
\hline 2 & 0.857 & 0.842 & 0.826 \
\hline 3 & 0.794 & 0.772 & 0.751 \
\hline 4 & 0.735 & 0.708 & 0.683 \
\hline 5 & 0.681 & 0.65 & 0.621 \
\hline 6 & 0.63 & 0.596 & 0.564 \
\hline 7 & 0.583 & 0.547 & 0.513 \
\hline
\end{array}$$

Question

John wins the lottery and has the following three payout options for after-tax prize money: 
1) $150,000 per year at the end of each of the next six years
2) $300,000 (lump sum) now
3) $500,000 (lump sum) six years from now
The required rate of return is 9%. What is the present value if he selects the first option? Round to nearest whole dollar.
Present value of annuity of $1:
$$\begin{array} { | r | r | r | r | } 
\hline & 8 \% & 9 \% & 10 \% \
\hline 1 & 0.926 & 0.917 & 0.909 \
\hline 2 & 1.783 & 1.759 & 1.736 \
\hline 3 & 2.577 & 2.531 & 2.487 \
\hline 4 & 3.312 & 3.24 & 3.17 \
\hline 5 & 3.993 & 3.89 & 3.791 \
\hline 6 & 4.623 & 4.486 & 4.355 \
\hline 7 & 5.206 & 5.033 & 4.868 \
\hline
\end{array}$$ Present value of $1:
$$\begin{array} { | r | r | r | r | } 
\hline & 8 \% & 9 \% & 10 \% \
\hline 1 & 0.926 & 0.917 & 0.909 \
\hline 2 & 0.857 & 0.842 & 0.826 \
\hline 3 & 0.794 & 0.772 & 0.751 \
\hline 4 & 0.735 & 0.708 & 0.683 \
\hline 5 & 0.681 & 0.65 & 0.621 \
\hline 6 & 0.63 & 0.596 & 0.564 \
\hline 7 & 0.583 & 0.547 & 0.513 \
\hline
\end{array}$$

Quizplus · Accepted Answer

To find the present value of the annuity, we need to use the annuity payment of $150,000 per year and the present value of annuity of $1 for 6 years and a 9% discount rate. 
PV = $150,000 x 4.486 (from the table) = $673,000 (rounded to the nearest thousand)
To find the present value of the lump sum option of $300,000 now, we simply use the present value of $1 table with a 9% discount rate and 0 periods (since it's a lump sum now). 
PV = $300,000 x 0.917 (from the table) = $275,100 (rounded to the nearest thousand)
To find the present value of the lump sum option of $500,000 in 6 years, we need to use the present value of $1 table with a 9% discount rate and 6 periods. 
PV = $500,000 x 0.564 (from the table) = $282,000 (rounded to the nearest thousand)
Therefore, the best choice is option B, taking the lump sum option of $300,000 now, since it has the highest present value.

John Wins the Lottery and Has the Following Three Payout