A geometric gradient has a positive cash flow of \$ 1,000 at EOY zero (now), and it increases 5 \% per year for the following 5 years. Another geometric gradient has a positive value of \$ 2,000 at the EOY 1, and it decreases 6 \% per year for years two through five. If the annual interest rate is 10 \%, which geometric gradient would you prefer? (4.12)
Question 4.T-Y-S.S: A geometric gradient has a positive cash flow of $1,000 at E...
\begin{aligned}&P_{\mathrm{S} 1}=\$ 1,000+\frac{\$ 1,000(1.05)[1-(P / F, 10 \%, 5)(F / P, 5 \%, 5)]}{0.10-0.05}=\$ 5,358.45 \\&P_{\mathrm{S} 2}=\frac{\$ 2,000\left[1-(P / F, 10 \%, 5)(1-0.06)^{5}\right]}{0.10+0.06}=\$ 6,804\end{aligned}
Choose S2.
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