# Spending $1,500 more today for a hybrid engine rather than a conventional gasoline engine will... ## Question: Spending$1,500 more today for a hybrid engine rather than a conventional gasoline engine will result in annual fuel savings of $300. How many years must these savings continue in order to justify the extra investment if money is worth 10% per year compounded monthly? ## Present Value of money Present value of money refers to the current value of the future cash flows, we accept any project or investment if the present value of future cash inflows is more than the initial investment. We need to compute the present value of inflows for this analysis which can be computed using the present value factor or present value annuity factor in case of multiple cash flows ## Answer and Explanation: • Present Value of the inflows should be at least equal to initial investment =$1500
• Effective annual rate => (1 + nominal rate / 12)^12 - 1 => (1 + 0.1 / 12)^12 = 10.47% or 0.1047
• Annual Cash inflow = $300 • Period = ?? Now, Present value = Cash inflow * ((1 - (1 + rate)^-period)/ rate$1500 = \$300 * ((1 - (1 + 0.1047)^-period) / 0.1047

0.5235 = 1 - (1.1047)^-period

(1.1047)^-period = 0.4765

1.1047 = (0.4765)^period

solving this we get period = 7.44 years or 7 years and 5 months

Answer is 7 years and 5 months