Question

XKL Co. plans a new project that will generate $135018 of continuous cash flow each year for 9 years and additionally $102141 at the end of the project. If the continuously compounded rate of interest is 3.06%, estimate the present value of the cash flows. (Please use formula & SHOW ALL STEP-BY-STEP NOT excel)

Answer 1

Present Value=135018*e^(-3.06%*1)+135018*e^(-3.06%*2).....135018*e^(-3.06%*9)+102141*e^(-3.06%*9)

We see that the cash flow of 135018 follows a geomteric progression with first term as 135018*e^(-3.06%*1), number of terms as 9, common ratio as e^(-3.06%*1)
Sum of a GP=a*(r^n-1)/(r-1)
Here, a=135018*e^(-3.06%*1)
r=e^(-3.06%*1)
n=9

Hence, Present Value=135018*e^(-3.06%*1)*(1-e^(-3.06%*1*9))/(1-e^(-3.06%*1))+102141*e^(-3.06%*9)

=$1,123,576.74