Question

Find the value of x below such that the positive cash flows will be exactly equivalent to the negative cash flows, if the interest rate is 10% per year

Find the value of x below such that the positive cash flows will be exactly equivalent to the negative cash flows, if the interest rate is 10% per year. $700 $700 Answer: Year 0 1 2 3 4 5 6 7 8 9 10 11 12 HHHHHHHHHHHH Equation: $800 $800 $950

Answer 1

As per the information given in the question

rate of interest (i) =10%

Period of the cash flow = 12

The present worth of negative cashflow = 800 + 800(P/F,10%,1) + 950(P/A,10%,2)(P/F,10%,6) + 800(P/A,10%,3)(P/F,10%,9)

= 800 + 800(0.90909) + 950(1.73554)( 0.56447) + 800(2.48685)( 0.42410)

= 800 + 727.272 + 930.6772 + 843.7385 =$3301.6877

The present worth of negative cashflow =$3301.6877

The present worth of positive cashflow =700(P/F,10%,2) + 700(P/F,10%,5)+ X(P/F,10%,9)

=700(0.82645) + 700(0.62092)+ X(0.42410)

=578.515 + 434.644+ X(0.42410) = $1013.159 + X(0.42410)

The present worth of positive cashflow =$1013.159 + X(0.42410)

As per the question the value of the positive cash flow equals with the value of negative cash flow, therefore

The present worth of positive cashflow = The present worth of negative cashflow

$1013.159 + X(0.42410) = $3301.6877

X(0.42410) = $2288.5287

X = ($2288.5287)/(0.42410) = $5396.2006 or Approx $5396.20

The value of X = $5396.20