Question

a) For the cash flows shown below, determine the present worth at an interest rate of 12% per year.    Draw the cash flow diagram.

(b) If the cash flow is converted into an A series from year 1 through year 5, what would be the amount of the uniform cash flow series?

cash flow for yr 0 is $0, for yr 1 is $0, for yr 2 is $800, for yr 3 is $600, for yr 4 is $400, for year 5 is $200

Answer 1

a)

It is s a cash ordinary annuity with uniform arithmetic gradient of -$200 which starts at year 2.

PW of cash flows=[800*(P/A,0.12,4)-200*(P/G,0.12,4)]*(P/F,0.12,1)

Let us calculate the interest factors

(P/F,0.12,1)=1/(1+0.12)^1=0.892857

So,

PW of cash flows=PW=[800*3.037349-200*4.127309]*0.892857=$1432.52

b)

Uniform cash flow series=PW*(A/P,0.12,5)=1432.52*(A/P,0.12,5)

Let us calculate the interest factor

So,

Uniform cash flow series=1432.52*0.277410=$397.40