Question

please help me draw the labelled cash flow

For the cash flows shown below, determine the present worth & the equivalent uniform worth in years 1 through 5 at an interest rate of 18% per year compounded monthly. Draw the cash flow diagram as well. (6+ 2 + 2 pts) Year 0 1 2 3 4 5 Cash Flows, s 0 200,000 0 350,000 0 400,000

Answer 1

Years 3 0 1 2 4 5 2000000 3500000 400000 Cash Inflow

Years 3 0 1 2 4 5 A A A A A Cash Inflow
Ans. Nominal interest rate, r = 18% per annum

=> Effective monthly interest rate, m = r/12 = 18/12 = 1.5% per month

=> Effective annual interest rate, i = (1+m)^12 -1 = (1+0.015)^12 - 1 = 0.19562 or 19.562%

Present worth of the cash flow at interest rate i,

PW = 0 + 200000/(1+i) + 0 + 350000/(1+i)^3 + 0 + 400000/(1+i)^5

=> PW = $535774.83

For equivalent uniform worth, we will use the formula for present worth of the annual equivalent cashflows (A) at interest rate 19.562% and  present worth $535774.83, we get

PW = 535774.83 = A*[(1-1/(1+0.19562)^5)/0.19562]

=> A = $177428.477

Thank You