the cash flow diagram below represents a series of future cash flows. determine the correct expression for…

the cash flow diagram below represents a series of future cash flows. determine the correct expression for their corresponding present worth, p.\np =?\ni = 10%\n0 1 2 3... 20 21 22 23... 50\na1 = $6,500\na2 = $8,500\n\na. 6,500(p/a, 10%, 20) + 8,500(p/a, 10%, 50)\nb. 6,500(p/a, 10%, 20) + 8,500(p/a, 10%, 30)\nc. 6,500(p/a, 10%, 20) + 8,500(p/a, 10%, 30)(p/f, 10%, 20)\nd. 6,500(p/a, 10%, 20) + 8,500(p/a, 10%, 30)(p/f, 10%, 30)

the cash flow diagram below represents a series of future cash flows. determine the correct expression for their corresponding present worth, p.\np =?\ni = 10%\n0 1 2 3... 20 21 22 23... 50\na1 = $6,500\na2 = $8,500\n\na. 6,500(p/a, 10%, 20) + 8,500(p/a, 10%, 50)\nb. 6,500(p/a, 10%, 20) + 8,500(p/a, 10%, 30)\nc. 6,500(p/a, 10%, 20) + 8,500(p/a, 10%, 30)(p/f, 10%, 20)\nd. 6,500(p/a, 10%, 20) + 8,500(p/a, 10%, 30)(p/f, 10%, 30)

Answer

Explanation:

Step1: Analyze first - stage cash - flow

The first - stage cash - flow $A_1 = 6500$ occurs from year 1 to year 20. The present - worth factor for an ordinary annuity is $(P/A,i,n)$. Here, $i = 10%$ and $n = 20$, so the present worth of this annuity is $6500(P/A,10%,20)$.

Step2: Analyze second - stage cash - flow

The second - stage cash - flow $A_2=8500$ occurs from year 21 to year 50. First, find the present worth of this 30 - year annuity at the end of year 20 using the annuity present - worth factor $(P/A,10%,30)$. Then, to get its present worth at time $t = 0$, we need to discount it back 20 years using the single - payment present - worth factor $(P/F,10%,20)$. So the present worth of the second - stage cash - flow is $8500(P/A,10%,30)(P/F,10%,20)$.

Step3: Calculate total present worth

The total present worth $P$ is the sum of the present worth of the first - stage and second - stage cash - flows, i.e., $P=6500(P/A,10%,20)+8500(P/A,10%,30)(P/F,10%,20)$.

Answer:

C. 6,500(P/A, 10%, 20) + 8,500(P/A, 10%, 30)(P/F, 10%, 20)