155k views
1 vote
PRESENT AND FUTURE VALUES OF A CASH FLOW STREAMAn investment will pay $150 at the end of each of the next 3 years, $250 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 11% annually, what is its present value? Its future value?

1 Answer

3 votes

Answer:

Explanation:

To calculate the present value (PV) and future value (FV) of the cash flow stream, we can use the following steps:

Calculate the present value of each cash flow using the formula:

PV = CF / (1 + r)^n

where CF is the cash flow, r is the annual interest rate, and n is the number of years until the cash flow is received.

For the first three cash flows of $150 at the end of each of the next 3 years, assuming a starting point of Year 0, we have:

PV1 = $150 / (1 + 0.11)^1 = $134.59 (Year 1)

PV2 = $150 / (1 + 0.11)^2 = $120.75 (Year 2)

PV3 = $150 / (1 + 0.11)^3 = $107.99 (Year 3)

For the cash flow of $250 at the end of Year 4:

PV4 = $250 / (1 + 0.11)^4 = $165.14

For the cash flow of $300 at the end of Year 5:

PV5 = $300 / (1 + 0.11)^5 = $179.34

For the cash flow of $500 at the end of Year 6:

PV6 = $500 / (1 + 0.11)^6 = $277.12

Add up the present values of each cash flow to find the present value of the entire stream:

PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6

PV = $134.59 + $120.75 + $107.99 + $165.14 + $179.34 + $277.12

PV = $985.93

Therefore, the present value of the cash flow stream is $985.93.

To find the future value of the cash flow stream, we can simply add up the cash flows and then apply the future value formula:

FV = CF x [(1 + r)^n - 1] / r

where CF is the sum of the cash flows, r is the annual interest rate, and n is the number of years from the present until the future value is calculated.

CF = $150 x 3 + $250 + $300 + $500 = $1,100

n = 6 (assuming a starting point of Year 0)

FV = $1,100 x [(1 + 0.11)^6 - 1] / 0.11

FV = $2,525.72

Therefore, the future value of the cash flow stream is $2,525.72.

User Chris Smith
by
7.6k points