Question

Suppose there is an investment project with the following cash flows to be received at the end of next three years. If the interest rate is 7 percent: (a) What is the value of these cash flows at the end of Year 3? (b) What is the value of these cash flows today (today is Year 0) ?

Answer 1

To calculate the value of cash flows at the end of Year 3 and the present value today, the formulas for future value and present value of money are used.

Step-by-step explanation:

To calculate the value of cash flows at the end of Year 3, you would use the formula for future value of money:

Future Value = Cash Flow / (1 + interest rate)^time

Substituting in the values given, the future value at the end of Year 3 can be calculated. To find the value of these cash flows today, you would use the formula for present value of money:

Present Value = Cash Flow / (1 + interest rate)^time

Again, substituting in the given values, you can calculate the present value of these cash flows.

Answer 2

The value of the cash flow of $1500.00 at the end of Year 3 is approximately $1224.51.

The present value of all cash flows is approximately $3205.61.

How is that so?

1. Define the variables:

• FV: Future value of each cash flow (given)
• PV: Present value of each cash flow
• r: Interest rate (given as 7%)
• n: Number of periods (year)

2. Calculate the individual present values:

2.1. Year 1:

FV: $1000.00

r: 7%

n: 1

`PV Year 1 =`
`FV / (1 + r)^n`

`PV Year 1 = 1000.00 / (1 + 0.07)^1`

≈ 934.58

2.2. Year 2:

FV: $1200.00

r: 7%

n: 2

`PV Year 1 = 1000.00 / (1 + 0.07)^1`

`PV Year 2 = 1200.00 / (1 + 0.07)^2`

≈ 1046.52

2.3. Year 3:

FV: $1500.00

r: 7%

n: 3

`PV Year 3 = FV / (1 + r)^n`

`PV Year 3 = 1500.00 / (1 + 0.07)^3`

≈ 1224.51

3. Calculate the total present value:

PV Total = PV Year 1 + PV Year 2 + PV Year 3

PV Total = 934.58 + 1046.52 + 1224.51 ≈ 3205.61

Therefore, the present value of all cash flows is approximately $3205.61.

Below is the complete question:

Suppose there is an investment project with the following cash flows to be received at the end of next three years $1000.00, $1200.00, $1500.00. If the interest rate is 7 percent: (a) What is the value of these cash flows at the end of Year 3? (b) What is the value of these cash flows today (today is Year 0) ?