Ricky is thinking about borrowing $10,000 from Fred. He promises Fred cash flows of $5000 for the next three years. If Fred’s cost of capital is 10%, what is the Net Present Value of the investment for Fred?

Answer: To calculate the Net Present Value (NPV) of the investment for Fred, we need to discount the promised cash flows from Ricky back to their present value using Fred's cost of capital as the discount rate.

Here are the steps to calculate the NPV:

1. Calculate the Present Value (PV) of each cash flow. This is done by dividing the future cash flow by (1 + r)^n, where r is the discount rate (Fred's cost of capital) and n is the number of periods into the future.

2. Sum up the Present Values of all future cash flows.

3. Subtract the initial investment from the sum of discounted cash flows to get the NPV.

Given: - Future cash flows = $5000 per year for three years - Cost of capital (discount rate, r) = 10% or 0.10 - Number of periods (n) = 3 years - Initial investment (loan amount) = $10,000

Now let's calculate it:

PV of cash flow for Year 1: PV1 = $5000 / (1 + 0.10)^1 = $5000 / 1.10 ≈ $4545.45

PV of cash flow for Year 2: PV2 = $5000 / (1 + 0.10)^2 = $5000 / (1.10)^2 ≈ $5000 / 1.21 ≈ $4132.23

PV of cash flow for Year 3: PV3 = $5000 / (1 + 0.10)^3 = $5000 / (1.10)^3 ≈ $5000 / 1.331 ≈ $3756.47

Sum of the present values: Total PV = PV1 + PV2 + PV3 Total PV ≈ $4545.45 + $4132.23 + $3756.47 ≈ $12434.15

Now, subtract the initial investment to find the NPV: NPV = Total PV - Initial Investment NPV ≈ $12434.15 - $10,000 ≈ $2434.15

Therefore, the Net Present Value of the investment for Fred would be approximately $2434.15, which implies the investment would be profitable for Fred, provided the assumptions hold true.