Question

determine the ror for a project that has an initial cost of $82,000 and would provide positive cash flows of $12,000 the first year, $14,000 the second year, $16,000 the third year, $18,000 the fourth year, $20,000 the fifth year, and $22,000 the sixth year.

Answer 1

To determine the ROR for the project, calculate the present value of the cash flows, subtract the initial cost, and divide by the initial cost multiplied by 100. In this case, the ROR is -17.85%.

Step-by-step explanation:

To determine the Rate of Return (ROR) for a project, we need to calculate the present value of the cash flows and the initial cost, and then use the formula:

ROR = (Present Value of Cash Flows - Initial Cost) / Initial Cost * 100

Here's how to calculate:

1. 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 discount rate, and n is the number of years.
2. Add up the present values of all the cash flows.
3. Subtract the initial cost from the total present value of the cash flows.
4. Divide the result by the initial cost and multiply by 100 to get the ROR as a percentage.

In this case, let's assume a discount rate of 10%. The present values of the cash flows are:

• Year 1: PV = $12,000 / (1 + 0.1)^1 = $10,909.09
• Year 2: PV = $14,000 / (1 + 0.1)^2 = $11,570.25
• Year 3: PV = $16,000 / (1 + 0.1)^3 = $11,561.98
• Year 4: PV = $18,000 / (1 + 0.1)^4 = $11,326.70
• Year 5: PV = $20,000 / (1 + 0.1)^5 = $11,111.11
• Year 6: PV = $22,000 / (1 + 0.1)^6 = $10,910.04

The sum of the present values is $67,389.17. Subtracting the initial cost of $82,000 gives a result of -$14,610.83. Dividing this by the initial cost and multiplying by 100 gives a ROR of -17.85%.

Answer 2

The rate of return (ROR) for the project is 13.79%.

How to solve

To calculate the rate of return (ROR) without using code, you can follow these steps:

Calculate the present value of the cash flows.

The present value (PV) of cash flows, determined by considering the $12,000 to $22,000 over six years at a 10% annual discount rate, represents their current worth when adjusted to present value from the future.

The formula for calculating the PV of a future cash flow is:

PV = CF / (1 + r)^n

Where:

PV is the present value

CF is the cash flow

r is the discount rate

n is the number of periods

Using this formula, you can calculate the PV of each cash flow. For example, the PV of the first cash flow is:

PV1 = $12,000 / (1 + 0.1)^1 = $10,909.09

You can calculate the PV of each of the other cash flows in the same way.

The total PV of the cash flows is the sum of the PVs of the individual cash flows. In this case, the total PV of the cash flows is:

TPV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6 = $121,283.56

Calculate the net present value (NPV) of the project.

The NPV of a project is the difference between the PV of the cash flows and the initial cost of the project. In this case, the initial cost of the project is $82,000.

NPV = TPV - IC = $121,283.56 - $82,000 = $39,283.56

Calculate the rate of return (ROR) of the project.

The Rate of Return (ROR) for a project is the discount rate where the present value of cash flows equals the initial project cost. Various methods, like financial calculators or trial and error, help find this rate. Trial and error involves adjusting discount rates until the Net Present Value (NPV) reaches zero.

In this case, the ROR of the project is approximately 13.79%.

Therefore, the rate of return (ROR) for the project is 13.79%.