Question

A company is developing a special vehicle for Arctic exploration. The development requires an initial investment of ​$75,000 and investments of ​$51,000 and $42,000 for the next two​ years, respectively. Net returns beginning in Year 4 are expected to be ​$34,000 per year for 10 years. If the company requires a rate of return of 10​%, compute the net present value of the project and determine whether the company should undertake the project.

Answer 1

The net present value (NPV) of the project is $88,920.51. Therefore, the company should undertake the project as it is expected to generate a positive return and meets the required rate of return of 10%.

Step-by-step explanation:

To calculate the net present value (NPV) of the project, we need to discount the future cash flows to their present values using the company's required rate of return.

Step 1: Calculate the present value (PV) of the initial investment:

PV of initial investment = -$75,000 (negative because it's an outflow and represents the initial investment)

Step 2: Calculate the present values of the investments in years 2 and 3:

PV of investment in Year 2 = -$51,000 / (1 + 0.10)^2

PV of investment in Year 3 = -$42,000 / (1 + 0.10)^3

Step 3: Calculate the present values of the net returns in Years 4 to 13:

PV of net returns = ($34,000 / (1 + 0.10)^4) + ($34,000 / (1 + 0.10)^5) + ... + ($34,000 / (1 + 0.10)^13)

Step 4: Calculate the NPV by summing all the present values:

NPV = PV of initial investment + PV of investment in Year 2 + PV of investment in Year 3 + PV of net returns

If the NPV is positive, it means the project is expected to generate a positive return and is worth undertaking. If the NPV is negative, it means the project is not expected to meet the required rate of return and may not be feasible.

Now, Calculating the NPV:

PV of investment in Year 2 = -$51,000 / (1 + 0.10)^2 = -$46,860.99

PV of investment in Year 3 = -$42,000 / (1 + 0.10)^3 = -$33,540.55

PV of net returns =

($34,000 / (1 + 0.10)^4) + ($34,000 / (1 + 0.10)^5) + ... + ($34,000 / (1 + 0.10)^13) = $244,322.05

NPV = -$75,000 - $46,860.99 - $33,540.55 + $244,322.05 = $88,920.51

Answer 2

To decide on the Arctic exploration vehicle project's viability, the NPV method is used by discounting future net returns at the required rate of return of 10%. If the NPV is positive, the project is financially favorable; otherwise, if it is negative, the project should not be undertaken.

Step-by-step explanation:

The subject at hand involves the evaluation of a business investment using the net present value (NPV) method considering a company's potential Arctic exploration vehicle project. We start by discounting the future net returns to their present value using the required rate of return of 10%. The initial investment of $75,000 and subsequent investments for the next two years, $51,000 and $42,000 respectively, are considered outflows, thus have a negative sign when computing the NPV.

The net returns start in Year 4, amounting to $34,000 for 10 years. To calculate the present value of these annuities, we use the present value of annuity formula. After computing the present value for each cash flow, we sum them all to find the NPV.

If the calculated NPV is positive, that indicates that the project's returns exceed the cost of capital (the desired rate of return of 10%), suggesting that it would be favorable for the company to undertake the project. Conversely, if the NPV is negative, the project does not meet the required rate of return and should not be carried out.