Questions: A company is developing a special vehicle for Arctic exploration. The development requires an initial investment of 80,000 and investments of 50,000 and 43,000 for the next two years, respectively. Net returns beginning in Year 4 are expected to be 22,000 per year for 12 years. If the company requires a rate of return of 5%, compute the net present value of the project and determine whether the company should undertake the project. The net present value of the project is (Round the final answer to the nearest dollar as needed. Round all intermediate values to six decimal places as needed)

Solution Steps

The cash flows for the project are defined as follows:

• Initial investment at Year 0: \( C_0 = -80000 \)
• Investment at Year 1: \( C_1 = -50000 \)
• Investment at Year 2: \( C_2 = -43000 \)
• Annual net returns from Year 4 to Year 15: \( C_t = 22000 \) for \( t = 4, 5, \ldots, 15 \)

The present value (PV) of each cash flow is calculated using the formula: \[ PV = \frac{C}{(1 + r)^t} \] where \( C \) is the cash flow, \( r = 0.05 \) is the rate of return, and \( t \) is the year.

• Present value of initial investment: \[ PV_0 = C_0 = -80000 \]
• Present value of Year 1 investment: \[ PV_1 = \frac{C_1}{(1 + r)^1} = \frac{-50000}{(1 + 0.05)^1} \]
• Present value of Year 2 investment: \[ PV_2 = \frac{C_2}{(1 + r)^2} = \frac{-43000}{(1 + 0.05)^2} \]
• Present value of annual returns from Year 4 to Year 15: \[ PV_t = \sum_{t=4}^{15} \frac{C_t}{(1 + r)^t} = \sum_{t=4}^{15} \frac{22000}{(1 + 0.05)^t} \]

The net present value (NPV) is the sum of all present values: \[ NPV = PV_0 + PV_1 + PV_2 + \sum_{t=4}^{15} PV_t \] Substituting the calculated present values into the equation gives: \[ NPV = -80000 + \frac{-50000}{(1 + 0.05)^1} + \frac{-43000}{(1 + 0.05)^2} + \sum_{t=4}^{15} \frac{22000}{(1 + 0.05)^t} \]

After performing the calculations, the net present value of the project is found to be \( NPV = 10242 \). Since the NPV is positive, the company should consider undertaking the project.

Final Answer