Question

Carson Trucking is considering whether to expand its regional service center. The expansion will require an expenditure of $10,000,000 for new service equipment and will generate annual net cash inflows by reducing operating costs by $2,500,000 per year for each of the next 8 years. In year 8, the firm will also get back a cash flow equal to the salvage value of the equipment, which is valued at $1,000,000. Thus, in year 8, the total cash inflow is $3,500,000. Assuming an 11% discount rate, calculate the project's NPV:

a) $3,500,000

b) $3,299,233

c) $2,500,000

d) $2,399,233

Answer 1

The correct answer is b) $3,299,233.

Step-by-step explanation:

To calculate the Net Present Value (NPV) of the Carson Trucking service center expansion project, we need to discount each year's cash flows back to their present value using the given 11% discount rate and then sum those amounts.

• For years 1 through 7, the annual cash inflow is $2,500,000.
• In year 8, the cash inflow is $3,500,000 ($2,500,000 operational savings + $1,000,000 salvage value).

The NPV formula is:

NPV = (Year 1 cash flow / (1+r)^1) + (Year 2 cash flow / (1+r)^2) + ... + (Year 8 cash flow / (1+r)^8) - Initial Investment

Therefore:

NPV = ($2,500,000 / (1+0.11)^1) + ($2,500,000 / (1+0.11)^2) + ... + ($2,500,000 / (1+0.11)^7) + ($3,500,000 / (1+0.11)^8) - $10,000,000

Calculating each term and summing gives the final NPV. After performing the calculations, the NPV is found to be $3,299,233.