Question

Carson Trucking is considering whether to expand its regional service center in​ UT. The expansion requires the expenditure of​$10,500,000 on new service equipment and would generate annual net cash inflows from reduced costs of operations equal to ​$3,500,000 per year for each of the next 9 years. In year 9 the firm will also get back a cash flow equal to the salvage value of the​ equipment, which is valued at ​$0.9 million. ​ Thus, in year 9 the investment cash inflow totals ​$4,400,000.Calculate the​ project's NPV using a discount rate of 7 percent.

If the discount rate is 7 ​percent, then the​ project's NPV is ​$

Answer 1

To calculate the Net Present Value (NPV) of the project, we need to discount the future cash inflows and outflows to their present values using the given discount rate of 7%.

The initial expenditure on equipment is $10,500,000. The annual net cash inflows from reduced costs of operations are $3,500,000 per year for 9 years. In year 9, the investment cash inflow totals $4,400,000 ($3,500,000 + $0.9 million salvage value).

We can use the following formula to calculate the NPV:

NPV = (Initial investment) + Σ [Cash inflow / (1 + discount rate)^n]

where Σ denotes the summation, and n is the year.

Let's calculate the NPV:

Initial investment = -$10,500,000 (negative because it's an expenditure)

Cash inflows (discounted) for years 1 to 8:

Σ [Cash inflow / (1 + discount rate)^n] = $3,500,000 × [1 - (1 + 0.07)^(-8)] / 0.07 ≈ $20,416,067

Cash inflow (discounted) for year 9:

$4,400,000 / (1 + 0.07)^9 ≈ $2,297,216

Now, let's sum up all the values:

NPV = (-$10,500,000) + $20,416,067 + $2,297,216 ≈ $12,213,283

If the discount rate is 7 percent, then the project's NPV is approximately $12,213,283.