Final answer:
The cost of the project is calculated by finding the present value of each of the annual cash flows using the IRR and summing them up. The total cost, with an IRR of 13% and annual cash flows of $15,000 for 4 years, is approximately $44,617.07, which is option d.
Step-by-step explanation:
The internal rate of return (IRR) of a project is the interest rate at which the net present value of all the cash flows (both positive and negative) from a project or investment equal zero. In the given scenario, we are asked to find out how much Samourai Corporation's project costs, given that the annual cash flows are $15,000 for 4 years and the IRR is 13%. We use the IRR to calculate the present value of these cash flows.
The present value (PV) of each cash flow can be calculated using the formula PV = Cash Flow / (1 + IRR)^n, where 'n' is the number of years until the cash flow occurs. For an annual cash flow of $15,000 at a 13% discount rate, the calculation for each year would be as follows:
- Year 1: PV = $15,000 / (1 + 0.13)^1 = $13,274.34
- Year 2: PV = $15,000 / (1 + 0.13)^2 = $11,741.89
- Year 3: PV = $15,000 / (1 + 0.13)^3 = $10,391.58
- Year 4: PV = $15,000 / (1 + 0.13)^4 = $9,195.54
Adding up these present values gives us the total cost of the project:
Project Cost = Year 1 PV + Year 2 PV + Year 3 PV + Year 4 PV
= $13,274.34 + $11,741.89 + $10,391.58 + $9,195.54
= $44,603.35
Therefore, the closest answer from the given options is $44,617.07, which is option d.