Final answer:
The payback period is 4 years. The discounted payback period is also 4 years. The modified IRR for this project is approximately 15.1%.
Step-by-step explanation:
Payback period:
The payback period is the time it takes for the initial investment to be recovered. We can calculate this by adding up the cash flows until the cumulative cash flow becomes positive. Based on the cash flows provided, the payback period is 4 years.
Discounted payback period:
The discounted payback period takes into account the time value of money by discounting the cash flows. We can calculate this by adding up the discounted cash flows until the cumulative discounted cash flow becomes positive. With a required rate of return of 12%, the discounted payback period is also 4 years.
Modified IRR:
The modified internal rate of return (IRR) is the rate of return at which the net present value (NPV) of an investment becomes zero. We can calculate this by adjusting the cash flows to include the initial investment and then finding the rate of return that makes the NPV zero. Based on the adjusted cash flows, the modified IRR for this project is approximately 15.1%.
Discounting approach:
The discounting approach calculates the net present value (NPV) of the cash flows by discounting them back to the present using the required rate of return. We can calculate this by multiplying each cash flow by the corresponding discount factor and then summing them up. With a required rate of return of 12%, the NPV of this project is approximately $34,561,894.
Reinvestment approach:
The reinvestment approach assumes that the cash flows generated by the project can be reinvested at the required rate of return. We can calculate this by finding the future value of each cash flow at the required rate of return and then summing them up. Using the required rate of return of 12%, the future value of this project is approximately $317,317,765.
Combination approach:
The combination approach combines the discounting and reinvestment approaches by discounting the cash flows back to the present and then finding the future value of the resulting discounted cash flows. We can calculate this by multiplying each cash flow by the corresponding discount factor, summing them up, and then finding the future value of the resulting discounted cash flows. With a required rate of return of 12%, the future value of this project is approximately $217,490,274.
Net present value (NPV):
The net present value (NPV) represents the difference between the present value of the cash inflows and the present value of the cash outflows. We can calculate this by subtracting the initial investment from the present value of the discounted cash flows. With a required rate of return of 12%, the NPV of this project is approximately $34,561,894.
Based on the analysis, since the net present value (NPV) is positive, the company should take the project as it is expected to generate positive returns.