DYI Construction Co.is considering a new inventory system that will cost $750,000.The system is expected to generate positive cash flows over the next four years in the amounts of $350,000 in year one,$325,000 in year two,$150,000 in year three,and $180,000 in year four.DYI's required rate of return is 8%.What is the modified internal rate of return of this project?
A) 10.87%
B) 11.57%
C) 13.68%
D) 15.13%

Question

Quizplus · Accepted Answer

To calculate the modified internal rate of return (MIRR), we need to determine the future values of all cash inflows and outflows from the investment and then solve for the discount rate that equates the sum of the present values of the outflows with the future value of the inflows. Unlike the regular internal rate of return (IRR), MIRR assumes that cash inflows are reinvested at a rate equal to the cost of capital, while cash outflows are financed at the same rate.

To apply this formula, we can first calculate the present value (PV) of the cash inflows using the required rate of return (r) of 8% as the discount rate:

PV1 = 350,000 / (1 + 0.08)^1 = 324,074.07
PV2 = 325,000 / (1 + 0.08)^2 = 284,090.91
PV3 = 150,000 / (1 + 0.08)^3 = 113,636.36
PV4 = 180,000 / (1 + 0.08)^4 = 125,560.54

Then, we can find the future value (FV) of the inflows using the same rate for reinvestment:

FV = 324,074.07 * (1 + 0.08)^3 + 284,090.91 * (1 + 0.08)^2 + 113,636.36 * (1 + 0.08)^1 + 125,560.54 = 956,161.01

Finally, we can solve for the MIRR by finding the discount rate that makes the PV of the outflows equal to the FV of the inflows:

PV(outflows) = 750,000 = -750,000 / (1 + r)^4
FV(inflows) = 956,161.01 = 350,000 / (1 + r)^1 + 325,000 / (1 + r)^2 + 150,000 / (1 + r)^3 + 180,000 / (1 + r)^4

Using this formula, we can find that the MIRR is approximately 11.57%, which is closest to answer choice B. Therefore, DYI Construction Co. should consider implementing the new inventory system since its MIRR is higher than the required rate of return of 8%, indicating a positive net present value.