Define internal rate of return (IRR) and modified internal rate of return (MIRR)

Question

Define internal rate of return (IRR) and modified internal rate of return (MIRR), accompanied by equations for clarity and preciseness. State significance of each. Provide two fictitious examples of investment in which IRR meets or exceeds the investor's expectation in one, and falls short of expectations in the other. Also, evaluate MIRR for each. You need to assume an opportunity cost to evaluate MIRR. Your example should contain non-uniform cash flows, and number of periods in each case should be at least 5. Provide your explanations and definitions in detail and be precise. Explain your work. Provide references for the content.

PLEASE ANSWER ALL THE QUESTIONS AND IN WORD FORMAT. DO)NT COPY PASTE

Explanation / Answer

Answer;

IRR: Internal rate of return is a rate of interest at which net present value of both the positive and negative cash flows for the projects is equal to zero. IRR equates the net present value of the cash flows to zero to figure out the attractiveness of the projects.

MIRR : The Modified internal rate of return is used to rank the projects under the capital budgeting exercise. As the name suggests MIRR is modified version of IRR under which the positive cashflows of the projects are being reinvested at cost of capital and an initial outlay of the project is being financed at the financing cost of the company. with a comparison to IRR under which project cash flows reinvested at IRR rate.

Comparison of IRR and MIRR:

1) IRR calculates the rate at which Net present value of various cash flows is equal to zero. The rate of interest which we derive is being used to reinvest the cash flows at that rate. IRR is better than Net prevent value since its tell in terms of percentage how much your project going to earn. However, it has some flaws which is being rectified while using MIRR.MIRR comes out with only one rate of interest as compared to a different rate of interest being given in case of IRR.

2) Projects with uneven cash flows: IRR may give confusing results while we have different uneven cash flows with longer duration since it will give multiple IRR owing to fluctuating cash flows. so, in this case, MIRR comes into the picture with coming up as a single rate at which the cash flows can be reinvested.

3) Reinvestment rate of cash flows: In case of IRR it assumes that all the positive cash flows will be reinvested at the cost of capital which looks difficult in the real-life scenario so MIRR is much more beneficial since it assumes that the positive cash flows are being reinvested at cost of capital while negative cash flows at cost of financing of the company.

4)Formula for IRR=0=-Co+C1/(1+IRR)^1+C2/(1+IRR)^3.....so on

Formula of MIRR =n(future value positive cashflows, cost of capital/ Present value(initial outlay, financing cost)^1/2-1

Examples of IRR:

1)To calculate the IRR and MIRR at opportunity cost of 10% of finance cost at the rate of IRR

we have calculated IRR by using formulae in excel with the syntax of IRR(values, guess). Under values, we have taken all the cash flows and guess as 0. it gives IRR of 19%.

we have calculated MIRR by using excel formulae in excel with the syntax of MIRR ( values, finance rate, reinvestment rate). under values are taken all the cash flows, under finance rate is taken as IRR% and reinvestment rate as an opportunity cost).

This project should be rejected since MIRR is lower than the IRR.

2)The opportunity cost assumes as 10% and rest is the same process as followed in the above mention example.

In this IRR and MIRR are almost same so project meets the expectation of the investor.  

(ends)

Years 0 1 2 3 4 5 cashflows -100000 18000 -50000 25000 25000 225000 IRR 19% MIRR 18%

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