Question

When NPV and IRR rules result in a conflicting decision regarding acceptance of a project managers could use the MIRR.

It assumes reinvestment of projects' cash flows at the WACC, so it produces results consistent with NPV method.

Let's try to find the MIRR for the project with the following cash flows:

Initial cost of -800 at time zero, CF1 = 400, CF 2 = 570, CF3 = -130.

Here we have two negative cash flows and two positive cash flows.

Step 1: find PV of two costs at the discount rate = WACC of 7%;

Step 2 : find FV of two inflows at 7%;

Step 3: find the discount rate that makes PV from step 1 equal to FV from step 2. That is MIRR.

Make a decision on accepting or rejecting the project by comparing MIRR to the WACC.

Can someone please show me how to get the answer using a financial calculator for example C0= etc... I don't understand the problem using the excel. I need an example with the finance calculator. Thank you

Answer 1

Note, MIRR is a rate such that it will satisfy-

PV(costs) * (1+MIRR)ⁿ = FV(inflows) ...(1)

{PV is at t=0 and we use borrowing/financing rate; & FV is at t=n and we use investment rate;}

Given: CF0=-800, CF1 = 400, CF 2 = 570, CF3 = -130. also given WACC=discount rate

[Note, underlined CF0 & CF3 are costs (negative), whereas CF1 & CF2 are inflows (positive)]

Step1) PV(costs) at _t=0 @ 7% = -800 + (-139)/1.07³ = -913.4654049 ...(2)

You can calculate above in calculator.

Alternately you can use CF function in financial calculator, especially when you have large number of cashflows given. In BA II Plus calculator-

(i) press CF

(ii) press 2nd + CLR WORK (will erase previous stored values in CF)

(iii) CF₀ = 800, then press (+/-) button to make 800 negative, value shown will be -800, press enter.

(iv) press down arrow button, it will display C01. In our case there is no negative value at C01, so put value '0' for it and press down. F01=1 (repetition frequency). For C02=0 & F02=0. {you need to press enter in order to assign values, so after typing value each time, hit enter for sure}

(v) C03 = -139 [as we did in iii using (+/-) button], F03=1 as it occurs only once.

(vi) As no more negative cashflows beyond t=3, press NPV button. It will ask for 'I' value which is rate to discount. type 7 and press enter.

(vii) Press down arrow button. it will display 'NPV', press 'CPT' which is compute button. You will get -913.4654049 as we got in (2).

{you might need to set precicion in your calculator if you want more or lesser decimal places displayed}

Step2) FV(inflows) at _t=2 @ 7% = 400*1.07 + 570 = 998 ...(3)

{we calculate FV of $400 at t=1 one period ahead at t=2 by multiplying by 1.07. Also $570 is already at t=2, so no need to multiply.}

Alternately you can use CF function in financial calculator, especially when you have large number of cashflows given. In BA II Plus calculator-

(i) press CF

(ii) press 2nd + CLR WORK (will erase previous stored values in CF)

(iii) CF₀ = 0 & enter, as we have no inflows at t=0.

(iv) press down arrow button, it will display C01. C01=400, F01=1 (frequency of repetition for 400 is 1) {you need to press enter in order to assign values, so after typing value each time, hit enter for sure}

(v) Press down arrow. C02=570, F02=1.

(vi) As no more positive cashflows beyond t=2, press NPV button. It will ask for 'I' value which is rate to discount. type 7 and press enter.

(vii) Press down arrow button. it will display 'NPV'. press down again, it will display 'NFV' (Net Future Value) press 'CPT' which is compute button. You will get '998' as we got in (3).

{you might need to set precicion in your calculator if you want more or lesser decimal places displayed}

Step3) Start with equation (1)

PV(costs) * (1+MIRR)ⁿ = FV(inflows) ...(1)

Substitute value for PV(costs) from (2) in (1), ignore negative value.

Substitute value for FV(inflows) from (3) in (1). Also note our FV is at n=2.

So we have (1) after substituting values,

913.4654049 (1+MIRR)² = 998

implies, (1+MIRR)² = 998/913.4654049

implies, MIRR = (998/913.4654049)^0.5-1 = 4.52477%

Since MIRR (4.53%) < WACC (7%), project does not looks favorable based on MIRR rule.