Question

Questions:

We know the following data of an investment that the company has made:

• An initial disbursement of € 2,000,000 and generates the collections and payments in the successive years of its duration that are shown in the following table:

Years	Collection (€)	Payments (€)
1 Year 2 Year 3 Year 4 Year	4.500.000 5.500.000 6.000.000 4.000.000	3.800.000 4.500.000 5.000.000 3.200.000

Calculate the IRR of the previous project. Justify for what type of discount this investment will be made.

Note: This questions has been submitted twice on this site already. I know that IRR of the project is 26.08% However, neither solution explains clearly enough (for me) how the number was obtained. Please explain.

Answer 1

Internal rate of return (IRR) is the rate at which present value of future cash flows equals to initial investment.

cin PVI = (1 + i) CF CF2 (1 + i)1*(1 + 2 + ......... + 17 (1 + i)"

where,

PVI = Present value of Initial investment

CF = Cash flow each period

i = Internal rate of return (IRR)

In above problem,

Initial investment (PVI) = 2,000,000

Annual Cash flow for next 4 years = Collection - Payments

IRR = i

putting the values in equation:

2,000,000 = 4, 500,000 -3, 800,000 (1+zil 5,500,000 -4,500,000 (1+z2 6,000,000 -5,000,000, 4,000,000 - 3, 200,000 (1+ 3 (1+ zj4

700,000 1,000,000 2,000.000 = = (1+1T (1+ i) | 1,000,000 (1+z)3 800,000 (1+)4

We can calculate IRR with excel or financial calculator very easily but manually we have to calculate it by trial and error method.

700,000 1,000,000 1,000,000 800,000 2,000,000 - (1+2)*(1+2 *(1+t) *(1+t) ="

we check net present values at i = 26% and i = 27%

700,000 = 2,000,000 - (1+0.26) 1,000,000 (1+0.2612 1,000,000 (1+0.2613 800,000 (1+0.264

by solving

= 2.743.80

and at i = 27%

700,000 1,000,000 1,000,000 800,000 = 2,000,000 - + 1) 0 . 27 ו( ) 1 + 0 . 27 2( ) 1 + 0 . 27 3( ) 1 + 0 . 27 4(

= -33, 106.47

at 26%, npv is positive and at 27%, npv is negative thus we know IRR lies between 26% and 27%. Now, we can use interpolation method to find IRR.

i=i+ NPV NPVI - NPVh

where,

l = lower rate

h = higher rate

NPV = net present value

putting the values:

2, 743.80 i = 26% +5 2, 743.80 +33, 106.47

i = 26% +0.08%

i = 26.08%

We can also find IRR of project in excel with "IRR" function.

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

в с D E Years Collection (€) O Year 1 Year 2 Year 3 Year 4 Year € 4,500,000.00 € € 5,500,000.00 € € 6,000,000.00 € € 4,000,000.00 € IRR Payments (€) Cash Flow € (2,000,000.00) 3,800,000.00 € 700,000.00 4,500,000.00 € 1,000,000.00 5,000,000.00 € 1,000,000.00 3,200,000.00 € 800,000.00 26.08%

Cell reference -

A B Ε Collection (€) Payments (€) Years O Year 1 Year 2 Year 3 Year 4 Year 4500000 5500000 6000000 4000000 3800000 4500000 5000000 3200000 Cash Flow -2000000 =C4-D4 =C5-D5 =C6-D6 =C7-D7 =IRR(E3:E7) IRR

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.