Question

I am having some difficulties finding the IRR and NPV, and the discounted payback period of a Capital project for Intel that will last 12 yrs:

Project Cost; 10% of PPE : 4,897,600

Annual Depreciation: 387,726.67 /yr over 12 yrs

Annual EBIT: 881,568

WACC: 6.55%

Free Cash Flows (Year 1-12): 825,038.54

Answer 1

The NPV of the project is calculated as follows:

= (4,897,600) + 825,038.54 / 1.0655¹ + 825,038.54 / 1.0655² + 825,038.54 / 1.0655³ + 825,038.54 / 1.0655⁴ + 825,038.54 / 1.0655⁵ + 825,038.54 / 1.0655⁶ + 825,038.54 / 1.0655⁷ + 825,038.54 / 1.0655⁸ + 825,038.54 / 1.0655⁹ + 825,038.54 / 1.0655¹⁰ + 825,038.54 / 1.0655¹¹ + 825,038.54 / 1.0655¹²

= 1,815,507.953

IRR of the project is calculated by using the below formula:

Lower Rate + [ ( Lower Rate NPV ) / ( Lower Rate NPV - Higher Rate NPV ) ] x ( Higher Rate - Lower Rate )

Lets calculate NPV of project at rate of say 12.5%

= (4,897,600) + 825,038.54 / 1.125¹ + 825,038.54 / 1.125² + 825,038.54 / 1.125³ + 825,038.54 / 1.125⁴ + 825,038.54 / 1.125⁵ + 825,038.54 / 1.125⁶ + 825,038.54 / 1.125⁷ + 825,038.54 / 1.125⁸ + 825,038.54 / 1.125⁹ + 825,038.54 / 1.125¹⁰ + 825,038.54 / 1.125¹¹ + 825,038.54 / 1.125¹²

= 96,751.17 Approximately

Now lets calculate NPV at a rate of say 13% ( Since the IRR is the rate at which the NPV of the project will be zero, hence we need to calculate the NPV at a higher rate)

= (4,897,600) + 825,038.54 / 1.13¹ + 825,038.54 / 1.13² + 825,038.54 / 1.13³ + 825,038.54 / 1.13⁴ + 825,038.54 / 1.13⁵ + 825,038.54 / 1.13⁶ + 825,038.54 / 1.13⁷ + 825,038.54 / 1.13⁸ + 825,038.54 / 1.13⁹ + 825,038.54 / 1.13¹⁰ + 825,038.54 / 1.13¹¹ + 825,038.54 / 1.13¹²

= ( 15,313.15) Approximately

Now by feeding these values in the above mentioned formula we shall get:

= 12.5% + [ ( 96,751.17) / ( 96,751.17 - (15,313.15) ] x ( 13 - 12.50)

= 12.93% Approximately

Calculation of Discounted Payback Period is as follows:

It is the period in which we shall recover our initial investment in the project i.e. 4,897,600

Year	Discounted Cash Flow	Cumulative Discounted Cash Flow
1	= 825,038.54 / 1.06551 = 774,320.54	774,320.54
2	= 825,038.54 / 1.06552 = 726,720.36	1,501,040.9
3	= 825,038.54 / 1.06553 = 682,046.33	2,183,087.23
4	= 825,038.54 / 1.06554 = 640,118.56	2,823,205.79
5	= 825,038.54 / 1.06555 = 600,768.24	3,423,974.03
6	= 825,038.54 / 1.06556 = 563,836.92	3,987,810.95
7	= 825,038.54 / 1.06557 = 529,175.90	4,516,986.85
8	= 825,038.54 / 1.06558 = 496,645.61	5,013,632.46

As we can see we are able to recover our initial investment in between 7 and 8 year, so our discounted payback period is as below:

7 years + ( Initial Investment - 7 years cumulative discounted cash flows ) / Next years discounted cash flow

= 7 years + ( 4,897,600 - 4,516,986.85 ) / 496,645.61

= 7.77 years Approximately

Feel free to ask in case of any query relating to this question