Question

P10–14 Internal rate of return  For each of the projects shown in the following table, calculate the internal rate of return (IRR). Then indicate, for each project, the maximum cost of capital that the firm could have and still find the IRR acceptable. I DO NOT HAVE A FINANCIAL CALCULATOR OR I CANNOT USE EXCEL SPREADSHEETS; CAN YOU PLEASE BREAK IT DOWN ON HOW TO FIND THE IRR....THANKS IN ADVANCE

		Project B	Project C
Initial investment (CF0)		−$490,000	−$20,000
Year (t)	Cash inflows (CFt)
1		$150,000	$7,500
2		150,000	7,500
3		150,000	7,500
4		150,000	7,500
5		—	7,500

Answer 1

Internal Rate of Return (IRR) for Project B

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 8% (R1)

Year	Annual Cash Flow ($)	Present Value factor at 8%	Present Value of Cash Flow ($)
1	1,50,000	0.925926	1,38,889
2	1,50,000	0.857339	1,28,601
3	1,50,000	0.793832	1,19,075
4	1,50,000	0.735030	1,10,254
TOTAL			496,819

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $496,819 - $490,000

= $6,819

Step – 2, NPV at 8% is positive, Calculate the NPV again at a higher discount rate, Say 9% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 9%	Present Value of Cash Flow ($)
1	1,50,000	0.917431	1,37,615
2	1,50,000	0.841680	1,26,252
3	1,50,000	0.772183	1,15,828
4	1,50,000	0.708425	1,06,264
TOTAL			485,958

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $485,958 - $490,000

= -$4,042 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.08 + [$6,819 x (0.09 – 0.08)]

              $6,819 – (-$4,042)

= 0.08 + [$68.19 / $10,861]

= 0.08 + 0.0063

= 0.0863 or

= 8.63%

“Internal Rate of Return (IRR) for Project B = 8.63%”

Internal Rate of Return (IRR) for Project C

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 25% (R1)

Year	Annual Cash Flow ($)	Present Value factor at 25%	Present Value of Cash Flow ($)
1	7,500	0.800000	6,000
2	7,500	0.640000	4,800
3	7,500	0.512000	3,840
4	7,500	0.409600	3,072
5	7,500	0.327680	2,458
TOTAL			20,170

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $20,170 - $20,000

= $170

Step – 2, NPV at 25% is positive, Calculate the NPV again at a higher discount rate, Say 26% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 26%	Present Value of Cash Flow ($)
1	7,500	0.793651	5,952
2	7,500	0.629882	4,724
3	7,500	0.499906	3,749
4	7,500	0.396751	2,976
5	7,500	0.314882	2,362
TOTAL			19,763

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $19,763 - $20,000

= -$237 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.25 + [$170 x (0.26 – 0.25)]

              $170 – (-$237)

= 0.25 + [$1.70 / $407]

= 0.25 + 0.0042

= 0.2542 or

= 25.42%

“Internal Rate of Return (IRR) for Project C = 25.42%”

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.