Question

Nobel Tech Inc. is building a new production line. The cost of the production line is $3 million in the current year and $2 million in the following year. The production line is expected to bring in cash inflow of $1.6 million in year 2, and $2 million each year from year 3 to year 7. The company uses a cost of capital of 10% on all the projects.

The IRR of the project is closest to ___________.

Group of answer choices

a. 27%

b. 24%

c. 17%

d. 18%

Answer 1

Answer:24%

IRR is the rate at which NPV=0. ie: PV of inflows = PV of outflows. It is calculated by trial and error method.

Lets find NPV at say 23%.

Year	0	1	2	3	4	5	6	7
Cashflow(in $)	(3,000,000)	(2,000,000)	1,600,000	2,000,000	2,000,000	2,000,000	2,000,000	2,000,000
PVF @23%	1	0.813	0.661	0.537	0.437	0.355	0.289	0.235
Discounted Cashflow (Cash flow * PVF)	(3,000,000)	(1,626,016)	1,057,572	1,074,768	873,795	710,402	577,563	469,563

NPV = PV of Inflows - PV of Outflows

= (1057572+1074768+873795+710402+577563+469563)-(3000000+1626016)

= 4763663-4626016

= 137647

Since NPV is positive, Take a higher rate say 24%

Year	0	1	2	3	4	5	6	7
Cashflow(in $)	(3,000,000)	(2,000,000)	1,600,000	2,000,000	2,000,000	2,000,000	2,000,000	2,000,000
PVF @24%	1	0.806	0.650	0.524	0.423	0.341	0.275	0.222
Discounted Cashflow (Cash flow * PVF)	(3,000,000)	(1,612,903)	1,040,583	1,048,975	845,947	682,215	550,174	443,689

NPV = PV of Inflows - PV of Outflows

= (1040583+1048975+845947+682215+550174+443689)-(3000000+1612903)

= 4611582-4612903

= -1321

Now we got two rates R1 and R2 such that NPV at R1(NPV1) is higher and NPV at R2(NPV2) is lower.

IRR = R1 + ((NPV1 x (R2 - R1)) / (NPV1 - NPV2))

= 23+((137647*(24-23))/(137647+1321)

= 23.99%