Question

Cordia Corporation is planning a 15 year project with an initial investment of $2,500,000.

The project will have $400,000 cash inflows per year in years 1-5 ;

$200,000 cash inflows in years 6-10, and

$40,000 cash inflows in years 11-15.

a) Determine this project's intemal rate of return.

b) If Cordia's opportunity cost of capital is 8%, should they accept or reject this project?

c) Explain your reason for your decision in part (b).

Answer 1

a) Computation of IRR:
IRR is an interest rate where the net present value of inflows are outflows equals zero.
With the help of trial and error method we can find the IRR:
First let us find from 5% rate and then we can increase or decrease as per the requirement (here, our target is to get NPV= 0).

		rate = 5%		rate = 6%
Year	Cash flows	discounting factor	PV	discounting factor	PV
0	(2,500,000)	1	(2,500,000)	1	(2,500,000)
1	400,000	0.952381	380,952	0.943396	377,358
2	400,000	0.907029	362,812	0.889996	355,999
3	400,000	0.863838	345,535	0.839619	335,848
4	400,000	0.822702	329,081	0.792094	316,837
5	400,000	0.783526	313,410	0.747258	298,903
6	200,000	0.746215	149,243	0.704961	140,992
7	200,000	0.710681	142,136	0.665057	133,011
8	200,000	0.676839	135,368	0.627412	125,482
9	200,000	0.644609	128,922	0.591898	118,380
10	200,000	0.613913	122,783	0.558395	111,679
11	40,000	0.584679	23,387	0.526788	21,072
12	40,000	0.556837	22,273	0.496969	19,879
13	40,000	0.530321	21,213	0.468839	18,754
14	40,000	0.505068	20,203	0.442301	17,692
15	40,000	0.481017	19,241	0.417265	16,691
NPV			16,559		(91,423)

IRR = 5% + [(16,559-0)/ (16,559-(-91,423))] = 5% + 0.15 = 5.15%

b) If Cordia's opportunity cost of capital is 8%, then NPV will be:

		rate = 8%
Year	Cash flows	discounting factor	PV
0	(2,500,000)	1	(2,500,000)
1	400,000	0.925926	370,370.37
2	400,000	0.857339	342,935.53
3	400,000	0.793832	317,532.90
4	400,000	0.73503	294,011.94
5	400,000	0.680583	272,233.28
6	200,000	0.63017	126,033.93
7	200,000	0.58349	116,698.08
8	200,000	0.540269	108,053.78
9	200,000	0.500249	100,049.79
10	200,000	0.463193	92,638.70
11	40,000	0.428883	17,155.31
12	40,000	0.397114	15,884.55
13	40,000	0.367698	14,707.92
14	40,000	0.340461	13,618.44
15	40,000	0.315242	12,609.67
NPV			(285,465.82)

They should reject this project.

c) The NPV in part b is negative, thus, we should reject this project in part (b).