Question

Consider the following two projects: Year 0 Yearl Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Discount Project C/E C/F C/E C/E C/F C/E C/F C/F Rate Alpha -79 20 25 30 35 40 N/A N/A 15% Beta -80 25 25 25 25 25 25 25 16% Which of the following statements is correct? Select one: A. You should invest in project Alpha since IRRAlpha > IRRBeta. B. You should invest in project Beta since NPVBeta 0. C. Your should invest in project Alpha since NPVAlpha 0. D. You should invest in project Beta since IRRBeta 0.

Answer 1

Year	Cash flows of Alpha	Present Value@15%	Cash flows of Beta	Present Value@16%
0	-79	-79	-80	-80
1	20	17.39	25	21.55
2	25	18.90	25	18.58
3	30	19.73	25	16.02
4	35	20.01	25	13.81
5	40	19.89	25	11.90
6			25	10.26
7			25	8.85
	NPV	16.92	NPV	20.96
IRR	22.68%		24.52%
Explaination:-
Internal rate of return is the rate where NPV of the project is zero. To calculate IRR, we should set NPV is equal to zero and solve for discount rate which is the IRR.
Using trial and error method we guessed the discounting rate for Alpha to be 22.68% and beta to be 24.52% .
Year	Cash flows of Alpha	Present [email protected]%	Present Value@20%	Cash flows of Beta	Present Value@20%	Present [email protected]%
0	-79	-79	-79	-80	-80	-80
1	20	16.30	0.43	25	20.83	20.08
2	25	16.61	0.17	25	17.36	16.12
3	30	16.25	0.07	25	14.47	12.95
4	35	15.45	0.03	25	12.06	10.40
5	40	14.39	0.01	25	10.05	8.35
6				25	8.37	6.71
7				25	6.98	5.39
	NPV	-	-78.30	NPV	10.11	-
IRR	22.68%		24.52%
Answer cannot be option A as IRR of Beta is more than IRR of Alpha.
Answer cannot be option C as NPV of Alpha is not less than 0. NPV of Alpha is 16.92.
Answer can be option B or option D as NPV of Beta > 0 and also IRR of Beta is > 0. But we have to choose one option of all the options given so we choose option B as the final answer. As a project is accepted if its NPV is > 0 and IRR is positive and here for project B both NPV and IRR are higher than project A.