Question

4. Two mutually exclusive projects have projected cash flows as follows: END OF YEAR 0 Project A$2,000 $1,000 $1,000 $1,000 1,000 Project B -2,000 0 0 6,000 a. Determine the internal rate of return for each project. b. Determine the net present value for each project at discount rates of 0, 5, 10, 20, 30, and 35 percent. c. Plot a graph of the net present value of each project at the different discount rates. d. Which project would you select? Why? What assumptions are inherent in your decision?

Answer 1

a. Internal Rate of return is calculated by outflow = inflow

Project A

We have to discount the inflows with a rate which will come equal to $2,000

So, internal rate of return is 34.80% for project A

Project B

If we discount $6000 with 31.5% by 4 times, then it is coming equal to $2,000.

Hence its internal rate of return is 31.5%

b. Net present Value for Project A

Years	Cash inflows ($)	Discounting factor 5%	Present value ($)
0	(2,000)	1	(2000)
1	1,000	.9524	952.4
2	1,000	.9070	907
3	1,000	.8638	863.8
4	1,000	.8227	822.7
			1545.9

Years	Cash inflows ($)	Discounting factor 10%	Present value
0	(2,000)	1	(2000)
1	1,000	.9091	909.1
2	1,000	.8264	826.4
3	1,000	.7513	751.3
4	1,000	.6830	683
			1169.8

Years	Cash inflows ($)	Discounting factor 20%	Present value
0	(2,000)	1	(2000)
1	1,000	.8333	833.3
2	1,000	.6944	694.4
3	1,000	.5787	578.7
4	1,000	.4823	482.3
			588.7

Same method will be used for 30% and 35%

Net Present Value for Project B

Years	Cash inflows ($)	Discounting factor 5%	Present value ($)
0	(2,000)	1	(2000)
1	0	0	0
2	0	0	0
3	0	0	0
4	6000	.8227	4936.2
			2936.2

Years	Cash inflows ($)	Discounting factor 10%	Present value
0	(2,000)	1	(2000)
1	0	0	0
2	0	0	0
3	0	0	0
4	6000	.6830	4098
			2098

Same method will be used with other rates.

d. Sometimes there is conflict between NPV and IRR, when 2 projects are under consideration, one project may give higher NPV and the other may give higher IRR. This will lead to a confusion in selection of project.

the reason for this conflict is that IRR is actually a percentage annual return on an investment, so if in the initial periods the inflow are big, the investment left will surely be small.

Now, a small return on this investment in monetary terms may result in to high percentage return.

Therefore in such situations IRR may be misleading. So, selection should be based on NPV.

In this case project A has higher IRR, and project B has higher NPV.

So with the above explanation. Project B will be selected as its NPV is higher than Project A