Question

. Douglas Controls, Inc. is considering two mutually exclusive, equally risky, and not repeatable projects, S and L. Their cash flows are shown below. The CEO believes the IRR is the best selection criterion, while the CFO advocates the NPV. If the decision is made by choosing the project with the higher IRR rather than the one with the higher NPV, how much, if any, value will be forgone, i.e., what's the chosen NPV versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs. NPV will not affect the value gained or lost.

Douglas has a weighted average cost of capital (WACC) of 8.50%

Year     0                      1                      2                      3                      4

CF S      -$1,100             $550                 $600                 $100                 $100

CF L      -$2,700             $550                 $725                 $845                 $1,400

Answer 1

Solution:

1) Concept

> NPV - Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. NPV is used in capital budgeting and investment planning to analyze the profitability of a projected investment or project.

> IRR - The internal rate of return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments. The internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero.

2) Calculation:

> NPV

- Project S

Year	Cashflows	Present Value @ 8.5%
0	-1100	-1100
1	550	506.91
2	600	509.67
3	100	78.29
4	100	72.15
	NPV	67.03

- Project L

Year	Cashflows	Present Value @ 8.5%
0	-2700	-2700
1	550	506.91
2	725	615.86
3	845	661.56
4	1400	1010.20
	NPV	94.53

> IRR

- Project S

Year	Cashflows	Present Value @ 12%	Present Value @ 13%
0	-1100	-1100	-1100
1	550	491.07	486.73
2	600	478.32	469.89
3	100	71.18	69.31
4	100	63.55	61.33
	PV	4.12	-12.75

IRR of the project lies between 12 and 13 %.

By interpolation we get IRR = 12.24%

- Project L

Year	Cashflows	Present Value @ 9%	Present Value @ 10%
0	-2700	-2700	-2700
1	550	504.59	500
2	725	610.22	599.17
3	845	652.50	634.86
4	1400	991.80	956.22
	PV	59.10	-9.75

IRR of the project lies between 9 and 10 %.

By interpolation we get IRR = 9.86%

3) Decision Making

Technique	Project S	Project L	Decision
NPV	67.03	94.53	Project L should be selected since it has higher NPV
IRR	12.24%	9.86%	Project S be selected since higher IRR.

If project is selected based on IRR than the NPV forgone would be $ 27.50 [94.53 - 67.03].

Note : As understood from the question, no other requirement was there. Please let us know if anything more to be added.

Hope you understand the solution.