Question

2. A company is considering two mutually exclusive expansion projects. Plan A requires a 21 million expenditure on a large scale integrated plant that would provide expected cash flows of $6.40 million per year for 6 years. Plan B requires a $7 million expenditure to build a somewhat less efficient, more labor-intensive plant with expected cash flows of $2.72 million per year for 6 years. The firm's WACC is 10%. (Timeline required) a. Calculate each project's NPV and IRR. b. Calculate the crossover rate where the two projects' NPVs are equal c. Based on your answer to (b), explain when there will be a conflict between NPV and IRR in making capital budgeting decisions regarding mutually exclusive projects.

Answer 1

A) Computation of each Project's NPV And IRR :

"Computation for Plan A" NPV		"Computation for Plan B" NPV
Computation Of PV Of CIF		Computation Of PV Of CIF
Years	Cash In flow	Pv factor @10%	$		Years	Cash In flow	Pv factor @10%	$
1	$6,400,000	0.9091	5818181.82		1	$2,720,000	0.9091	2472727.27
2	$6,400,000	0.8264	5289256.20		2	$2,720,000	0.8264	2247933.88
3	$6,400,000	0.7513	4808414.73		3	$2,720,000	0.7513	2043576.26
4	$6,400,000	0.6830	4371286.11		4	$2,720,000	0.6830	1857796.60
5	$6,400,000	0.6209	3973896.47		5	$2,720,000	0.6209	1688906.00
6	$6,400,000	0.5645	3612633.15		6	$2,720,000	0.5645	1535369.09
Total			27873668.48		Total			11846309.10
Initial Investment		21000000.00		Initial Investment		7000000.00
N.P.V.			6873668.48		N.P.V.			4846309.10

The IRR Formula : The IRR cannot be derived easily. "The only way to calculate IRR, by hand is through trial and error because we have trying to arrive at whatever rate which makes the NPV equal to zero.
IRR IS THE RATE WHEN NPV OF ANT PROJECT IS BEOCME ZERO.

IRR for Plan A : (By trail and error method)
Estimation of IRR Cash Inflow of the project with both rate, which are closest to is as follows :
At 20 % = $6,400,000 * PVAF (20%, 6 Years) At 21 % = $6,400,000 * PVAF (21%, 6 Years)   
= $6,400,000 * 3.3255 = $6,400,000 * 3.2446
= $21,283,200 = $20,765,440
The exact IRR by interpolating between 20% & 21% is worked out as follows :
IRR = 20% + (21,283,200 - 21,000,000) / (21,283,200 - 20,765,440) *1
= 20% + 283200 / 517760 *1
= 20% + 0.5469%
= 20.5469%

IRR for Plan B : (By trail and error method)
Estimation of IRR Cash Inflow of the project with both rate, which are closest to is as follows :
At 30 % = $2,720,000 * PVAF (30%, 6 Years) At 31 % = $2,720,000 * PVAF (31%, 6 Years)   
= $2,720,000 * 2.6427 = $2,720,000 * 2.5875
= $7,188,144 = $7,038,000
The exact IRR by interpolating between 30% & 31% is worked out as follows :
IRR = 30% + (7,188,144 - 7,000,000) / (7,188,144 - 7,038,000) *1
= 30% + 188144 / 150144 *1
= 30% + 1.2531%
= 31.2531%

B) Crossover rate where both Projects NPV are equal :
  NPV Of Project A = NPV Of Project B is known as Crossover rate
C0(A-B) = $21 Million - $7 Million = $14 Million
C1(A-B) = $6.4 Million - $ 2.72 Million = $3.68 Million
C2(A-B) = $6.4 Million - $ 2.72 Million = $3.68 Million
C3(A-B) = $6.4 Million - $ 2.72 Million = $3.68 Million
C4(A-B) = $6.4 Million - $ 2.72 Million = $3.68 Million
C5(A-B) = $6.4 Million - $ 2.72 Million = $3.68 Million
C6(A-B) = $6.4 Million - $ 2.72 Million = $3.68 Million
= [(3680000/(1+CR) + (3680000/(1+CR)2) + (3680000/(1+CR)3) + (3680000/(1+CR)4) + (3680000/(1+CR)5) +(3680000/(1+CR)6) ] - 14000000 = 0 => CR = 14.806 %. or say 14.81%

Both projects would deliver the same NPV at a discount rate of 14.806%. So that Crossover rate is 14.806%

C) Conflict between NPV And IRR in making capital budgeting decision regarding mutually exclusive projects :
Both NPV and IRR are popular techniques of capital budgeting. The NPV of a project is exactly the same as the increase in shareholders’ wealth. This fact makes it the correct decision rule for capital budgeting purposes. IRR is the rate of return on invested capital that the project is returning to the firm. Sometimes the NPV and IRR can favor conflicting project choices.
   Such conflicts may be dealt with by considering the mutuality of the project, value additivity principle ,multiple rates of return and reinvestment rate assumption. In reality, using the IRR method could lead to investment decisions that increase, but do not maximize wealth. Another reason for which IRR approach might not be usable-this is when projects have unconventional cash flow patterns.