[savio13]

Internal Rate of Return


Differences in the scale of investment

NPV and IRR may give conflicting decisions where projects differ in their scale of investment. Example:
Years 0 1 2 3
Project A -2,500 1,500 1,500 1,500
Project B -14,000 7,000 7,000 7,000
Assume k= 10%.
NPVA = Rs.1,500 x PVFA at 10% for 3 years
= Rs.1,500 x 2.487
= Rs.3,730.50 - Rs.2,500.00
= Rs.1,230.50.
NPVB == Rs.7,000 x PVFA at 10% for 3 years
= Rs.7,000 x 2.487
= Rs.17,409 - Rs.14,000
= Rs.3,409.00.
IRRA = 36%
IRRB = 21%
Decision:
Conflicting, as:
• NPV prefers B to A
• IRR prefers A to B
NPV IRR
Project A Rs. 3,730.50 36%
Project B Rs.17,400.00 21%

i) the NPV prefers B, the larger project, for a discount rate below 20%
ii) the NPV is superior to the IRR
a) Use the incremental cash flow approach, "B minus A" approach
b) Choosing project B is tantamount to choosing a hypothetical project "B minus A".


0 1 2 3
Project B - 14,000 7,000 7,000 7,000
Project A - 2,500 1,500 1,500 1,500
"B minus A" - 11,500 5,500 5,500 5,500
IRR"B Minus A"
= 20%
c) Choosing B is equivalent to: A + (B - A) = B
d) Choosing the bigger project B means choosing the smaller project A plus an additional outlay of Rs.11,500 of which Rs.5,500 will be realized each year for the next 3 years.
e) The IRR"B minus A" on the incremental cash flow is 20%.
f) Given k of 10%, this is a profitable opportunity, therefore must be accepted.
g) But, if k were greater than the IRR (20%) on the incremental CF, then reject project.
i) If k = 20% (IRR of "B - A") the company should accept project A.
• This justifies the use of NPV criterion.
Advantage of NPV:
• It ensures that the firm reaches an optimal scale of investment.
Disadvantage of IRR:
• It expresses the return in a percentage form rather than in terms of absolute dollar returns, e.g. the IRR will prefer 500% of Rs.1 to 20% return on Rs.100. However, most companies set their goals in absolute terms and not in % terms, e.g. target sales figure of Rs.2.5 million.
The timing of the cash flow
The IRR may give conflicting decisions where the timing of cash flows varies between the 2 projects.

Note that initial outlay Io is the same.
0 1 2
Project A - 100 20 125.00
Project B - 100 100 31.25
"A minus B" 0 - 80 88.15
Assume k = 10%
NPV IRR
Project A 17.3 20.0%
Project B 16.7 25.0%
"A minus B" 0.6 10.9%
IRR prefers B to A even though both projects have identical initial outlays. So, the decision is to accept A, that is B + (A - B) = A
The horizon problem
NPV and IRR rankings are contradictory. Project A earns Rs.120 at the end of the first year while project B earns Rs.174 at the end of the fourth year.
0 1 2 3 4
Project A -100 120 - - -
Project B -100 - - - 174
Assume k = 10%
NPV IRR
Project A 9 20%
Project B 19 15%
Decision:
NPV prefers B to A
IRR prefers A to B.