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**Unformatted text preview: **e two project profiles intersect at a point we shall call the
crossover point. We observe that at costs of capital greater than the crossover point, the project with the greater
IRR (Project S, in this case) also has the greater NPV. But at costs of capital less than the crossover point, the
project with the lesser IRR has the greater NPV. This relationship is the source of discrepancy between the NPV
and IRR methods. By looking at the graph, we see that the crossover appears to occur at approximately 7%.
Luckily, there is a more precise way of determining crossover. To find crossover, we will find the difference between
the two projects cash flows in each year, and then find the IRR of this series of differential cash flows.
Expected after-tax
net cash flows (CFt)
Cash flow Alternative: Use Tools > Goal Seek to find WACC when NPV(S) =
Year (t) Project S Project L differential NPV(L). Set up a table to show the difference in NPV's, which we
0
($1,000) ($1,000)
0
want to be zero. The following will do it, g etting WACC = 7.17%.
1
5 00
100
4 00
Look at B57 for the answer, then restore B57 to 10%.
2
4 00
300
100
NPV S = $ 78.82
3
300
4 00
(100)
NPV L = $ 4 9.18
4
100
6 00
(500)
S - L = $ 29.64 I RR = Crossover rate = G277 7.17% The intuition behind the relationship between the NPV profile and the crossover rate is as follows: (1) Distant cash
flows are heavily penalized by high discount rates--the denominator is (1+r)t, and it increases geometrically, hence
gets very large at high values of t. (2) Long-term projects like L have most of their cash flows coming in the later
years, when the discount penalty is largest, hence they are most severely impacted by high capital costs. (3)
'Therefore, Project L's NPV profile is steeper than that of S. (4) Since the two profiles have different slopes, they
cross one another.
Modified Internal Rate of Return (MIRR)
The modified internal rate of return is the discount rate that causes a project's cost (or cash outflows) to equal the
'present value of the project's terminal value. The terminal value is defined as the sum of the futur...

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