Additional Solutions: Chapter Five: Comparison Methods 2
5S.1
The present worth of payments is (in thousands of dollars)
50 + 5
((P/F, i,
2
) + (P/F, i
, 4
) + (P/F, i
,6))
The present worth of receipts is
25
(P/A, i,
8) + 10
(P/F, i,
8)
To find the IRR, we could set these two quantities equal to each other and solve for
i
. However, an
easier solution method is to note that the present worth of the investment is positive for an interest rate
of zero, and becomes negative as the interest rate increases without limit. Since the MARR is 20%, the
question is whether the graph of present worth versus interest rate crosses the axis at an interest rate
greater than 20%. Evaluating the present worth at
i
=20%, we find it is positive. So the IRR must be
greater than 20%, and the project is therefore acceptable.
*5S.2
The approach here is to construct a table of incremental rates of return:
Alternative
Initial Cost
Revenue
IRR
Waterfront(`W’)
10 000
11 200
12%
Signal Hill (`X’)
12 000
13 800
15%
Cape Grace (`Y’)
15 000
16 950
13%
Camps Bay (`Z’)
20 000
22 500
12.5%
W to X
2 000
2 600
30%
X to Y
3 000
3 150
5%
X to Z
8 000
8 700
8.7%
All the projects individually have rates of return greater than 10%, so if they are not mutually
exclusive, Cape Town Pizza should do all of them.
If they are mutually exclusive, we find that the incremental rate of return upgrading from Waterfront to
Signal Hill is 30%, while the rates of return for upgrading from Signal Hill to anything else are less
than 10%. So the company should open its franchise in Signal Hill.
5S.3
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View Full DocumentIf Ntombela does accept the offer, he is getting money for nothing, which is effectively an infinite rate
of return. But he still needs to consider the incremental benefit of turning it down.
Consider the incremental benefit to Ntombela of not accepting
Van Den Akker’s offer. Refusing his
offer means that opening his hotel in Pretoria has an effective cost of R 11 000 000: ten million rand of
his own money, and one million that he could otherwise have received. So his incremental rate of return
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 Fall '08
 Dr.JohnJones
 Time Value Of Money, Net Present Value, Internal rate of return

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