chapter5A

# chapter5A - Additional Solutions Chapter Five Comparison...

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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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If 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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chapter5A - Additional Solutions Chapter Five Comparison...

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