Question

In: Finance

You are considering the following two mutually exclusive projects. The crossover rate between these two projects...

You are considering the following two mutually exclusive projects. The crossover rate between these two projects is ___ percent and Project ___ should be accepted if the required return is greater than the crossover rate.

Year Project A Project B
0 −$24,000 −$24,000
1 8,500 16,570
2 8,500 6,500
3 16,500 8,590

Multiple Choice

  • 12.17%; B

  • 12.17%; A

  • 17.82%; A

  • 16.49%; A

  • 16.49%; B

Solutions

Expert Solution

12.00% 13.00%
Year Cash Flow-A Cash Flow-B Differential cashflow- Cashflow B less Cashflow A PV factor = 1/ (1+r)^t PV PV factor = 1/ (1+r)^t PV
0 $             (24,000.00) $(24,000.00) $              -   1.000 $            -   1.000 $            -  
1 $               16,570.00 $    8,500.00 $ (8,070.00) 0.893 $(7,205.36) 0.885 $(7,141.59)
2 $                 6,500.00 $    8,500.00 $    2,000.00 0.797 $ 1,594.39 0.783 $ 1,566.29
3 $                 8,590.00 $ 16,500.00 $    7,910.00 0.712 $ 5,630.18 0.693 $ 5,482.03
Total $       19.21 Total $     (93.27)
NPV @ 0.12                          19.21
NPV @ 0.13                        (93.27)
Difference in both                        112.49
Cross over-rate =Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
'=12%+ (13%-12%)*(19.212/(19.212+93.272)
Cross over-rate 12.17%

IRR-project A

17.00% 18.00%
Year Cash Flow-A PV factor = 1/ (1+r)^t PV PV factor = 1/ (1+r)^t PV
0 $             (24,000.00) 1.000 $(24,000.00) 1.000 $(24,000.00)
1 $               16,570.00 0.855 $ 14,162.39 0.847 $ 14,042.37
2 $                 6,500.00 0.731 $    4,748.34 0.718 $    4,668.20
3 $                 8,590.00 0.624 $    5,363.34 0.609 $    5,228.14
Total $       274.07 Total $       (61.29)
NPV @ 0.17                        274.07
NPV @ 0.18                        (61.29)
Difference in both                        335.36
Required rate =Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
'=17%+ (18%-17%)*(274.07/(274.07+61.289)
Required rate 17.81%

IRR Project-B

16.00% 17.00%
Year Cash Flow-B PV factor = 1/ (1+r)^t PV PV factor = 1/ (1+r)^t PV
0 $             (24,000.00) 1.000 $(24,000.00) 1.000 $(24,000.00)
1 $                 8,500.00 0.862 $    7,327.59 0.855 $    7,264.96
2 $                 8,500.00 0.743 $    6,316.88 0.731 $    6,209.37
3 $               16,500.00 0.641 $ 10,570.85 0.624 $ 10,302.11
Total $       215.32 Total $     (223.56)
NPV @ 0.16                        215.32
NPV @ 0.17                      (223.56)
Difference in both                        438.89
Required rate =Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
'=16%+ (17%-16%)*(215.32/(215.32+223.56)
Required rate 16.49%

Since, IRR is higher in Project A, Project A should be selected.


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