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 −$39,000 −$39,000
1 21,500 13,720
2 13,500 11,500
3 13,500 25,600
  • 12.85%; B

  • 12.52%; A

  • 12.52%; B

  • 12.93%; A

  • 12.93%; B

Solutions

Expert Solution

The crossover rate is the rate at which the NPV of the two projects is the same

Substituting the option values, the equation holds at 12.52% so the crossover rate is 12.52%

Below is the NPV schedules for both the projects at the crossover rates:

Project A:

Year CF Discount Factor Discounted CF
0 $-39,000.00 1/(1+0.125176224326535)^0= 1 1*-39000= $      -39,000.00
1 $ 21,500.00 1/(1+0.125176224326535)^1= 0.888749672 0.888749671722349*21500= $        19,108.12
2 $ 13,500.00 1/(1+0.125176224326535)^2= 0.789875979 0.789875978986583*13500= $        10,663.33
3 $ 13,500.00 1/(1+0.125176224326535)^3= 0.702002017 0.702002017025695*13500= $          9,477.03
NPV = Sum of all Discounted CF $              248.47

Project B:

Year CF Discount Factor Discounted CF
0 $-39,000.00 1/(1+0.125176224326535)^0= 1 1*-39000=          -39,000.00
1 $ 13,720.00 1/(1+0.125176224326535)^1= 0.888749672 0.888749671722349*13720=            12,193.65
2 $ 11,500.00 1/(1+0.125176224326535)^2= 0.789875979 0.789875978986583*11500=              9,083.57
3 $ 25,600.00 1/(1+0.125176224326535)^3= 0.702002017 0.702002017025695*25600=            17,971.25
NPV = Sum of all Discounted CF $              248.47

We need to create an NPV profile to see which project has higher NPV and should thus be selected:

Cost of capital A B
0.00% $     9,500.00 $   11,820.00
12.00% $         567.58 $         639.30
12.52% $         247.02 $         247.02
12.53% $         240.90 $         239.20
12.55% $         228.66 $         224.23
12.56% $         222.55 $         216.75
12.57% $         216.44 $         209.27
12.58% $         210.33 $         201.80
12.59% $         204.22 $         194.32
13.00% $         -44.79 $       -110.14
13.01% $         -50.83 $       -117.51

So we can see that the NPV is higher for Project A beyond 12.52% so it should be selected.


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