Question

Consider the following two mutually exclusive projects and their Cash Flows ($)

Project                                            C₀                               C₁                               C₂                               C₃

K                                                       –$100                 +$45 +$45 +$60    

W                                                     –$150                 +$45 +$45 +$125

Which statement is correct based on the above information about Projects K and W?

a. If the discount rate is 7.5%, accept project W because the cross-over rate is 9%

b. Accept project K, because at a 9% discount rate K and W have the same net present value.

c. If the discount rate is 9.5%, reject project K, because the cross-over rate is 9%.

d. If the discount rate is 7.5%, accept project W because the IRR of W is 17%.

e. Accept project K because the IRR of K is larger than the IRR of W.

Answer 1

Given, The Cash Flows Of Project K

CF [email protected]%   [email protected]%

Year 0 (100) (100) (100)

Year 1 45 45/1.075   45/1.095

Year 2 45 45/(1.075*1.075)   45/(1.095*1.095)

Year3 60 60/(1.075*1.075*1.075)   60/(1.095*1.095*1.095)

_____________________________________________________________________________

NPV 29.09 24.32

The Cash Flows Of Project W

CF [email protected]%   [email protected]%

Year 0 (150) (150) (150)

Year 1 45 45/1.075 45/1.095

Year 2 45 45/(1.075*1.075) 45/(1.095*1.095)

Year3 125 125/(1.075*1.075*1.075) 125/(1.095*1.095*1.095)

_____________________________________________________________________________

NPV 24.32 23.83

Cross over rate

Equating NPV of K & W

NPV of K= NPV of W

45/(1+r)+45(1.r)^2+60/(1+r)^3-100=45/(1+r)+45(1.r)^2+125/(1+r)^3-150

=>r=9.14%

IRR of K

100=45/(1+r)+45(1.r)^2+60/(1+r)^3

r=>22%

IRR of W

150=45/(1+r)+45(1.r)^2+125/(1+r)^3

r=>17%

Therefore, Option (e), i.e Accept project K because the IRR of K is larger than the IRR of W.is correct