Question

You are considering the following two projects and can take only one. Your cost of capital is 11.0 %. The cash flows for the two projects are as follows (S million): Year 3 $40 $30 Year 0 -$100 -$100 Project Year 2 Year 4 Year 1 $50 $25 $50 $30 $40 $20 1,42 B a. What is the IRR of each project? b. What is the NPV of each project at your cost of capital? c. At what cost of capital are you indifferent between the two projects? d. What should you do?

Answer 1

Solution:

We will be using our BA II plus calculator Cash Flow Row in order to calculate the respective entities.

a) Calculating the IRR of each project.

Project A:

C0 = -100 , C1 = 25 F1=1 , C2 = 30 F2 =1 , C3 = 40 F3 =1 , C4 =50 F4=1

After entering these values we press IRR in the second row and then CPT

We get the IRR for project A as : 14.69%

Project B:

C0 = -100 , C1 = 50 F1=1 , C2 = 40 F2 =1 , C3 = 30 F3 =1 , C4 =20 F4=1

After entering these values we press IRR in the second row and then CPT

We get the IRR for project B as : 17.804%

b) Calculating the NPV of each project.

Project A:

C0 = -100 , C1 = 25 F1=1 , C2 = 30 F2 =1 , C3 = 40 F3 =1 , C4 =50 F4=1

We hit the NPV button and will be asked to enter the rate , we enter 11% i.e. our cost of capital and then CPT

We get the NPV for project A as : 9.0553

Project B:

C0 = -100 , C1 = 50 F1=1 , C2 = 40 F2 =1 , C3 = 30 F3 =1 , C4 =20 F4=1

We hit the NPV button and will be asked to enter the rate , we enter 11% i.e. our cost of capital and then CPT

We get the NPV for project B as : 12.620

c) Calculating the cross over point of the two projects i.e. the rate at which the two becomes indifferent.

This can be calculated by putting the differences in the cash flows of the two projects in the NPV equation and putting the final value of difference NPV 0. (Two NPV s should be same)

C0 A - C0 B = 0

C1A - C1 B = 25 - 50 = -25

C2A - C2B = 30 - 40 = -10

C3A - C3B = 40 - 30 = 10

C4A - C4B = 50 - 20 = 30

Now we will be again using our BA II plus calculator and enter the final values as :

C0 = 0 , C1 = -25 F1=1, C2=-10 F2=1, C3=10 F3=1, C4=30 F4=1

Hitting the IRR and then CPT

We get the IRR as 5.56% or the Cost of capital at which the projects are indifferent.

d) As we can see that the two projects have different NPV but Project B has a higher IRR (17.80%) and also major cash flows takes place in the early years so we will be going ahead with project B.