Question

NPV

Your division is considering two projects with the following cash flows (in millions):

0

1

2

3

Project A	-$31	$7	$12	$22
Project B	-$19	$13	$6	$5

What are the projects' NPVs assuming the WACC is 5%? Round your answer to two decimal places. Do not round your intermediate calculations. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Negative value should be indicated by a minus sign.
Project A    $   million
Project B    $   million

What are the projects' NPVs assuming the WACC is 10%? Round your answer to two decimal places. Do not round your intermediate calculations. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Negative value should be indicated by a minus sign.
Project A    $   million
Project B    $   million

What are the projects' NPVs assuming the WACC is 15%? Round your answer to two decimal places. Do not round your intermediate calculations. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Negative value should be indicated by a minus sign.
Project A    $   million
Project B    $   million

What are the projects' IRRs assuming the WACC is 5%? Round your answer to two decimal places. Do not round your intermediate calculations.
Project A   %
Project B   %

What are the projects' IRRs assuming the WACC is 10%? Round your answer to two decimal places. Do not round your intermediate calculations.
Project A   %
Project B   %

What are the projects' IRRs assuming the WACC is 15%? Round your answer to two decimal places. Do not round your intermediate calculations.
Project A   %
Project B   %

If the WACC was 5% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 10.72%.)  
-Select-Project AProject BNeither A, nor BItem 13

If the WACC was 10% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 10.72%.)  
-Select-Project AProject BNeither A, nor BItem 14

If the WACC was 15% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 10.72%.)  
-Select-Project AProject BNeither A, nor B

Answer 1

The NPV of project A at 5% will be as below:

NPV = -31 + 7/(1+5%) + 12/(1+5%)²? + 22/(1+5%)³? = $5.56 million

Similarly, NPV for project B at 5% will be as below:

NPV = -19 + 13/(1+5%) + 6/(1+5%)²? + 5/(1+5%)³? = $3.14 million

Now if the WACC changes to 10%, we will discount the same cash flows at higher rate. The NPV will as below:

Project A NPV = -31 + 7/(1+10%) + 12/(1+10%)²? + 22/(1+10%)³? = $ 1.81 million

Project B NPV = -19 + 13/(1+10%) + 6/(1+10%)²? + 5/(1+10%)³? = $ 1.53 million

Now if the WACC changes to 15%, we will discount the same cash flows at this still higher rate. The NPV will as below:

Project A NPV = -31 + 7/(1+15%) + 12/(1+15%)²? + 22/(1+15%)³? = - $ 1.37 million

Project B NPV = -19 + 13/(1+15%) + 6/(1+15%)²? + 5/(1+15%)³? = $ 0.13 million

Now we move to calculating the IRR. IRR is simply the discount rate at which the NPV equals zero. It will not be impacted by changes in the WACC, hence at all the WACC levels, the IRR will be same.

Project A IRR = 12.74%

Project B IRR = 15.49%

We can look at the IRR and know that as long as the WACC (discount rate) is below IRR, a project NPV will be positive and it can be considered for investment.

At WACC of 5%, we will choose Project A since the present value of the cash flows (NPV) is significantly higher than Project B. Note that though Project B has higher IRR, due to different cash flow pattern, we will still choose higher NPV project since IRR has an inbuilt assumption of reinvestment at IRR rate while in NPV the same assumption is at discount rate. Given that the discount rate is lower and more realistic for a firm as a reinvestment rate, we should choose higher NPV project.

At WACC 10%, we will still choose Project A since the NPV is higher even though the differential is less. The reason for not choosing Project B which has higher IRR is given above.

At WACC 15%, only Project B has postive NPV and its IRR is also higher than 15%, hence we should choose Project B.