Question

You are choosing between two projects. The cash flows for the projects are given in the following table​ ($ million):

Project	Year 0	Year 1	Year 2	Year 3	Year 4
A	−$51	$26	$18	$19	$16
B	−$100	$20	$41	$51	$60

a. What are the IRRs of the two​ projects?

b. If your discount rate is

5.4%​,

what are the

NPVs

of the two​ projects?

c. Why do IRR and NPV rank the two projects​ differently?

a. What are the IRRs of the two​ projects?

The IRR for project A is

nothing​%.

​(Round to one decimal​ place.)

PLEASE HELP FOR A,B, AND C TOO!

Answer 1

Answer-

Project	Year 0	Year 1	Year 2	Year 3	Year 4
A	- $ 51	$ 26	$ 18	$ 19	$ 16
B	- $ 100	$ 20	$ 41	$ 51	$ 60

a)

IRRs of Project A

IRR is the value when the NPV = 0

0 = - $ 51 + $ 26 / ( 1 + IRR) + $ 18 / ( 1 + IRR)² + $ 19 / ( 1 + IRR)³ + $ 16 / ( 1 + IRR)⁴

By using financial calculator we get

IRR Project A = 22.1 %

IRRs of Project B

IRR is the value when the NPV = 0

0 = - $ 100 + $ 20 / ( 1 + IRR) + $ 41 / ( 1 + IRR)² + $ 51 / ( 1 + IRR)³ + $ 60 / ( 1 + IRR)⁴

By using financial calculator we get

IRR Project B = 21.59 %

b)

Discount rate = 5.4 % = 0.054

NPV of Project A

NPV = - $ 51 + $ 26 / ( 1 + 0.054) + $ 18 / ( 1 + 0.054)² + $ 19 / ( 1 + 0.054)³ + $ 16 / ( 1 + 0.054)⁴

NPV = - $ 51 + $ 26 / ( 1.054) + $ 18 / ( 1.054)² + $ 19 / ( 1.054)³ + $ 16 / ( 1.054)⁴

NPV - $ 51 + $ 26 / 1.054 + $ 18 / 1.11 + $ 19 / 1.17 + $ 16 / 1.234

NPV = - $ 51 + $ 24.67 + $ 16.22 + $ 16.24 + $ 12.96

NPV = $ 19.09

NPV of Project A = $ 19.09

NPV of Project B

NPV = - $ 100 + $ 20 / ( 1 + 0.054) + $ 41 / ( 1 + 0.054)² + $ 51 / ( 1 + 0.054)³ + $ 60 / ( 1 + 0.054)⁴

NPV = - $ 100 + $ 20 / ( 1.054) + $ 41 / ( 1.054)² + $ 51 / ( 1.054)³ + $ 60 / ( 1.054)⁴ ​​​​​​​

NPV - $ 100 + $ 20 / 1.054 + $ 41 / 1.11 + $ 51 / 1.17 + $ 60 / 1.234

NPV = - $ 100 + $ 18.97 + $ 36.94 + $ 43.59 + $ 48.62

NPV = $ 48.12

NPV of Project B = $ 48.12

c)

As per IRR ranking Project A should be selected as it has higher IRR than project B's IRR ( IRR A ( 22.1 %) > IRR B ( 21.59 %)

As per NPV ranking Project B should be selected as it has higher NPV than Project A ( NPV B ( $48.12 ) > NPV A ( $ 19.09 )

The Project B should be selected over Project A as NPV ranking should be considered when there are conflicting results from NPV and IRR. The higher NPV adds value to the Project and company as a whole.