Question

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

                    0                     1       2 3     

Project A       - $25                   $5                 $10                  $17

Project B        -$20                   $10               $9                     $6

ANSWER THIS. What are the projects’ NPVs assuming the discount interest rate is 12%?

Please explain and show work

ANSWER THIS What are the projects’ IRRs?

Please explain and show work.

Answer 1

Net present value :

Project A :

NPV = Cash flow / ( 1 + r )1 + Cash flow / ( 1 + r )2 + Cash flow / ( 1 + r )n - initial investment

NPV = 5 / ( 1 + 0.12) + 10 / (1+0.12)2 + 17 / (1+0.12)3 - 25

= (5 / 1.12) + (10 / 1.2544) + ( 17 / 1.404928) - 25

= 4.464 + 7.971 + 12.100 - 25

= 24.535 - 25

= $-0.465

Project B :

NPV =  10 / ( 1 + 0.12) + 9 / (1+0.12)2 + 6 / (1+0.12)3 - 20

= ( 10 /1.12) + (9 / 1.2544) + (6 / 1.404928) - 20

= 8.928 + 7.174 + 4.2706 - 20

= 20.372 - 20

= $ 0.372

Internal rate of return ;

Project A :

Trial and error method , discount rate 11 %

NPV = 5 / ( 1 + 0.11) + 10 / (1+0.11)2 + 17 / (1+0.11)3 - 25

= 4.504 + 8.116 + 12.430 - 25

= 25.05 - 25

= 0.05

IRR = A + [( C-O) / (C -D ) ] * [B - A]

A = lower discount rate

C-O = lowest discount rate NPV

C = lowest discount rate total of cash flows

D =Higher discount rate cash flow total

B = Higher discount rate

IRR = 11 % + [( 0.05) / (  25.05 - 20.37)] * [ 12 - 11]

= 11% + [ 0.05 / 4.678] * 1

= 11 % + (0.010 * 1)

= 11 % + 0.01

=11.01 %

Project B :

Discount rate @14%

NPV =  10 / ( 1 + 0.14) + 9 / (1+0.14)2 + 6 / (1+0.14)3 - 20

= 8.771+ 6.925+ 4.049 - 20

= 19.745 - 20

= -0.255

IRR = A + [( C-O) / (C -D ) ] * [B - A]

  = 12 % + [ ( 0.37) / ( 20.37 - 19.74 )] * [ 14-12]

= 12% + [0.37 / 0.63] * 2

= 12% + (0.5873 *2 )

= 12% + 1.174

= 13.17 %

Project B have higher NPV than project A. it is accepted. project A should be rejected

Project B have higher IRRand project A have lower IRR