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%.)
-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%.)
-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%.)
-Project AProject BNeither A, nor BItem 15

Answer 1

For project A

Cash flow for year 1, C1 = $7

Cash flow for year 2, C2 = $12

Cash flow for year 3, C3 = $22

Initial investment , IA = $31

For project B

Cash flow for year 1, B1 = $13

Cash flow for year 2, B2 = $6

Cash flow for year 3, B3 = $5

Initial investment , IB = $19

a)

(i) WACC = 5% = 0.05

NPV of project A = [ (C1/(1.05)¹) + (C2/(1.05)²) + (C3/(1.05)³) ] - IA

[ (7/(1.05)¹) + (12/(1.05)²) + (22/(1.05)³) ] - 31 = [6.66667 + 10.88435 + 19.00443] -31 = $5.5554 million or $5.56 million

NPV of project B = [ (B1/(1.05)¹) + (B2/(1.05)²) + (B3/(1.05)³) ] - IB

[ (13/(1.05)¹) + (6/(1.05)²) + (5/(1.05)³) ] - 19 = [12.38095 + 6.615 5.250] -19 = $3.1423 million or $3.14million

(ii)

WACC = 10% = 0.10

NPV of project A = [ (C1/(1.10)¹) + (C2/(1.10)²) + (C3/(1.10)³) ] - IA

[ (7/(1.10)¹) + (12/(1.10)²) + (22/(1.10)³) ] - 31 = $1.8099 million OR $1.81million

NPV of project B = [ (B1/(1.10)¹) + (B2/(1.10)²) + (B3/(1.10)³) ] - IB                   

[ (13/(1.10)¹) + (6/(1.10)²) + (5/(1.10)³) ] – 19 = $1.5334 million or $1.53 million

(iii)

WACC = 15% = 0.15

NPV of project A = [ (C1/(1.15)¹) + (C2/(1.15)²) + (C3/(1.15)³) ] - IA

[ (7/(1.15)¹) + (12/(1.15)²) + (22/(1.15)³) ] - 31 = $-1.374 million or -$1.37 million

NPV of project B = [ (B1/(1.15)¹) + (B2/(1.15)²) + (B3/(1.15)³) ] - IB

[ (13/(1.15)¹) + (6/(1.15)²) + (5/(1.15)³) ] – 19 = $0.1288 million or $0.13 million

b)

(i) For project A

IRR is the rate of return for which NPV = 0

NPV = Present value of cash inflows of the project - initial investment

Putting NPV = 0

Present value of cash inflows of the project = initial investment

[ (C1/(1+IRR)¹) + (C2/(1+IRR)²) + (C3/(1+IRR)³) ] = I

[ (7/(1+IRR)¹) + (12/(1+IRR)²) + (22/(1+IRR)³) ] = 31

We have to find IRR by trial and error method

by assuming any value and substituting the assumed value in the above equation

we want IRR such that

Leht Hand side of equation(LHS) = Right hand side of equation (RHS) = 31

by following this method we find that for IRR = 12.7447% or 12.74% ( rounding off to 2 decimal places)

LHS = RHS

hence IRR 12.7447% or 12.74% ( rounding off to two decimal places)

this is the IRR for WACC = 5% , 10%, 15%

(ii) For project B

IRR is the rate of return for which NPV = 0

NPV = Present value of cash inflows of the project - initial investment

Putting NPV = 0

Present value of cash inflows of the project = initial investment

[ (B1/(1+IRR)¹) + (B2/(1+IRR)²) + (B3/(1+IRR)³) ] = I

[ (13/(1+IRR)¹) + (6/(1+IRR)²) + (5/(1+IRR)³) ] = 19

We have to find IRR by trial and error method

by assuming any value and substituting the assumed value in the above equation

we want IRR such that

Leht Hand side of equation(LHS) = Right hand side of equation (RHS) = 19

by following this method we find that for IRR = 15.4929% or 15.49% ( rounding off to 2 decimal places)

LHS = RHS

hence IRR= 15.4929% or 15.49% ( rounding off to two decimal places)

this is the IRR for WACC = 5% , 10%, 15%

c)

(i) if WACC = 5%

crossover rate = 10.72%

for WACC < crossover rates, Project A would be selected, since NPV of A > NPV of B

(ii) if WACC = 10%

crossover rate = 10.72%

for WACC < crossover rates ,

hence project A would be selected, since since NPV of A > NPV of B

(iii) WACC =15%

crossover rate = 10.72%

for WACC > crossover rates ,

hence project B would be selected, since since NPV of B > NPV of A For WACC = 15%