Question

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

0 1 2 3

Project A - $35 $4 $14 $20

Project B - $15 $8 $5 $4

B. 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   %

C. If the WACC was 5% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 1.66%.)
1. Project A 2. Project B 3. Neither A, nor B

If the WACC was 10% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 1.66%.)
1. Project A 2. Project B 3. Neither A, nor B

If the WACC was 15% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 1.66%.)
1. Project A 2. Project B 3. Neither A, nor B

Answer 1

For project A

Cash flow for year 1, C1 = $4

Cash flow for year 2, C2 = $14

Cash flow for year 3, C3 = $20

Initial investment , IA = $35

For project B

Cash flow for year 1, B1 = $8

Cash flow for year 2, B2 = $5

Cash flow for year 3, B3 = $4

Initial investment , IB = $15

a)

(i) WACC = 5% = 0.05

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

[ (4/(1.05)¹) + (14/(1.05)²) + (20/(1.05)³) ] - 35 = [3.80952 + 12.69841 + 17.27675] -35 = -$1.2153million or -$1.22 million

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

[ (8/(1.05)¹) + (5/(1.05)²) + (4/(1.05)³) ] - 15 = [7.61905 + 4.53515+ 3.45535] -15 = $0.6095 million or $0.61 million

(ii)

WACC = 10% = 0.10

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

[ (4/(1.10)¹) + (14/(1.10)²) + (20/(1.10)³) ] - 35 = -$4.7671 million OR -$4.77 million

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

[ (8/(1.10)¹) + (5/(1.10)²) + (4/(1.10)³) ] – 15 = -$0.5898 million or -$0.59 million

(iii)

WACC = 15% = 0.15

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

[ (4/(1.15)¹) + (14/(1.15)²) + (20/(1.15)³) ] - 35 = -$7.7854 million or -$7.79 million

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

[ (8/(1.15)¹) + (5/(1.15)²) + (4/(1.15)³) ] – 15 = -$1.6327 million or -$1.63 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

[ (4/(1+IRR)¹) + (14/(1+IRR)²) + (20/(1+IRR)³) ] = 35

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) = 35

by following this method we find that for IRR = 3.4665% or 3.47% ( rounding off to 2 decimal places)

LHS = RHS

hence IRR 3.4665% or 3.47% ( 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

[ (8/(1+IRR)¹) + (5/(1+IRR)²) + (4/(1+IRR)³) ] = 15

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) = 15

by following this method we find that for IRR = 7.4515% or 7.45% ( rounding off to 2 decimal places)

LHS = RHS

hence IRR= 7.4515% or 7.45% ( rounding off to two decimal places)

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

c)

(i) if WACC = 5%

crossover rate = 1.66%

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

(ii) if WACC = 10%

crossover rate = 1.66%

NEITHER of the projects will be selected since NPV for both projects are negative

(iii) WACC =15%

crossover rate = 1.66%

NEITHER of the projects will be selected since NPV for both projects are negative