Question

11-2: Net Present Value (NPV) 11-7: NPV Profiles NPV Your division is considering two projects with the following cash flows (in millions): 0 1 2 3 Project A -$27 $13 $17 $8 Project B -$25 $14 $11 $2 What are the projects' NPVs assuming the WACC is 5%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A    $   million Project B    $   million What are the projects' NPVs assuming the WACC is 10%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A    $   million Project B    $   million What are the projects' NPVs assuming the WACC is 15%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A    $   million Project B    $   million What are the projects' IRRs assuming the WACC is 5%? Round your answer to two decimal places. Project A   % Project B   % What are the projects' IRRs assuming the WACC is 10%? Round your answer to two decimal places. Project A   % Project B   % What are the projects' IRRs assuming the WACC is 15%? Round your answer to two decimal places. Project A   % Project B   % If the WACC were 5% and A and B were mutually exclusive, which would you choose? (Hint: The crossover rate is 90.37%.)   -Select- (Project A) (Project B) (Neither A, nor B) If the WACC were 10% and A and B were mutually exclusive, which would you choose? (Hint: The crossover rate is 90.37%.)   -Select-(Project A) (Project B) (Neither A, nor B) If the WACC were 15% and A and B were mutually exclusive, which would you choose? (Hint: The crossover rate is 90.37%.)   -Select- (Project A) (Project B) (Neither A, nor B)

Answer 1

For project A

Cash flow for year 1, C1 = $13

Cash flow for year 2, C2 = $17

Cash flow for year 3, C3 = $8

Initial investment , IA = $27

For project B

Cash flow for year 1, B1 = $14

Cash flow for year 2, B2 = $11

Cash flow for year 3, B3 = $2

Initial investment , IB = $25

a)

(i) WACC = 5% = 0.05

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

[ (13/(1.05)¹) + (17/(1.05)²) + (8/(1.05)³) ] - 27 = [12.380952 + 15.419501 + 6.9107007] -27 = $7.711154 million or $7.71 million

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

[ (14/(1.05)¹) + (11/(1.05)²) + (2/(1.05)³) ] - 25 = [13.3333 + 9.977324 + 1.727675] -25 = $0.038332 million or $0.04 million

(ii)

WACC = 10% = 0.10

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

[ (13/(1.10)¹) + (17/(1.10)²) + (8/(1.10)³) ] - 27 = [11.8181 + 14.0495 + 6.0105] -27 = $4.87828 million = -$4.88 million

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

[ (14/(1.10)¹) + (11/(1.10)²) + (2/(1.10)³) ] - 25 = [12.7272 + 9.0909 + 1.5026] -25 = -$1.6791 million or -$1.68 million

(iii)

WACC = 15% = 0.15

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

[ (13/(1.15)¹) + (17/(1.15)²) + (8/(1.15)³) ] - 27 = [11.3043 + 12.8544 + 5.2601] -27 = $2.4189 million or $2.42 million

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

[ (14/(1.15)¹) + (11/(1.15)²) + (2/(1.15)³) ] - IB = [12.1739 + 8.3175 + 1.3150] -25 = -$3.1934 million or -$3.19 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

[ (13/(1+IRR)¹) + (17/(1+IRR)²) + (8/(1+IRR)³) ] = 27

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) = 27

by following this method we find that for IRR = 20.6723% or 20.67% ( rounding off to 2 decimal places)

LHS = RHS

hence IRR = 20.6723% or 20.67% ( 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

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

[ (14/(1+IRR)¹) + (11/(1+IRR)²) + (2/(1+IRR)³) ] = 25

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) = 25

by following this method we find that for IRR = 5.10476% or 5.10% ( rounding off to 2 decimal places)

LHS = RHS

hence IRR = 5.104% or 5.10% ( rounding off to two decimal places)

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

c)

(i) if WACC = 5%

crossover rate = 90.37%

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

(ii) if WACC = 10%

crossover rate = 90.37%

for WACC < crossover rates ,

hence project A would be selected, since project B's NPV is negative

(iii) WACC =15%

crossover rate = 90.37%

Project A would be selected, since project B's NPV is negative