Question

There are two projects that the company is considering:

Project A costs 10,000 to implement today, and it brings subsequent cash flows of 5,900 at the end of year 1; 2,000 at the end of year 2; 5,000 at the end of year 3.

Project B's initial cost is 7,500, and subsequent cash flows are 5,000 per year for 3 years.

WACC is 8% for both projects.

Calculate NPV and IRR for each project, and decide which to recommend.

Answer 1

For project A

Cash flow for year 1, C1 = $5900

Cash flow for year 2, C2 = $2000

Cash flow for year 3, C3 = $5000

Initial investment , IA = $10,000

For project B

Cash flow for year 1, B1 = $5000

Cash flow for year 2, B2 = $5000

Cash flow for year 3, B3 = $5000

Initial investment , IB = $7500

WACC = 8% = 0.08

NPV of project A = [ (C1/(1.08)¹) + (C2/(1.08)²) + (C3/(1.08)³) ] - IA

= [ (5900/(1.08)¹) + (2000/(1.08)²) + (5000/(1.08)³) ] - 10,000 = [5462.963 + 1714.678 + 3969.161] -10000= $1146.802 or $1146.80

NPV of project B = [ (B1/(1.08)¹) + (B2/(1.08)²) + (B3/(1.08)³) ] - IB

[ (5000/(1.08)¹) + (5000/(1.08)²) + (5000/(1.08)³) ] - 7500 = [4629.63 + 4286.694 + 3969.161] -7500= $5385.485 or $5385.49

b)

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

[ (5900/(1+IRR)¹) + (2000/(1+IRR)²) + (5000/(1+IRR)³) ] = 10000

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) = 10000

by following this method we find that for IRR = 14.558% or 14.56% ( rounding off to 2 decimal places)

LHS = RHS

hence IRR for project A = 14.558% or 14.56% ( rounding off to two decimal places)

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

[ (5000/(1+IRR)¹) + (5000/(1+IRR)²) + (5000/(1+IRR)³) ] = 7500

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) = 7500

by following this method we find that for IRR = 44.631% or 44.63% ( rounding off to 2 decimal places)

LHS = RHS

hence IRR for project B = 44.631% or 44.63% ( rounding off to two decimal places)