Net Present Value (NPV) problems with solutions for MBA course

1. E-MBA 1 Nilesh Parab
Net Present Value (NPV)
Payback Period (PBP) = Cost of Investment / Net Annual Cash Inflows
Net Present Value (NPV) = Net Cash Inflow – Net Cash Outflow
Payback Period (PBP)
Q1. The cost of the machine is $28,120 and it is expected to bring the company a net cash flow of $7,600
per year for the next fifteen years of the machine's useful life. Calculate the payback period.
A1. Information available:
Cost of Investment (C) = $28,120
Useful Life (N) = 15 Years
Cash Inflows (CI) = $7,600 p.a.
Payback Period (PBP) = Cost of Investment / Net Annual Cash Inflows
∴ PBP = 28,120 / 7,600
∴ PBP = 3.7 years
Q2. The management of Health Supplement Inc. wants to reduce its labor cost by installing a new
machine. Two types of machines are available in the market – machine X and machine Y. Machine X
would cost $18,000 whereas machine Y would cost $15,000. Both the machines can reduce annual
labor cost by $3,000. Which is the best machine to purchase according to payback method?
A2. Information available:
Cost of Investment (X) = $18,000
Cost of Investment (Y) = $15,000
Cash Inflows (CI_X) = $3,000 p.a.
Cash Inflows (CI_Y) = $3,000 p.a.
Payback Period (PBP) = Cost of Investment / Net Annual Cash Inflows
∴ PBP X = 18,000 / 3,000
∴ PBP X = 6 years
∴ PBP Y = 15,000 / 3,000
∴ PBP Y = 5 years
According to payback method, machine Y is more desirable than machine X because it has a shorter
payback period.
Q3. An investment of $200,000 is expected to generate the following cash inflows in six years. Calculate
the payback period.
Year 1 $70,000
Year 2 $60,000
Year 3 $55,000
Year 4 $40,000
Year 5 $30,000
Year 6 $25,000
A3. Information available:
Cost of Investment (C) = $200,000
Because the cash inflow is uneven, the payback period formula cannot be used to compute the
paybackperiod. We cancomputethe payback periodby computingthe cumulative net cash inflows
as follows:

2. E-MBA 2 Nilesh Parab
Year Cash Inflow
Cumulative
Cash Inflow
Year 1 $70,000 $70,000
Year 2 $60,000 $130,000
Year 3 $55,000 $185,000
Year 4 $40,000 $225,000 ←
Year 5 $30,000 $255,000
Year 6 $25,000 $280,000
Investment of $200,000 gets recovered in 4th
year. To find the exact duration, first let us find the
unrecovered Investment at the start of 4th
year.
= Initial cost – Cumulative cash inflow at the end of 3rd
year
= $200,000 – $185,000
= $15,000
Pay Back Period = 3 + (15,000/40,000)
= 3.375 years
Net Present Value (NPV)
Q1. Sunlight company needs a machine for its manufacturing process. The cost of the new machine is
$80,700. The expected useful life of the machine is 8 years. At the end of 8-year period, the machine
wouldhave no salvagevalue. After installation,the machinewouldincrease cashinflows by $30,000
per year. Sunlight is interested to know the net present value of the machine to accept or reject this
investment. The minimumrequired rate of return of the company is 16% on all capital investments.
1. Compute net present value of the machine.
2. Is it acceptable to purchase the machine?
A1. Information available:
Cost of Investment (C) = $80,700
Useful Life (n) = 8 Years
Cash Inflows (CI) = $30,000 p.a. (also referred as Annuity Value A)
Rate of Return (r) = 16% p.a.
Present Value of Annuity (PVA) = Annuity Value (A) x PVIFA (16%, 8)
∴ PVA = 30,000 x [1-1/(1+r) ^n)/r]
∴ PVA = 30,000 x 4.3436
∴ PVA = 130,308
1. Net Present Value (NPV)= Net Cash Inflow – Net Cash Outflow
∴ NPV = 130,308 – 80,700
∴ NPV = $49,608
2. Since the NPV is positive, the purchase of machine is acceptable.
Q2. The management of Fine Electronics Company is considering purchasing an equipment to be
attached with the main manufacturing machine. The equipment will cost $6,000 and will increase
annual cash inflow by $2,200. The useful life of the equipment is 6 years. After 6 years it will have no
salvage value. The management wants a 20% return on all investments.
A2. Information available:
Cost of Investment (C) = $6,000
Useful Life (n) = 6 Years
Cash Inflows (CI) = $2,200 p.a. (also referred as Annuity Value A)
Rate of Return (r) = 20% p.a.
Present Value of Annuity (PVA) = Annuity Value (A) x PVIFA (20%,6)

3. E-MBA 3 Nilesh Parab
∴ PVA = 2,200 x [1-1/(1+r) ^n)/r]
∴ PVA = 2,200 x 3.3255
∴ PVA = 7,316
Net Present Value (NPV)= Net Cash Inflow – Net Cash Outflow
∴ NPV = 7,316 – 6,000
∴ NPV = $1,316
Since the NPV is positive, the purchase of equipment is acceptable.
Q3. Windsor Ltd is considering a project, which will involve the following cash inflows and outflows.
Initial Outlay /Outflow -400,000
After 1 Year 40,000
After 2 Years 300,000
After 3 Years 300,000
What will be the NPV (net present value) of this project if a discount rate of 15% is used?
A3. Information available:
Cash Outflow = 400,000
Rate of Return (r) = 15% p.a.
Since the inflows are uneven, we have to use FV & PVIF.
PV1 = 40,000 X PVIF (15%, 1) = 40,000 x 0.8696 = 34,784
PV2 = 300,000 X PVIF (15%, 2) = 300,000 x 0.7561 = 226,830
PV3 = 300,000 X PVIF (15%, 3) = 300,000 x 0.6575 = 197,250
PV = PV1 + PV2 + PV3 = 458,864
NPV = Net Cash Inflow – Net Cash Outflow
∴ NPV = 458,864 – 400,000
∴ NPV = 58,864
Since the NPV is positive, the Project is viable.
Q4. A project requires an initial investment of $225,000 and is expected to generate the following net
cash inflows. Compute net present value of the project if the minimum desired rate of return is 12%.
Year 1 $95,000
Year 2 $80,000
Year 3 $60,000
Year 4 $55,000
A4. Information available:
Cash Outflow = 225,000
Rate of Return (r) = 12% p.a.
Since the inflows are uneven, we have to use FV & PVIF.
Year (n) FV PVIF (12%, n) PV
Year 1 $95,000 0.893 84,835
Year 2 $80,000 0.797 63,760
Year 3 $60,000 0.712 42,720
Year 4 $55,000 0.636 34,980
PV Total 226,295
NPV = Net Cash Inflow – Net Cash Outflow
∴ NPV = 226,295 - 225,000
∴ NPV = $1,295
The project seems attractive because its net present value is positive.

4. E-MBA 4 Nilesh Parab
Q5. Smart Manufacturing Company is planning to reduce its labor costs by automating a critical task
that is currently performed manually. The automation requires the installation of a new machine.
The cost to purchase and install a new machine is $15,000. The installation of machine can reduce
annual labor cost by $4,200. The life of the machine is 15 years. The salvage value of the machine
after fifteen years will be zero. The required rate of return of Smart Manufacturing Company is 25%.
Should Smart Manufacturing Company purchase the machine?
A5. Information available:
Cost of Investment (C) = $15,000
Useful Life (n) = 15 Years
Cash Inflows (CI) = $4,200 p.a. (also referred as Annuity Value A)
Rate of Return (r) = 25% p.a.
Present Value of Annuity (PVA) = Annuity Value (A) x PVIFA (25%,15)
∴ PVA = 4,200 x [1-1/(1+r) ^n)/r]
∴ PVA = 4,200 x 3.859
∴ PVA = 16,208
Net Present Value (NPV)= Net Cash Inflow – Net Cash Outflow
∴ NPV = 16,208 – 15,000
∴ NPV = $1,208
Since the NPV is positive, the purchase of equipment is acceptable.