Net Present Value final

8/7/2019 Net Present Value final

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Let’s say FIRMEX Corporation (PLC) is interested to invest in a 4 year long project. The firm

has two projects in hand; Project A & project B. The expected cash flows are also given.

Requirements

1. Calculate the NPV of both projects.

• Which project should the firm undertake if it is not financially constrained?

• Suppose the company lacks the capital to undertake both projects. Which of the

two projects then should the company select?

2. Calculate the IRR for both projects.

• Do the IRR results confirm those obtained from the NPV analysis in terms of

which project adds greater value to the firm?

We know,

NPV :

Net Present Value (NPV) measures the viability of a project or investment by taking intoaccount the investments (outflow) and returns generated (inflow) from the investments. It is

computed based on the sum of a series of cash flows in and out. NPV takes into account the

series of cash paid or received in today’s value. This is different from a layman calculation of

cash flows which only takes into account the dollar value of the cash flows.

( http://www.advanced-excel.com/net_present_value.html)

NPV Formula:



Accept-Reject Criteria

According to this method any project with a positive NPV will be accepted and projects with anegative NPV will be rejected. In other words, if present value of cash inflows is greater or equal

to present value of outflows, than the project will be accepted and rejected if not. Then again, in

case of mutually competitive projects the project with the greater positive NPV should be

selected while rejecting the rest. In order to make it easier projects are ranked according to

greater positive NPV. (M.S. MINA, (2006) Fundamentals of Finance )

IRR:

The discount rate often used in capital budgeting that makes the net present value of all cash flows from a

particular project equal to zero. Generally speaking, the higher a project's internal rate of return, the more

desirable it is to undertake the project. As such, IRR can be used to rank several prospective projects a

firm is considering. Assuming all other factors are equal among the various projects, the project with the

highest IRR would probably be considered the best and undertaken first.IRR is sometimes referred to

as "economic rate of return (ERR)".( http://www.investopedia.com/terms/i/irr.asp )

IRR Formula

Accept-Reject Criteria

According to IRR method the projects with IRR greater than all the project’s cost of capital those

will be accepted and rest rejected. In case of mutually competitive projects the project with thegreater IRR will be accepted. In general the acceptable projects are ranked in a descending

manner determined by IRR value, and then the projects can gradually be selected from greater

IRR to less. (M.S. MINA, (2006) Fundamentals of Finance )



Calculation

FIRMEX Corporation (PLC):

Project A

Cost of capital- 10%

Discount factor- 1/ (1+r) n, where ‘r’ is the cost of capital

Discounted Cash Flow for Project A

Year Cash Flow Amount($) Discount Factor Present Value($)

0 Initial Cost (200) 1.000 (200)

1 Net Cash flow 200 0.909 181.8

2 Net Cash flow 800 0.826 660.8

3 Net Cash flow (800) 0.751 (600.8)

NPV = ($200) + $181.8 + $660.8 + ($600.8) = $41.8

Discounted Cash Flow for Project B


0 Initial Cost (150) 1.000 (150)

1 Net Cash flow 50 0.909 45.45

2 Net Cash flow 100 0.826 82.60

3 Net Cash flow 150 0.751 112.65

NPV = ($150) + $45.45 + $82.60 + $112.65 = $90.7



Project A

NPV of f Project A at 0% discount rate


0 Initial Cost (200) 1.000 (200)

1 Net Cash flow 200 1.000 200

2 Net Cash flow 800 1.000 800

3 Net Cash flow (800) 1.000 (800)

NPV = $0

At 0% discount rate, NPV of Project A is zero

At 10% discount rate, NPV of Project A is $41.8

NPV of f Project A at 101% discount rate


0 Initial Cost (200) 1.000 (200)

1 Net Cash flow 200 0.497 99.50

2 Net Cash flow 800 0.247 198.0

3 Net Cash flow (800) 0.123 (98.48)

NPV = ($98.48)

At 101% discount rate, NPV of Project A = ($0.98)

IRR of Project A = 10% + [{$41.8 ÷ ($41.8 + $0.98)} × (101%-10%)] = 99%

So, IRR of Project A =99%



Project B

NPV of f Project B at 40% discount rate

Year Cash Flow Amount($) Discount Factor Present Value($)0 Initial Cost (150) 1.000 (150)

1 Net Cash flow 50 0.714 35.7

2 Net Cash flow 100 0.510 51.0

3 Net Cash flow 150 0.364 54.6

NPV = ($8.7)

At 10% discount rate, NPV of Project B is $90.7

At 40% discount rate, NPV of Project B is ($8.7)

Therefore, the project’s IRR will be between 10% and 40%

IRR of Project B = 10% + [{$90.7 ÷ ($90.7 + $8.7)} × (40%-10%)] = 37.37%

So, IRR of Project B =37.37%

Recommendations

• According to the math, if it is not financially constrained, I would say, Project B and

a both could be accepted depending on the NPV, as they both show potential positive

NPV. Considering other factors it is better to undertake Project B.

• IF the company lacks the capital to undertake both projects I would say Project B is the

better option to undertake.



• The IRR results conflict with the obtained results from the NPV analysis in terms of

which project adds greater value to the firm. The analysis supports project A as more

feasible. Whereas Project A in reality is too risky and unwise.

References

Book

1. M.S. MINA, (2006) Fundamentals of Finance, 2nd Edition, Dhaka, S.N Publications.

Internet

2. Internal Rate of Return Revisited -http://members.tripod.com/~Ray_Martin/DCF/nr7aa003.html

http://members.tripod.com/~Ray_Martin/DCF/nr7aa003.html




Bibliography

Book

1. M.S. MINA, (2006) Fundamentals of Finance, 2nd Edition, Dhaka, S.N Publications.p-

284,290.

Internet

2. Internal Rate of Return Revisited -


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Net Present Value final