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# Question about Finance problems: IRR and NPV.

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Part 1. Capital Budgeting Practice Problems

a. Consider the project with the following expected cash flows:

Year Cash flow
0 - \$500,000
1 \$100,000
2 \$110,000
3 \$550,000
If the discount rate is 0%, what is the project's net present value?
If the discount rate is 4%, what is the project's net present value?
If the discount rate is 8%, what is the project's net present value?
If the discount rate is 10%, what is the project's net present value?
What is this project's internal rate of return?
Now draw (for yourself) a chart where the discount rate is on the horizontal axis (the "x" axis) and the net present value on the vertical axis (the Y axis). Plot the net present value of the project as a function of the discount rate by dots for the four discount rates. connect the four points using a free hand 'smooth' curve. The curve intersects the horizontal line at a particular discount rate. What is this discount rate at which the graph intersects the horizontal axis?

[You can't upload the graph unto Coursenet. Look at the graph you draw and write a short paragraph stating what the graph 'shows"]..

b. Consider a project with the expected cash flows:

Year Cash flow
0 - \$615,000
1 + 141,000
2 + 300,000
3 + \$300,000
What is this project's internal rate of return?
If the discount rate is 0%, what is this project's net present value?
If the discount rate is 4%, what is this project's net present value?

If the discount rate is 8%, what is this project's net present value?

If the discount rate is 12%, what is this project's net present value?

Now draw (for yourself) a chart where the discount rate is on the horizontal axis (the "x" axis) and the net present value on the vertical axis (the Y axis). Plot the net present value of the project as a function of the discount rate by dots for the four discount rates. connect the four points using a free hand 'smooth' curve. The curve intersects the horizontal line at a particular discount rate. What is this discount rate at which the graph intersects the horizontal axis?

[You can't upload the graph unto Coursenet. Observe the graph and write a short paragraph stating what the graph 'shows

c. A project requiring a \$3.2 million investment has a profitability index of 0.97. What is its net present value? (Remember: Profitability Index is defined as Present Value of the proceeds divided by the initial investment)

Part 2.

Which method do you think is the better one for making capital budgeting decisions - IRR or NPV?

Internal rate of return (IRR) is the flip side of net present value (NPV) and is based on the same principles and the same math. NPV shows the value of a stream of future cash flows discounted back to the present by some percentage that represents the minimum desired rate of return, often a company's cost of capital. IRR, on the other hand, computes a break-even rate of return. It shows the discount rate below which an investment results in a positive NPV and above which an investment results in a negative NPV. It is the breakeven discount rate, the rate at which the value of cash outflows equals the value of cash inflows.

WEAKNESSES: it's not as easy to understand as some measures and not as easy to compute (even Excel uses approximations). Computational anomalies can produce misleading results, particularly with regard to reinvestments.

Enlarge 200%
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INTERNAL RATE OF RETURN:
What It Looks Like

IRR is the flip side of net present value (NPV) and is based on the same principles and the same math. NPV shows the value of a stream of future cash flows discounted back to the present by some percentage that represents the minimum desired rate of return, often your company's cost of capital.

IRR, on the other hand, computes a break-even rate of return. It shows the discount rate below which an investment results in a positive NPV (and should be made) and above which an investment results in a negative NPV (and should be avoided). It's the breakeven discount rate, the rate at which the value of cash outflows equals the value of cash inflows.

Consider the three scenarios shown here (see table), each involving an initial investment of \$1 million. The investment returns \$300,000 (undiscounted) per year in each of the five years after the initial investment, for a net return of \$500,000.

A company evaluating this investment using cash flow discounted at 10% would compute an NPV of \$137,000, a decent but not spectacular result. But if the company evaluates the same investment at 15%, the project has a present value of only \$6,000, essentially just breaking even, and at 20% the project's present value is negative. The IRR is a fraction of a percentage point above 15%; at that discount percentage, the investment's NPV is zero.

IRR is often used as a hurdle rate, a sort of go/no-go investment threshold. Gaylord Entertainment Co. in Nashville, for example, has computed its weighted average cost of capital -- a percentage that it won't disclose -- and a "hurdle" percentage rate a few points higher. An investment's IRR must generally equal or exceed the hurdle rate to be approved by management, says CIO Kent Fourman.

"We calculate the IRR and then compare that to our hurdle rate," Fourman says. "And we compare that IRR against every other [project's] IRR, because you always have limited cash."

But the IRR cutoff isn't an absolute test, he says. For example, management's subjective assessment of risk may influence an investment decision, he says. "But if you can't show that IRR exceeds our hurdle rate, then you'll have to have a lot of the soft justifications to get it approved," Fourman says.

Not everyone is as enthusiastic about IRR. Like NPV, it doesn't measure the absolute size of the investment or its return. And because of the way the math works, the timing of periods of negative cash flow can affect the value of IRR without accurately reflecting the underlying performance of the investment.

IRR can also produce misleading results because, as classically defined, it assumes that the cash returned from an investment is reinvested at the same percentage rate, which may not be realistic. That error is magnified when comparing two investments of different durations. Some software, such as Microsoft Excel, will compute an optional "modified IRR" that allows the user to specify a different reinvestment rate.

IRR becomes increasingly misleading the more it diverges from the cost of capital, says Ian Campbell, chief research officer at Nucleus Research Inc. in Wellesley, Mass. "IRR is a terrible metric, and it should never be used," he asserts.

The key metric for IT projects, Campbell says, is payback period, because it favors short-term, and hence less risky. projects that IT should be doing.

##### Solution Summary

The problem set deals with determining the net present value and internal rate of return for a set of cashflows.

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###### Education
• B. Sc., University of Nigeria
• M. Sc., London South Bank University
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