Week 2

Question 1

How is NPV calculated?

What will we typically need to estimate?

Answer 1

NPV = discounted FVs - initial costs.

To estimate, we need to future CF estimate (both how much and when), The discount rate estimate, and estimated initial costs.

Question 2

Minimum acceptance criteria for a project using NPV?

How do we rank them?

Answer 2

Minimum acceptance = NPV > 0.

If there are multiple projects to choose from we should choose the one with the highest NPV.

Question 3

How will our minimum return relate to net present value?

Answer 3

The minimum we would want an investment to return is the amount which makes our net present value 0.

Question 4

How should our discount rate relate to the riskiness of the investment?

Answer 4

Our discount rate should depend on the riskiness of the investment.

Question 5

Does the term structure of the discount rate have to be flat?

What else could it be?

Answer 5

No it doesn’t, instead

• We can use the YTM of different risk free maturity investments for the different CFs.
• We could use the short rate of each year leading up to the CF’s year.

Question 6

How can we find the expected value of a cash value if the events are uncertain?

Answer 6

If we know their probability, we can use the expected value (sum of probability x probability’s associated value) for our CF.

Question 7

What is the IRR?

Answer 7

The discount rate that sets net present value to 0.

Question 8

Acceptance criteria for projects using IRR?

What is the ranking criteria?

Answer 8

We will only accept a project if the IRR > required return.

When ranking different projects we will prefer projects with a higher IRR.

Question 9

Reinvestment assumption for IRR?

Why is it wrong?

Answer 9

That all future CFs can be reinvested at the IRR.

This assumption is wrong, as these modified CFs produced by reinvestment cannot be associated with the project.

So we do not need to consider this assumption when considering a project.

Question 10

If we graph the net present value versus the discount rate, where do we find the IRR?

Answer 10

If we graph NVP vs discount rate, the IRR is the x-axis intercept.

Question 11

Main problems with the IRR?

Answer 11

1. NPV easier to calculate
2. A higher IRR is better for investment projects, while a lower IRR is better for financing projects.
3. The IRR doesn’t exist
4. When there are multiple IRRs
5. The IRR assumes the term structure is flat. When term structure is not flat using IRR can lead to bad decisions.
6. IRR does not help you choose between mutually exclusive projects that involve size, scale and timing problems

Question 12

Difference between an investment project and financing project in terms of CFs?

What will be the relationship between the NPV and the discount rate in both?

When will the IRR be the same for a financing and investment project?

Answer 12

Investment project = Initial cash outflow then cash inflows, this will have a downward sloping relationship between NPV and discount rate.

Financing project = Cash inflow then cash outflows, there will be an upward sloping relationship between NPV and the discount rate.

IRR will be same for both if we flip the signs on each CF.

Question 13

How is the no or multiple IRR problem typically solved?

Answer 13

MIRR. Though it is not actually the internal rate of return of the project.

Question 14

MIRR using the discounting approach?

Answer 14

Discount all negative CFs back to time zero and add them to the initial CF, then calculate the MIRR as we would the IRR.

Question 15

MIRR using the reinvestment approach?

Answer 15

Compound all CFs except for the time zero CF to the end of the project’s life and sum them.

Then,
Initial CF/terminal value = (1+MIRR)^maximum period.

Question 16

MIRR using the combination approach?

Answer 16

Discount all costs back to the initial period, then get the FV of the CFs.
Present value costs = terminal/future value of cash inflows divided by (1+MIRR)^maximum period.

Question 17

Can we use different rates for the FV and PV in calculating the MIRR?

Answer 17

Yes,

the discounting rate and compounding rate can be different for the MIRR equations.

Question 18

How do we treat projects differently if they are independent vs if they are mutually exclusive?

Answer 18

• Independent they must exceed a minimum acceptance criteria.
• Mutually exclusive, we rank all alternatives and select the best one.

Question 19

Why can the IRR be misleading when choosing between mutually exclusive projects?

Answer 19

Scale/size disparity problem.

This occurs because the project may have a high IRR but is a small project, meaning we may turn down a project with a higher NPV.

As such, we should sometimes takes an investment with a lower IRR if the NPV is higher and the investments are mutually exclusive.

Question 20

Timing problem with regards to the IRR?

Answer 20

Its an IRR problem associated with mutually exclusive projects, it occurs when the timing of CF is substantially different.

The crossover rate is the discount rate at which the NPV of one project is the same as the other project, after this rate the better project changes.

Essentially, the timing of CFs can affect which project is better depending on the discount rate used, even though one may have a higher IRR.

Question 21

How do we solve the IRR timing problem?

Answer 21

Compute the IRR for either project A-B or B-A. The IRR for these projects is the same, and will be the crossover rate.

If the required rate < crossover rate, we choose the project with the later CFs,
If the required rate > crossover rate we choose the project with the earlier CFs.

Question 22

When do NPV and the IRR not lead to the same decision?

Answer 22

NPV and the IRR will generally give the same decision, though there are exceptions:

• Non-conventional CFs (CF signs change more than once),
• Mutually exclusive projects with substantially different timing of CFs or substantially different initial CFs.

Question 23

What is the payback period?

What is the ranking criteria?

Answer 23

The payback period is the number of years to recover initial costs,

The minimum acceptance criteria and ranking criteria is set by management. It is any point where the cumulative CFs become 0.

Question 24

What are the main problems of the payback rule?

What are its main disadvantages?

What are its main advantages?

Answer 24

• The choice of payback period is arbitrary, and may ignore any CFs beyond the length of the payback rule.
• It also does not discount the CFs.

Its disadvantages are: it ignores time value of money, ignores CFs after the payback period, is biased against long-term projects, requires an arbitrary cutoff point, projects accepted based on payback criteria may not have a positive NPV.

However, it is easy to understand, and biased toward liquidity.

Question 25

How does the discounted payback period work?

What is the acceptance criteria, what is a drawback related to NPV?

Answer 25

How long does the project take to “pay back” its initial investment, taking the time value of money into account.

We accept the project if it pays back on a discounted basis within the timeline, though by the time you have discounted the CFs you might as well calculate the NPV.

Question 26

What is the profitability index?

What is the minimum acceptance criteria and ranking criteria?

Answer 26

PI is given by: total PV of future CFs / initial investment.

The minimum acceptance criteria is to accept if the PI > 1,

The ranking criteria is to select the alternative with the highest PI.

Question 27

What does the profitability index have problems with?

What is it good for?

Answer 27

Mutually exclusive investments on account of scale problems,

Useful when available investment funds are limited, it’s easy to understand, and it is the correct decision when evaluating independent projects.

Question 28

What is the most popular method of analysing

investment projects?

Answer 28

The most popular is the IRR and the VPV, particularly for large corporations.

For small companies payback time becomes more important.