Week 2

Question 1

How is net present value calculated? What will we typically need to estimate?

Answer 1

Net present value is the sum of the discounted future values - any initial costs. To estimate it we need to estimate the future cash flows, both how much and when, estimate the discount rate, and estimate the initial costs.

Question 2

What is the minimum acceptance criteria for a project using Net Present value? How do we rank them?

Answer 2

The minimum acceptance criteria for an investment is to accept if the net present value is greater than 0, if there are multiple projects to choose from we should choose the one with the highest net present value.

Question 3

What are the components needed to calculate Net present value in excel?

Answer 3

The first component of the excel NPV function is the required return(in decimal form), the second is the array of cash flows beginner with year 1 (not year 0, the investment). We then subtract the initial costs.

Question 4

How will our minimum return relate to net present value?

Answer 4

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

Question 5

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

Answer 5

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

Question 6

Does the term structure of the discount rate have to be flat? What else could it be?

Answer 6

The term structure of the discount rate does not necessarily have to be flat, instead we can use the yield to maturity of different risk free maturity investments for the different cash flows. Or we could use the short rate of each year leading up to the cash flow’s year, this would mean discounting a fourth year cash flow effectively four times, each one with a different interest rate.

Question 7

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

Answer 7

If the events are uncertain, but we know their probability, we can use the expected value (sum of probability * probability’s associated value) for our cash flow.

Question 8

What is the internal rate of return?

Answer 8

The internal rate of return (IRR) is the discount rate that sets net present value to 0.

Question 9

What is our acceptance criteria for projects using IRR? What is the ranking criteria?

Answer 9

We will only accept a project if the internal rate of return exceeds the required return. When ranking different projects we will prefer projects with a higher internal rate of return.

Question 10

What is the reinvestment assumption for IRR? Why is it wrong?

Answer 10

One reinvestment assumption for IRR is that all future cash flows can be reinvested at the internal rate of return, though this assumption is wrong, as these modified cash flows produced by reinvestment cannot be associated with the project, as such we do not need to consider this assumption when considering a project.

Question 11

What are the main disadvantages and advantages of the internal rate of return?

Answer 11

The primary disadvantages are that it does not distinguish between investing and borrowing, the IRR may not exist, there could be multiple IRRs, it has problems with mutually exclusive investments (scale disparity).

However, one advantage is that it is easy to understand and communicate.

Question 12

How do we use the IRR function in excel?

Answer 12

To use the IRR function in excel we first enter our array of cash flows, beginning with the initial cash flow(investment, this should be negative), we can enter a guess (not required), we will normally need to increase the number of decimals shown.

Question 13

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

Answer 13

If we graph Net Present value versus the discount rate, the internal rate of return is the x-axis intercept.

Question 14

What are some of the main problems with the internal rate of return?

Answer 14

1. Relative to NPV, IRR is difficult to calculate, and cannot be solved by hand easily.
2. A higher IRR is better for investment projects, while a lower IRR is better for financing projects.
3. The IRR doesn’t always exist (when there is a sign change more than once).
4. When there are multiple changes in cash flow signs, the IRR is not uniquely defined (Multiple IRRs)
5. The IRR implicitly 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 significantly different initial outlays (size disparity/scale problem).
7. Timing problems with mutually exclusive projects.

Question 15

What is the difference between an investment project and financing project in terms of cash flows? What will be the relationship between the net present value and the discount rate in both? When will the IRR be the same for a financing and investment project?

Answer 15

In an investment project we have an initial cash outflow followed by cash inflows, this will have a downward sloping relationship between net present value and the discount rate.
In a financing project we receive a cash inflow at the start and then have to pay cash outflows in the following periods, in this there will be an upward sloping relationship between net present value and the discount rate.
The internal rate of return will be the same for an investment project and financing project if we flip the signs on each cash flow.

Question 16

How is the no or multiple internal rates of return problem typically solved?

Answer 16

The multiple internal rate of return problem is often solved using the modified internal rate of return (MIRR), though it is not actually the internal rate of return of the project.

Question 17

How do we calculate the MIRR using the discounting approach?

Answer 17

To calculate the modified internal rate of return using the discounting approach we discount all negative cash flows back to time zero and add them to the initial cash flow, then calculate the MIRR as we would the IRR.

Question 18

How do we calculate the MIRR using the reinvestment approach

Answer 18

To calculate the modified internal rate of return using the reinvestment approach we compound all cash flows except for the time zero cash flow to the end of the project’s life and sum them. Then the initial cash flow divided by the terminal value = (1+MIRR)^maximum period.

Question 19

How do we calculate the MIRR using the combination approach?

Answer 19

To calculate the modified internal rate of return using the combination approach we discount all costs back to the initial period, then get the future value of the cash inflows.
Present value costs = terminal/future value of cash inflows divided by (1+MIRR)^maximum period.

Question 20

Can we use different rates for the future value and present value in calculating the MIRR?

Answer 20

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

Question 21

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

Answer 21

If projects are independent they must exceed a minimum acceptance criteria, if projects are mutually exclusive, we rank all alternatives and select the best one.

Question 22

Why can the Internal rate of return be misleading when choosing between mutually exclusive projects?

Answer 22

The internal rate of return can be misleading because of the scale/size disparity problem. This occurs because the project may have a high internal rate of return but a small scale, meaning we may turn down a project with a higher net present value.
As such, we should sometimes takes an investment with a lower internal rate of return if the net present value is higher and the investments are mutually exclusive.

Question 23

What is the timing problem with regards to the IRR?

Answer 23

The timing problem is an internal rate of return problem associated with mutually exclusive projects, it occurs when the timing of cash flows is substantially different.
The crossover rate is the discount rate at which the net present value of one project is the same as the other project, after this rate the better project changes.

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

Question 24

How do we solve the IRR timing problem?

Answer 24

To solve the IRR timing problem we comput the IRR for either project A-B or B-A. The internal rate of return for these projects is the same, and will be the crossover rate. If the required rate is less than this rate we choose the project with the later cash flows, if the required rate is more than this rate we choose the project with the earlier cash flows.

Question 25

When do Net present value and the internal rate of return not lead to the same decision?

Answer 25

Net present vlaue and the internal rate of return will generally give the same decision, though there are exceptions: Non-conventional cash flows (cash flow signs change more than once), mutually exclusive projects with substantially different timing of cash flows or substantially different initial cash flows.

Question 26

What is the payback period? What is the ranking criteria?

Answer 26

The payback period is the number of years to recover initial costs, the minimum acceptance criteria (typically this is more of a maximum acceptance criteria) and ranking criteria is set by management. It is any point where the cumulative cash flows become 0.

Question 27

What are the main problems of the payback rule? What are its main disadvantages? What are its main advantages?

Answer 27

The two main problems of the payback rule are: The choice of payback period is arbitrary, and may ignore any cash flows beyond the length of the payback rule. It also typically does not discount the cash flows.
Its disadvantages are: it ignores time value of money, ignores cash flows 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 28

How does the discounted payback period work? What is the acceptance criteria, what is a drawback related to NPV?

Answer 28

The discounted payback period asks 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 cash flows you might as well calculate the NPV.

Question 29

What is the profitability index? What is the minimum acceptance criteria and ranking criteria?

Answer 29

The profitability index(PI) is given by: total present value of future cash flows / initial investment. The minimum acceptance criteria is to accept if the profitability index is greater than one, the ranking criteria is to select the alternative with the highest profitability index.

Question 30

What does the profitability index have problems with? What is it good for?

Answer 30

The profitability index has problems with mutually exclusive investments on account of scale problems, but may be useful when available investment funds are limited, it is easy to understand and communicate, and is the correct decision when evaluating independent projects.

Question 31

What is the most popular method of analysing investment projects?

Answer 31

Firms tend to use multiple methods when evaluating capital investment projects, with the most popular being the internal rate of return and the net present value, particularly for large corporations. For small companies payback time becomes more important.