13.2: Evaluating Investment Alternatives

Question 1

Which capital budgeting techniques are frequently used by Canadian CFOs according to the 2011 survey?

Answer 1

The frequently used techniques include

net present value (NPV) analysis,
internal rate of return (IRR),
payback period,
discounted payback period,
profitability index,
and modified internal rate of return.

Question 2

What is the payback period in capital budgeting?

Answer 2

The payback period is the number of years required to fully recover the initial cash outlay associated with a capital expenditure.

Question 3

How is the payback period calculated?

Answer 3

The payback period is calculated by adding up the cash flows from an investment until the initial investment is recovered.

The formula is:

Paybackperiod = 𝑇

where

T is the time when the cumulative cash flows equal the initial investment

CF _0

Question 4

What is the main advantage of using the payback period?

Answer 4

The payback period provides a simple measure of how quickly an investment’s initial outlay can be recovered, which can help assess the riskiness of a project.

Question 5

What are some drawbacks of using the payback period?

Answer 5

Drawbacks include

ignoring the time value of money, disregarding cash flows received after the payback period,
and the arbitrary choice of the cutoff date.

Question 6

What is the discounted payback period?

Answer 6

The discounted payback period is the number of years required to fully recover the initial cash outlay associated with a capital expenditure in terms of discounted cash flows.

Question 7

How is the discounted payback period calculated?

Answer 7

The discounted payback period is calculated by discounting the cash flows and then determining the time it takes for the discounted cash flows to recover the initial investment.

The formula is:
∑ (t=1)(T): (CF_t)/(1+k) ^t = CF_0

where

k is the discount rate and

CF_t is the cash flow at time t.

Question 8

How does the discounted payback period address the shortcomings of the simple payback period?

Answer 8

The discounted payback period accounts for the time value of money, providing a more accurate measure of the investment’s risk and return.

Question 9

What is net present value (NPV) analysis in capital budgeting?

Answer 9

NPV analysis is the sum of the present value of all future after-tax incremental cash flows generated by an initial cash outlay, minus the present value of the investment outlays.

It represents the present value of expected cash flows net of costs needed to generate them.

Question 10

How is NPV calculated?

Answer 10

NPV is calculated using the formula:
𝑁𝑃𝑉=∑(𝑡=1)(𝑛):((𝐶𝐹_𝑡)/(1+𝑘)^𝑡) −𝐶𝐹_0

CF _t is the cash flow at time t,

k is the discount rate,

and CF_0 is the initial cash outlay.

Question 11

What does “incremental” mean in the context of NPV?

Answer 11

Incremental refers to the change in revenues or costs resulting from the investment decision, ignoring cash flows that do not change as a result of the decision (sunk costs).

Question 12

What is a risk-adjusted discount rate (RADR)?

Answer 12

RADR is a discount rate set based on the overall riskiness of a project, used to discount future cash flows in NPV calculations.

Question 13

Why should projects with positive NPV be accepted?

Answer 13

Projects with positive NPV add value to the firm by generating returns that exceed the cost of capital, thus increasing shareholder wealth.

Question 14

What is the result of NPV for the given example using a Texas Instruments BA II Plus financial calculator?

Answer 14

The NPV is 1,388.67, indicating that the project should be accepted as it adds value to the firm.

Question 15

How do you use a Texas Instruments BA II Plus financial calculator to compute NPV?

Answer 15

Press CF to enter the cash flow register.

Enter -12000 for CF0 and press ENTER.

Use the down arrow ↓ to move to CF1, enter 5000, and press ENTER.

Use the down arrow ↓ to move to CF2, enter 5000, and press ENTER.

Use the down arrow ↓ to move to CF3, enter 8000, and press ENTER.

Press NPV.

Enter 15 for the interest rate and press ENTER.

Press CPT to compute the NPV, which should display 1388.67.

Question 16

How do you use a Texas Instruments BA II Plus financial calculator to compute NPV for an annuity?

Answer 16

Press CF to enter the cash flow register.

Enter -30000 for CF0 and press ENTER.

Use the down arrow ↓ to move to CF1, enter 5000, and press ENTER.

Use the down arrow ↓ to move to F1, enter 9, and press ENTER (since $5,000 occurs 9 times).

Use the down arrow ↓ to move to CF10, enter 6000, and press ENTER.

Press NPV.

Enter 12 for the interest rate and press ENTER.

Press CPT to compute the NPV, which should display -1426.91.

Question 17

What is the internal rate of return (IRR) in capital budgeting?

Answer 17

The internal rate of return (IRR) is the discount rate that makes the present value of future cash flows equal to the initial cash outlay.

It is the rate of return that sets the NPV to zero for a given set of cash flows.

Question 18

How is the IRR calculated?

Answer 18

The IRR is calculated by solving the following equation:

∑ (t=1)(n):(CF_t) / (1+IRR)^t = CF_0

This requires a trial-and-error process or the use of financial calculators or computer spreadsheets to find the discount rate that sets the NPV to zero.

Question 19

What is the general rule for accepting a project based on IRR?

Answer 19

A project should be accepted if the IRR is greater than the appropriate risk-adjusted discount rate (k), which is usually the firm’s cost of capital.

Question 20

How do you use a Texas Instruments BA II Plus financial calculator to compute IRR?

Answer 20

Press CF to enter the cash flow register.

Enter -12000 for CF0 and press ENTER.

Use the down arrow ↓ to move to CF1, enter 5000, and press ENTER.

Use the down arrow ↓ to move to CF2, enter 5000, and press ENTER.

Use the down arrow ↓ to move to CF3, enter 8000, and press ENTER.

Press IRR.

Press CPT to compute the IRR, which should display 21.31.

Question 21

Provide an example of calculating IRR for an annuity.

Answer 21

For an investment of $30,000 with cash flows of $5,000 per year for 9 years and $6,000 in year 10:

Using the financial calculator:
Press CF to enter the cash flow register.

Enter -30000 for CF0 and press ENTER.

Use the down arrow ↓ to move to CF1, enter 5000, and press ENTER.

Use the down arrow ↓ to move to F1, enter 9, and press ENTER (since $5,000 occurs 9 times).

Use the down arrow ↓ to move to CF10, enter 6000, and press ENTER.

Press IRR.

Press CPT to compute the IRR, which should display 10.84.

Question 22

What does the NPV profile diagram illustrate?

Answer 22

The NPV profile diagram graphs the NPV against the discount rate and shows how the NPV depends critically on the appropriate discount rate.

It illustrates the point where the NPV curve crosses the x-axis, which corresponds to the IRR.

Question 23

What is the crossover rate in the context of NPV and IRR?

Answer 23

The crossover rate is the special discount rate at which the net present value profiles of two projects are equal.

Question 24

How do NPV and IRR rank projects differently?

Answer 24

NPV and IRR can rank projects differently because NPV depends on the discount rate used.

For instance, project A might have higher NPV at low discount rates, while project B might have higher NPV at high discount rates.

Question 25

What does the NPV profile indicate about project acceptance?

Answer 25

According to the NPV profile, a project should be accepted if the NPV is positive for the given discount rate.

Conversely, it should be rejected if the NPV is negative.

Question 26

What are mutually exclusive projects?

Answer 26

Mutually exclusive projects are situations where the acceptance of one project precludes the acceptance of one or more alternative projects.

Question 27

What is the key difference between NPV and IRR in project evaluation?

Answer 27

NPV assumes all cash flows are reinvested at the discount rate, whereas IRR assumes all cash flows are reinvested at the IRR.

Question 28

How is the decision made if using either NPV or IRR?

Answer 28

The decision to accept or reject a project should be the same using either NPV or IRR if the discount rate is appropriately considered.

For instance, accept a project if k is less than the IRR and reject it if k is greater than the IRR.

Question 29

What are the issues with IRR mentioned in Table 13.1?

Answer 29

Issues with IRR include multiple IRRs when future cash flows change sign, ranking projects differently than NPV, and the assumption that cash flows are reinvested at the IRR, which can be unrealistic.

Question 30

What are the key points from the “Finance in the News” section regarding art investment?

Answer 30

Key points include the high value of art investments driven by status and low interest rates, art market resilience despite economic tensions, and the importance of art as a status symbol.

Question 31

What is the profitability index (PI) in capital budgeting?

Answer 31

The profitability index (PI) is another discounted cash flow (DCF) approach used to evaluate capital expenditure decisions.

It is defined as the ratio of a project’s discounted net incremental after-tax cash inflows divided by the discounted cash outflows, which are usually the initial after-tax cash outlays.

Question 32

How is the PI calculated?

Answer 32

PI is calculated using the formula:

PI= PV(cashoutflows) / PV(cashinflows)

Question 33

What does a PI greater than one indicate?

Answer 33

A PI greater than one indicates that the project should be accepted because it has positive NPV, meaning the project’s returns exceed the cost of investment.

Question 34

Provide an example of calculating PI for an annuity.

Answer 34

For an investment of $30,000 with cash flows of $5,000 per year for 9 years and $6,000 in year 10, at a 12% discount rate:

PI= 28,573.09 / 30,000
28,573.09 = 0.952

The project should be rejected because its PI is less than 1.

Question 35

How do you use a Texas Instruments BA II Plus financial calculator to compute PI?

Answer 35

Press CF to enter the cash flow register.

Enter -30000 for CF0 and press ENTER.

Use the down arrow ↓ to move to CF1, enter 5000, and press ENTER.

Use the down arrow ↓ to move to F1, enter 9, and press ENTER (since $5,000 occurs 9 times).

Use the down arrow ↓ to move to CF10, enter 6000, and press ENTER.

Press NPV.

Enter 12 for the interest rate and press ENTER.

Press CPT to compute the NPV, which should display 28573.09.

Calculate PI as
28573.09 / 30000
which gives 0.952.

Question 36

Why is the PI considered a relative measure?

Answer 36

The PI is considered a relative measure because it expresses the value of returns in relation to the cost of the investment, unlike NPV which provides an absolute measure of wealth.

Question 37

What are some weaknesses of the PI method?

Answer 37

Weaknesses of the PI method include its relative nature, which may not always align with the goal of maximizing total NPV for the firm, and it can lead to incorrect decisions when projects are mutually exclusive or when there is capital rationing.

Question 38

Why is the PI useful despite its weaknesses?

Answer 38

The PI is useful because it is simple to understand and apply, especially when firms face capital rationing or need to rank projects based on the efficiency of resource use.