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What are the advantages of NPV

▪ Takes into account the time value of money
▪ Absolute measure of return
▪ Based on cash, rather than accounting profits

▪ Considers the whole life of the project which Payback Period doesn't

▪ It considers the required return from investors i.e. cost of capital

▪ Therefore, ultimately NPV represents the increase in shareholders wealth that would arise if a new investment is undertaken by the amount of NPV

Therefore should lead to the maximization of shareholder's wealth

Higher discount rates can be used for riskier project


What are the disadvantages of NPV

▪ Difficult to understand and explain to managers

▪ Cost of capital should be known. However is difficult to determine accurately. Whole thing is based on discount rate

▪ Difficult to forecast future cash flows accurately especially more important for NPV but also true of other techiniques


What are the terms used for the cost of capital?

Rate of return
Rate of interest
Discount rate
Required return


What are the assumptions used in a discounting?

• The date of the initial investment is time 0

• Cash flows are assumed to arise at the end of accounting periods unless told otherwise e.g. sales during the first year are assumed to arise at time 1.

In other words we assume that T1 is at the end of the first year. This is as we do not discount daily

• Never include interest payments as cash flows within a NPV calculation as these are taken account of by the cost of capital. Cost of capital reflects the cost of financing the project. The cost of financing includes the cost of debt and equity financing. The interest payments are a distribution to the providers of debt capital. To include interest payments and discount would be double counting.


What is perpetuity and the formula and when does it assume the CF begins

P is an equal CF starting at T1 and continuing to infinity. PC of the CF can be found quickly by the following formula:

PV= Annual CF x Perpetuity factor

Perpetuity factor: (1÷r)


How do you calculate advanced annuity and Perpetuity where the cash flow starts at T0 instead of T1

add 1 to the annuity factor


What is IRR and what does it represent

The IRR is another project appraisal method using DCF techniques.

The IRR represents the discount rate at which the NPV of an investment is zero. As such, it represents a breakeven cost of capital.


What is the formula for IRR



What is the formula for IRR of perpetuity

i.e. only if it is a perpetuity

IRR= [Annual net inflow ÷ Initial Investment] x 100%


What are the advantages of IRR

▪ Reflects the time value of money
▪ Based upon cash and not profit
▪ % Answer – makes it easier to understand and compare for someone who is not in finance
▪ Does not need the cost of capital to be known
▪ Considers the whole life of the project

IRR is based on discounted cash flow principles. It therefore considers all of the cash flows in a project


What are the disadvantages of IRR

▪ Difficult to calculate

▪ Interpolation only provides an estimate

▪ There can be more than one IRR or no IRR’s for a project. This may happen if a project involves unusual/unconventional cash flows e.g. an outflow then a series of inflows then a further outflow

▪ When comparing mutually exclusive projects the project with the highest IRR may not have the highest NPV at the company’s cost of capital. There is therefore a conflict between NPV and IRR in terms of which project is best. (in this case you would choose the Highest NPV)

▪ Can be confused with ARR/ROCE by management


What is an annuity

annuity is an equal cash flow where the first cash flow is at T1 and the cashflows continue for a certain number of years


Why is NPV better than IRR when choosing between two mutually exclusive projects

NPV as it tells us the absolute increase in shareholder wealth so it is the better technique for this purpsose


How do you know how many IRRs there are going to be for a project?

It is possible for a project to have up to as many IRRs as there are sign changes in the cash flows.


What is the relationship between payback period and internal rate of return when there is inflation?

Payback period decreases and IRR increases

The payback period will decrease and the IRR will increase because at T0 the outflow is unaffected by inflation


Net investment - $732k
Equal inflow of $146.4k to perpetuity

If the first inflow from the investment is a year after the initial investment, what is the IRR of the project?

IRR is at the interest rate at which NPV = 0
IRR is where ($146.4k/R)= $732k
therefore IRR = 20%


Is it possible to have a negative REAL discount rate to apply to the cash flow estimates made in current terms when making investment decision?

Yes, the reason is that it will happen if the rate of inflation exceeds the money cost of capital.

Negative interest rates have happened in the past. The European central bank recently introduced negative rates which have been seen in sweden, switzerland.

Negative inflation (Deflation) is likely to increase the change of having a positive real discount rate (unless your money cost of capital is even more negative.


What are the reasons why NPV is superior to IRR- list them

Due to 4 reasons

1) NPV and shareholder wealth
2) absolute measure
3) Non conventional cash flows
4) Mutually exclusive projects
5)changes in cost of capital


why is NPV superior to IIR due to NPV and shareholder wealth

the NPV of a proposed project, if calculated at an appropriate cost of capital, is equal to the increase in shareholder wealth which the project offers.

In this way NPV is directly linked to the assumed financial objective of the company, the maximisation of shareholder wealth.

IRR calculates the rate of return on projects, and although this can show the attractiveness of the project to shareholders, it does not measure the absolute increase in wealth which the project offer


why is NPV superior to IIR due to absolute measure

NPV looks at absolute increases in wealth and thus can be used to compare projects of different sizes.

IRR looks at relative rates of return and in doing so ignores the relative size of the compared investment project


why is NPV superior to IIR due to non conventional cash flows

In situations involving multiple reversals in project cash flows, it is possible that the IRR method may produce multiple IRRs (that is, there can be more than one interest rate which would produce an NPV of zero).

If decision-makers are aware of the existence of multiple IRRs, it is still possible for them to make the correct decision using IRR, but if unaware they could make the wrong decision.


why is NPV superior to IIR due to mutually exclusive cash flows

In situations of mutually-exclusive projects, it is possible that the IRR method will (incorrectly) rank projects in a different order to the NPV method. This is due to the inbuilt reinvestment assumption of the IRR method.

The IRR method assumes that any net cash inflows generated during the life of the project will be reinvested at the project’s IRR.

NPV on the other hand assumes a reinvestment rate equal to the cost of capital. Generally NPV’s assumed reinvestment rate is more realistic and hence it ranks projects correctly


why is NPV superior to IIR due to changes in cost of capital

NPV can be used in situations where the cost of capital changes from year to year.

Although IRR can be calculated in these circumstances, it can be difficult to make accept or reject decisions as it is difficult to know which cost of capital to compare it with.


why is money received today worth more than money receivved on fture

Potential for earning interest from reinvestment

Inflation- wipes out the value of the money

Impact of risk


What is delayed annuity and delayed perpetuities

A delayed annuity or perpetuity is where the first cash flow starts at a late date than time 1. The first cash flow might, for example, start at time 5. The cash flows will then either continue for a certain number of years or they will continue to infinity.

The approach used to find the present value of a delayed annuity or perpetuity is to:

a) Apply the annuity or perpetuity factor as normal to the cash flows and then

b) Multiply the answer by the single discount factor for the year before the first of the cash flows