Finance Acumen for Non Finance

7/28/2019 Finance Acumen for Non Finance

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ZF Wind Power Coimbatore Limited


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Time Value of Money

Capital Investment Decisions


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Time Value of Money

What do we mean by it ?

For most people consumption todaymoredesirable than consumption tomorrow.

Moreover, money to be received in future isuncertain than money in hand now.

So people tend to attach a kind of premium(Interest) or value to money in hand now comparedto money that we are supposed to receive in futureand this brings us to the idea of Time Value ofMoney.

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Time Value of Money


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Compounding and Future value of Money

Future Value : The amount an investment is worth afterone or more periods ( after accruing interest)

One period case : if the interest rate is r per year, an

investment of Rs.1 will become (1+r) at the end of 1year

Multiperiod Case: Algebraically, we say that if r is theinterest rate per year, Rs.1 becomes (1 + r ) after 1 yr and(1+r) X(1+r) i.e (1+r)^2 after 2 yrs

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More generally , P Rupees @ r% pa after t yearswill become : P(1+r)^t

Time Value of Money


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FVIF(r,t) and PVIF(r,t)The factor ( 1+r)^t is called the Future Value Interest

Factor or FVIF(r,t).

The factor is called the discount factor or Present

value Interest Factor --- PVIF(r,t)

The process of finding the future value by multiplying asum with FVIF(r,t) is called COMPUNDING while, the

process of finding the present value of a future cash flow, bymultiplying the future cash flows with PVIF(r,t) is calledDISCOUNTING or Discounted Cash Flow (DCF) Valuation

tr)1(

1

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Time Value of Money


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Future value of Multiple Cash Flows

Future Value of Multiple cash Flows :Find the time period for which each cash flow remains invested

at the given rate of interest and find the FV of each.Add up the FVs to get the future value of the cash flow stream

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0 1 2 3 45

Rs.2000Rs.2000Rs.2000Rs.2000Rs.2000

Time (yrs)

x 1.14

x 1.13

x 1.12

x 1.11 Rs.2200

Rs.2420

Rs.2662

Rs.2928

Total value Rs.12,210

Time Value of Money


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Present values of Multiple Cash Flows

Present value of Future Cash Flows :Discount each of the future cash flows to the desired point

in time line, to get individual PVs.

Then add the PVs to get the PV of the cash flow stream.

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0 1 2 3 45

Rs.1000Rs.1000Rs.1000Rs.1000Rs.1000

Time (yrs)

x 1/ 1.064

x 1/1.063

x 1/ 1.062

x 1/1.061Rs.943

Rs.890

Rs.792

Total PV

Rs.839

x 1/ 1.065Rs.747

Rs.4212

Time Value of Money


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Level cash Flows ..PerpetuitiesA perpetuity is a constant stream of cash flows toinfinite time (a very large time for all practical

purposes)

common example -preferred stocks-- the holderis promised a fixed dividend payment from the

corporation for ever . In UK and Canada, there arebonds which are called consols which oncepurchased assures fixed interest payment from theGovt. for ever.

C2= C

0 1 2 3

C1= C C3= C

T

Time Value of Money


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Present Value of a perpetuity :The PV of the perpetuity is given by :

PV = C/r

where C is the constant cash flow to be received afterevery time interval and r is the rate of interestavailable for similar investment opportunities

What is FV of Perpetuity ?

Time Value of Money


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Level cash Flows AnnuityA series of similar cash flows that occur at the endof each period for a pre specified number of

periods is called an annuity. (Example: EMI paidagainst a house loan).

C2= C

0 1 2 3

C1= C C3= C

T

Time Value of Money


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Present and Future values --- Annuity

r

r)(1

1

-1 t

PVIFA(r,t)= and FVIFA(r,t)=

r

rt 1)1(

r

rCFV

r

rCPV

t

t

1)1(

)1(11

Time Value of Money


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Annuity Due

It is an annuity where the cash flow occurs at the beginningof each period ( contrary to the assumption that it occurs atthe end ).

Annuity due value = Ordinary Annuity value x (1+r)

Time Value of Money


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Capital Investment DecisionsWhat long term investments should the firm take on ?

Capital budgeting

Investments like :

Plant and equipment, new projects like CONDORA fleet of new Aircrafts for an airlines company

Issues Involved :

1. What are the time, quantum and risk of the cash

flowsvis-a vis- cost involved in the projects ?2. Is it Profitable for the company to go for the project?

3. Whether the investment decision is going to createvalue for the company ?

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Problems managers face when

they make investment decisions1. They have to search out for new opportunities or

projects in the marketplace

2. The expected cash flows from the project need tobe estimated.

3. The projects acceptability has to be decidedaccording to sound decision rules.

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What is a sound decision rule to

make investment decisions ?The best technique or decision rule should have thefollowing properties :

1. All cash flows should be considered2. The cash flows time value of money should be

considered at a suitable discount rate

3. The technique should be able to select one from a set

ofmutually exclusive projects

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Commonly used Investment Decision criteria

Following investment decision criteria are primarilyused for taking such decisions:

1. Net Present Value (NPV)2. The Payback Rule

3. The Discounted Payback

4. The Average Accounting Return (ACR)

5. The Internal Rate of Return (IRR)6. Modified Internal Rate of Return (MIRR)

7. The Profitability Index (PI)


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Net Present Value ( NPV)

Defined as the difference between the value( PV of theexpected cash flows ) of a project and its cost

How do we find NPV of a project or generally aninvestment?

STEP I:

The first step is to estimate the expected future cash flows.( notearnings or other accounting numbers it is the incremental or netcash flows that matter for capital budgeting decisions)

STEP II :

The second step is to estimate the required return for projects ofthis risk level, i.e the opportunity cost ofcapital.


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NPVcontd..Opportunity Cost of Capital : This is the discount rate that is

used to discount the expected cash flows from an investmentand to find the NPV.

It is the opportunity cost of taking the project, (Why?)..

This is the return the shareholders would have earned themselves by investing in financial assets, if

the project was not taken and the cash distributed as dividends to shareholders.

STEP III

The third step is to find the present value of the cash flows,by discounting them by the opportunity cost of capital, andsubtract the initial investment.

So NPV = PV of the expected cash flows from the project (discounted at Opportunity cost of capital) the PV of theinvestment made

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NPV Decision Rule

If the NPV is positive, accept the project

A positive NPV means that the project is expectedto add value to the firm and will therefore increasethe wealth of the owners.

Because the goal of the financial manager is toincrease owners wealth, NPV is a direct measureof how well this project will meet their goal.


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NPVDecision Rule contd..Suppose you are looking at a new project and you have

estimated the following cash flows:

1. Year 0: CF = -165,0002. Year 1: CF = 63,120;3. Year 2: CF = 70,800;4. Year 3: CF = 91,080;

Your required return for assets of this risk is 12%.

NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 165,000 =12,627.42

So Shall we consider this Project ?YES


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The Payback rule :

The amount of time required for an investment togenerate cash flows sufficient to recover its initialcost is called the payback period of theinvestment.

Example: A project requiring an initialinvestment of $500 is expected to generate thefollowing cash f lows over the next three years :Year 1 $100

Year 2 $200Year 3 $500

What will be the payback period for this project ?

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The payback rule contd..

Soln :

During the first 2 years cash generated = $300 andremaining amount of cash to be recovered for fullpayback = $200 which should happen sometimeduring year 2 and year 3. The exact time ( assuminguniform inflow of cash during the year 3= 200/500 =

0.4 years.

Thus payback period for this project = 2.4 years orroughly 2 years and 5 months.

The payback rule says :An investment is acceptable if its payback period is less

than some pre specified number of years.

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What are the problems with Payback rule?

To find out lets examine the following 3 projects, allhaving the same payback of 3 years i.e they shouldbe equally attractive as per payback rule.

Expected Cash Flows for Projects A through C

Year A B C

0 -100 -100 -100

1 20 50 50

2 30 30 303 50 20 20

4 60 60 60,000

Payback

Period

3 3 3

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Problems with payback rule.. Contd..

Problem-1Timing of cash flows within the payback periodnot considered:

If we compare projects A and B, at 15% discount rate, NPV

of A = 7.26 while that of B =13.62 so B is more attractivethan A although as per payback rule they are equallyattractive. Why does this happen ?

Because, payback method does not take into account anytime value of money.

Project B has larger cash inflows early in its life comparedto A. Payback method completely ignores this.

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Problem 2) Payments after the payback period ignored:

Compare B and C. NPV of B =13.62 while that of C = 34284.51, but theyappear equally attractive by payback method. Why does this happen?Because payback method completely ignores the cash flows after thepayback period.

Because of short term orientation of Payback method, some valuablelong term projects may be ignored.

Year B C

0 -100 -100

1 50 502 30 30

3 20 20

4 60 60,000

Payback Period 3 3 26


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Problem 3)Biggest problem is to select a proper cut off payback period. There isno objective basis or economic rationale for selection of the same.

So is the payback method not used at all in practice?

Often used by large, sophisticated companies when makingrelatively small decisions. The principal advantages of thepayback rule perceived by the practitioners are as follows :

It is easy to understand and interpret Adjust for uncertainty of later cash flows

Biased towards Liquidity This could be important forsmall businesses although less significant for largebusinesses

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The Discounted Payback Period Rule

How long does it take the project to pay back itsinitial investment taking the time value of money intoaccount?

Compute the present value of each cash flow and then

determine how long it takes to pay back on a discountedbasis.

Compare to a specified required period

Decision Rule - Accept the project if it paysback on a discounted basis within thespecified time

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Discounted payback period rule example

Assume a project that needs Rs. 165,000 as initial investmentand is expected to generate Rs. 63120, Rs. 70800, and Rs.91080 in years 1 , 2 and 3. We will accept the project if it paysback on a discounted basis in 2 years. Use 12% as theappropriate discount rate.

Do we accept or reject the project?Compute the PV for each cash flow and determine the paybackperiod using discounted cash flows

1. Year 1: 165,000 63,120/1.121 = 108,643

2. Year 2: 108,643 70,800/1.122

= 52,2023. Year 3: 52,202 91,080/1.123 = -12,627 project pays back inyear 3

So we do not accept.But NPV = + 12,627 still we reject.

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Discounted Payback Period. Contd..

1. But if a project pays back on a discounted basis ever,with some cash flows still remaining, it is bound tohave a positive NPV( assuming that all the cash flowsfrom the project are positive)

2. This is because by definition, the NPV is zero when thesum of the discounted cash flows equals the initialinvestment. So if a project pays back on a discountedbasis, then some cash flows may still remain whichmust add up to give a positive NPV.

3. This implies that if we use a discounted payback, wewont be accidentally taking up any projects with anegative NPV. But we may reject some with positiveNPV like the one we just discussed.

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Advantages and Disadvantages of Discounted Payback :

Advantages Includes time value of money Easy to understand Does not accept negative NPV investments when all future

cash flows are positive

Biased towards liquidity

Disadvantages May reject positive NPV investments Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff point Biased against long-term projects, such as R&D and new

products

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The Internal Rate of Return (IRR) Rule

IRR: the discount rate that sets NPV to zero

Minimum Acceptance Criteria:

Accept if the IRR exceeds the requiredreturn.

Ranking Criteria:

Select alternative with the highest IRR

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The Internal Rate of Return: Example

Consider the following project:

0 1 2 3

$50 $100 $150

-$200

The internal rate of return for this project is 19.44%

How ?

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)1(

150$

)1(

100$

)1(

50$2000

IRRIRRIRR

NPV

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The NPV Payoff Profile for the previous problem

Discount Rate NPV

0% $100.00

4% $71.04

8% $47.3212% $27.79

16% $11.65

20% ($1.74)

24% ($12.88)

28% ($22.17)

32% ($29.93)36% ($36.43)

40% ($41.86)

If we graph NPV versus discount rate, we can see the IRR as thex-axis intercept the discount rate that makes the NPV=0

IRR = 19.44%

($60.00)

($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00$80.00

$100.00

$120.00

-1% 9% 19% 29% 39%

Discount rate

NPV

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Internal rate of return contd

Example:A project has a total up front cost of Rs.435.44.The cashflows are Rs.100 in the first year,Rs.200 in the secondyear and Rs.300 in the third year. Whats the IRR of theproject? If we require an 18% return should we take this

investment?

Soln : The IRR can be given by the following equation,NPV=0= -435.44 + 100/(1+IRR) + 200/(1+IRR)2 + 300/(1+IRR)3

A little trial and error shows that the IRR comes out to be15%.( CHECK NPV =0 for discount rate = 15%)

So shall we Accept the project ?

NO 35


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Internal rate of return contd

Problems with IRR rule :The IRR Investment Rule will give the same answer as the NPV rulein many, but not all, situations.

Problem 1 ) Non Conventional Cash Flows :

In general, the IRR rule works for a stand-alone project if all of

the projects negative cash flows precede its positive cashflows.In other cases, the IRR rule may disagree with the NPV rule andthus be incorrect.Situations where the IRR rule and NPV rule may bein conflict are as follows :

Delayed Investments

Nonexistent IRR

Multiple IRRs

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Problems with IRR.contd..Multiple IRRs

Assume you have just retired as the CEO of a successfulcompany. A major publisher has offered you a book deal. Thepublisher will pay you $1 million upfront if you agree to write abook about your experiences. You estimate that it will take 3

years to write the book. The time you spend writing will cause

you to give up speaking engagements amounting to $500,000per year. ( This is effectively an outflow to you). TakeOpportunity cost as 10%.

Now assume the lecture deal fell through. You inform thepublisher that it needs to increase its offer before you will

accept it. The publisher then agrees to make royalty paymentsof$20,000 per year forever, starting once the book is publishedin 3 years.

Should you accept or reject the new offer?

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Problems with IRR.contd..Multiple IRRs contd..

The cash flows would now look like:

The NPV is calculated as:

2 3 4 5

3 3

500,000 500,000 20,000 20,000 20,0001,000,000

1 (1 ) (1 ) (1 ) (1 )

500,000 1 1 20,0001,000,000 1(1 ) (1 )

NPVr r r r r

r r r r

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By setting the NPV equal to zero and solving for r, we find the

IRR. In this case, there are two IRRs: 4.723 % and 19.619 % .


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Problems with IRR.contd..

If the opportunity cost of capital is either below 4.723 % or above 19.619

%, you should accept the deal.Between4.723 % and19.619 %, the bookdeal has a negative NPV. Since your opportunity cost of capital is 10 % ,

you should reject the deal. 39


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Multiple IRRs contdDescartes rule of signs :

The number of IRRs will be the same as the number ofchanges of signs in cash flows i.e from negative topositive or positive to negative( or less than it by amultiple of 2).

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Problem 2) Mutually Exclusive Projects:Mutually exclusive projects If you choose one, youcant choose the other

Decision rules:1. NPV Choose the project with the higher NPV

2. IRR Choose the project with the higher IRR butis that always correct ?

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Example:

The required return for both projects is 10%.

Which project should you accept and why?

Period Project A Project B

0 -500 -400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV 64.05 60.74

The required return

for both projects is10%.

Which project shouldyou accept and why?

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($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

$140.00

$160.00

0 0.05 0.1 0.15 0.2 0.25 0.3

Discount Rate

NPV A

B

NPV Profiles

IRR for A = 19.43%

IRR for B = 22.17%

Crossover Point = 11.8%

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A has a higher total cash flow, but it pays back at aslower rate than B. So its NPV is higher at lowdiscount rates but as the discount rates increase,

the effect of the distant cash flows is reduced to agreat extent and the NPV of B starts exceeding itsNPV.

Moral of the example is when we have mutuallyexclusive projects we should not rank them basedon their IRRs. Instead we need to look at relativeNPVs and the required rate of return.44


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Advantages and Disadvantages of IRR:

Advantages Closely Related to NPV, Often Leading to

Identical decisions Easy to understand and communicate

Disadvantages

May result in multiple answers Not Deal with non conventional cash flows

May Lead to incorrect decisions in comparisonto mutually exclusive investments

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Modified Internal rate of Return ( MIRR)

To address some of the problems with conventional

IRR ( like multiple IRRs) sometimes a modified IRRis used.

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0 1 2

-$ 60 +$ 155 - $ 100

IRR = 25% and

IRR = 33.33%


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Modified Internal rate of Return ( MIRR)Approach 1 : The discounting approach :1. Discount all negative cash flows at the required rate of

return and add them to the initial cost. ..2. Calculate the IRR.3. The discount rate used might be the required return.

In this example , if the projects required rate of return is20%, then the modified cash flows look as follows :

Time 0 : -$60 + (-$100/1.22)=-$129.44

Time 1 : +$155Time 2 : +$0If you calculate the IRR now, you should get IRR =

19.71%

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MIRR contd..Approach 2 : The Reinvestment approach :1. Compound all cash flows (positive and negative) except the

first one, to the end of the projects life at the required rate ofreturn.

2. Calculate the IRR.

In this example , if the projects required rate of return is 20%,then the modified cash flows look as follows :

Time 0 : -$60 Time 1 : 0 Time 2 : +$155*1.2 -$100= $86 If you calculate the IRR now, you should get IRR = 19.72%

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MIRR contd..Approach 3.. Combination1. Discount all the negative cash flows back to the

present2. Compound all the positive cash flows to the end.

3. Calculate IRR

For our example modified cash flows become :

At time 0 : -$60+(-$100/1.22)=-$129.44 Time 1 : +$0 Time 2 : $155x 1.2 = $186 Calculate the MIRR = 19.87%

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MIRR problems MIRRs are controversial. Detractors sayitsMeaningless IRR Many analysts claim that MIRRs are superior to IRRs,. For example by design

they clearly do not suffer from the multiple rate of return problem.

One problem with MIRRs is however there are different ways to calculate itand we get different results with each and there is no clear reason which oneis better.

Because MIRR depends on an externally supplied discount rate, the answer

that one gets is not trulyinternal

which by definition should depend onlyon the projects cash flows and nothing else.

If we have the discounting rate, why not calculate the NPV and be done withit ?

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Average Accounting Return Rule

The average accounting return is interpreted as anaverage measure of the accounting performance of aproject over time, computed as some average profitmeasure attributable to the project divided by someaverage balance sheet value for the project.Expression : Average net income / average book valueNeed to have a target cutoff rate of return. ( which is aproblem)

Decision Rule: Accept the project if the AAR is greaterthan a preset rate.51


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Example AAR

You are looking at a three year project with aprojected net income of $2000 in year 1, $4000 inyear 2, and $6000 in year 3. The cost is $12000and that will be depreciated over the three year life

of the project. What is the AAR for the project?Solution : Average net income for the project is =(2000

+4000 +6000)/3 =4000

Average book value of the project = (12000 +8000+4000 +0)/4 = 6000 ( or =12000/2 =6000)

AAR = 4000/6000 = 66.67%

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Advantages and Disadvantages of AAR

Advantages Easy to calculate and understand

Disadvantages Not a true rate of return; time value of money is

ignored completely. Uses an arbitrary benchmark cutoff rate

Based on accounting net income and book values,not real cash flows and market values53


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The Profitability Index (PI) Rule

Example : if a project costs Rs. 200 crores and the presentvalue of the future cash flows discounted at a suitableopportunity cost is Rs. 220 crores then, the PI is 220/200 =1.1.

If a project has a PI > 1 it implies that the PV of the futurecash flows > the initial cost i.e the project has a positiveNPV.

Thus , Minimum Acceptance Criteria: Accept if PI > 1

InvestentInitial

FlowsCashFutureofPVTotal

PI

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The Profitability Index (PI) Rule contd..

Advantages Closely related to NPV, generally leading to identical

decisions

Easy to understand and communicate

Disadvantages May lead to incorrect decisions in comparisons of

mutually exclusive investments of different scale.

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Thank You

Finance Acumen for Non Finance

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