3.8+Investment+Appraisal

3.8 INVESTMENT APPRAISALS
a starter exercise. //if you are not a football fan, then think Person X in Industry Y, the principles are the same// //Not// //so easy is it? - but give it a try ..// //..// //..//

//Did your answer look something like that outlines on the ppt below (you may have to adjust 'size' to get it to fit into one screen)//

//NOTE :// This starter activity is done retrospectively ie AFTER both players have come and gone. It is about deciding which one __**was**__ a better investment - in the past tense.

For the rest of this unit we look at Investment Appraisal in the future tense. Trying to work out which __**will be**__ the better investment, //before// we make a decision.

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This is done to help with decision-making, in the field of investment.
 * Should I invest or simply save?
 * Should I invest in option A or B?

INVESTMENTS should, by their nature, generate return. A new machine produces more, faster. Moving to a new location produces more sales, Hiring a better employee creates grater efficiency etc etc In this context 'return' has been created whether an investment actively produces greater sales, or instead cuts down on costs. Either way profit should be up!

There are 3 ways to quantifiably appraise an investment.

I invest $10,000 in a project, that project earns me a net $10,000 in 6 years and 2 months, then 6 years and 2 months is my PAY BACK PERIOD! // The Payback formula/s are __ NOT __ given to you on the IB formula sheet. //
 * __**Pay Back**__ - is measured in TIME : //how quickly will i get paid back? 2 years 4 months, 6 years 9 months ? etc etc//

In this context 'return' means pretty much the same as it did in R.O.C.E. (Return on Capital Employed). I have invested $10,000 in a project, that projects earns me a net $5,000 each year then my ARR is 50%. // The ARR formula is given to you on the IB formula sheet. //
 * __**Average Rate of Return**__ - is measured as a PERCENTAGE : //what portion of my investment will i get back each year, on average?//

If i add all the net values that my investment will earn me each year of its life ($X) then subtract the cost of the invetsment ($Y) from that number i get the NET VALUE of my investment over its entire life time ($Z : where Z = X- Y). If i want to know what is the value of $Z in the present day ($A) i multiply it by the Discount Factor (eg 0.75). So i get the NET PRESENT VALUE of investment from $Z x 0.75 = $A. // The NPV formula is given to you on the IB formula sheet. //
 * __**Net Present Value**__ - is measured in MONETARY UNITS (eg $$).

When addressing this topic in an IB exam remember to analyse, or qualify your recommendation. If you recommend option B, over option A because it produces better results, remember these are formulaes that consider only numbers and figures. Qualitative information, like the effect on staff morale, or customers perception etc need to be considered too, before actually making a final decision.

I like to look at all of these 3 Appraisal options via the table method. This basically involves setting up all the details in column titles and then using each future year as a new row in the table The 3 different Investment Appraisal techniques will some unique columns and some shared columns. Here is a generic table



In reality the Inflows and Outflows are probably determined by the Finance Department as they look over previous internal figures and external market conditions etc etc. They are essentially forecasts, and seldom 100% reliable. In an IB exam, you will either be given them directly (most likely) or given the raw data, so you can work them out (less likely, but possible)

So by adding or changing columns you can use the table approach for all 3 appraisal techniques : lets start with Pay Back.

PAY BACK PERIOD
"the amount of time it takes for an investor to get their investment returned to them" - and we are referring to the exact amount here, ie i invest $75, when do i get //my $75// back.

So adopting the exact same columns as previously, but for varieties sake I have changed the numbers, we can see a table taking shape below So .. > =420 / 12= > $35
 * at the End of Year 2, the Investment is still ($210) and we want it to be $0. So there is $210 of the investment still to be returned.
 * In the 12 months that constitute Year 3 the Investment generates a Netflow of $420
 * So how many months of the 3rd year do we need to get ($210) to $0 ? ANSWER : work out how much on average is earned each month in Year 3
 * Year 3 monthly average = **Year 3 Netflow / 12**
 * **Now divide the Unreturned Investment by the Monthly Average** ........ 210 / 35 = 6
 * we are going to need 6 months of the 3rd year to reach the Pay Back Point

We express our answer as "__//**the Pay Back Period is**//__ 2 years and 6 months ".

NOTE : As mentioned we tend not to bother going as precise as calculating how many DAYS. Instead we round up or down and use the expressions... "just under" or "just over" Example : if the answer above was in fact //6.1// and not //6.0// we would say "__//**the Pay Back Period is**//__ just over 2 years and 6 months ". if the answer above was in fact //5.9// and not //6.0// we would say "__//**the Pay Back Period is**//__ just under 2 years and 6 months ".

In terms of making a decision - you simply chose the Investment that pays you back your money quicker!

BIG LIMITATION of Pay Back Period as a means of appraising an investment? It doesn't look **beyond** the Pay Back period What happens in Year 4, or Year 5, is there even a Year 5?! Its not an in-depth appraisal technique.

This limitation is highlighted below. The figures in black, and figures in red indicate two different investments, both of which cost $500

If we only consider the Pay Back period we would recommend/select the 1st investment (represented by the numbers in black) - although the overall figures certainly give some reason for saying that despite a slower Pay Back the best decision to take would be the 2nd investment (represented by the figures in red). See why its not "an in-depth appraisal technique"?- and why many investors want to use other methods too ?..

.. other methods such as AVERAGE RATE OF RETURN!

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=AVERAGE RATE OF RETURN= - or ACCOUNTING RATE OF RETURN - either way the abbreviation is the same : A.R.R.

Measures the PROFITABILITY of a product over its useful life.

How much of this investment is going to return to me… .. on average .. each year.



Might be worthwhile at this point to clarify that most investments will have.. [1] an ‘initial investment’ value [2] an estimated life span

The ‘initial investment’ value can be complicated by the concept of an [3] ‘end of life’ value.

There are ** various ways ** of calculating these figures, some more accurate than others.. take for example the investment in a vehicle (see below)




 * You find your Initial Investment easy enough from the seller
 * You //could use// the Sellers guarantee, for the Life Span
 * You could use the //selling price of a similar model// to determine its End Of Life value
 * In the example, set in the year 2000, a five year old Buster is worth $2,000.
 * In this case the Initial Investment figure which you put into the formulas (see below) will be $8,000 (calculated by the Initial Price – End Of Life Value)
 * It might be easier to think that ALL investments will have a End of Life Value, but sometimes that value will be $0.

So now to work out the ARR, we first And then 2. Calculate the Average RATE of Return
 * 1) Work out the AR, the Average Return

Just like with the Pay Back there is a table for this, and the first set of columns are exactly the same //* you might see some example that add a 5th column "accumulative netflows" - that's all good if you need it, if it helps, add it.//

So in the final row, the row with TOTALS, you have the information you need.

To work out the Average Return: = 59,000 / 4 = 14,750 = $14,750 OVER THE 4 YEARS OF ITS LIFE SPAN THE INVESTMENT WILL RETURN, ON AVERAGE, __**$14,750**__
 * = Total Netflows / Life Span**

In this context the “return’ is AFTER the initial investment has been considered. This figure is essentially ‘profit’.

Covert this figure into a __//Rate//__, because whether $14,750 is a good return or not, will largely depend on the effort (investment) spent generating it. Eg if I invest $1,000,000 and get $14,750 back each year its not as good as if I get the same return and only invested $10,000!

So lets convert the Average Return into a Rate

= **Average Return / Initial Investment x 100** =14,750 / 100,000= 0.1475= 0.1475 x 100 = 14.75%

The AVERAGE RATE OF RETURN IS __14.8%__
and in terms of making an investment decision? __** Golden Rule **__ : select the investment with the highest ARR!

to analyse the ARR appraisal technique.

GOOD : [A] Unlike the Pay Back it covers the entire life of the investment [B] It measures the profitability, which is often a key concern for investors BAD [C] It ignores issues like inflation and depreciation, that devalue inflows over time [D] It ignores the timing of inflows. Bearing in mind point D above, take a look at the summarised table below that shows two possible investment options. The option represented by green figures will give you the higher ARR, while most investors will probably look at the data and think the option represented by purple data is the better choice! ie ARR will mislead you.

Generally speaking the further into the future your forecasts go the less reliable they are - this is true of pretty much all forecasting, think 'weather' for example, i can reasonably accurately predict the weather in 2 minutes time, but in 2 weeks time, or two months time?!?!

so ARR is good,but not perfect.

while we know 'perfect' is seldom achieved in business we can get closer to perfect than ARR. Find an appraisal technique that factors in timings, inflation and depreciation .............. NET PRESENT VALUE

_ = = =NET PRESENT VALUE=



So here is a question that I believe has a simple answer Which would you prefer? [A] $1,000 now, or [B] $1,000 in 50 years time?

Now you might start analyzing it, and think “perhaps when I am older I will use the money wiser, so B please”, or “I have plenty money now so it might be good to have a guarantee in 50 years time of at least having $1000, so B please” – unlikely, but maybe.

While these are valid considerations…
 * Most people will worry about their very existence in 50 years time and //choose the money now//,
 * equally if they are business minded they might know that $1000 in 50 years time will be able to buy you way less than $1000 now, so //choose the money now//
 * AND
 * These two considerations above are //qualitative// factors, and right now we are focused on //quantitative// factors

The key point being : A forecasted $200 for 5 years time, doesn’t have the same value as a $200 payment received now. ** Future money is worth less than current money **

This becomes important when one looks at the timing of the net flows of rivalrous investment opportunities – as was hinted at while discussing the limitations of ARR.

Net Present Value, as an Investment Appraisal technique seeks to (at least partially) resolve this issue. But wow???

Net Present Value method looks at the year-by-year timings of the foretasted netflows and tries to convert them into '__**present' day**__ value.

It kind of follows the burger example, which essentially was based on inflation (def/ "a general rise in prices over time") - though of course you cant just look at one product, because the prices of different products inflate at a different rates. So what you have to do is look at a 'basket of products' and the average price of that basket. DO NOT WORRY HERE, THE IB GIVES YOU THE 'INFLATION RATES' (real name in the 5th column of the table below), No need to //calculate// it, just need to //apply// it.

This can be seen clearly by returning to the table method. All the same columns as your ARR table, but this time you add a few more.

This table says that "Receiving $18,000 in 12 months time (end of Year 1) has the same value as receiving $17,100 now (Year 0)" It calculates this by taking the End of Year 1 value and multiplying it by the discount factor 18,000 x 0.95 = 17,100 (rounded up) and does the same for Year 2 and 3, though of course the further into the future you go the more the value depreciates, so for each new year there is an additional new Discount Rate.


 * ===Add all the Present Values together to get the (Total) Present Value of the Inevestment===
 * ===Subtract the initial Investment from this Total Present Value to get the __Net Present Value__===

The small complication is getting the **Discount Rate**. Like i said it will be given to you, but not always in a straight forward manner. A table will normally be issued. The table will,like always have columns and rows. The __column__ titles will be different inflation rates - expressed as percentages. This should make sense because the rate at which money devalues over time depends on the state of the economy //(a weak and dying economy can have hyperinflation where money devalues incredibly fast etc etc)//, so you need to have different rates for different economic conditions. The __row__ titles will be for the different forecasted years. And then its a case of cross referencing the given inflation rate, with the given year to find the right Discount rate to put in the cashflow table. See tables below

- and thats how you know what discount rate to use :-)

and in terms of making an investment decision? __** Golden Rule **__ : select the investment with the highest NPV!

to analyse the NPV appraisal technique.

GOOD : [A] The most accurate of all, as it considers (i) the full life span (ii) the timing of the net-flows, to some extent, in that net flows that occur later get discounted greater (iii) it factors in inflation and money devaluation BAD [B] it doesnt fully consider the timing of the netflows [C] Its complicated, and despite its complication still not fully reliable as forecasting errors can often occur. Its a dynamic business environment after all - things change and the discount factors may mislead decision making.

TIME TO TRY A FEW EXAMPLES AND MAKE SOME DECISIONS _

__Figure 1 below is an example we went over in class.__ __The Loykie book goes over each InvApp method too. Loykie does it spererately, we did it one-in-three__ __In real life the Finance Department will be__ forecasting__ these figures figure1 NOTES : (i) The Initial Investment is $100 (ii) the Discount Factor is made up and as result of inflation gets lower and lower over time, - for example in Year4 0.08 of the value is being subtracted, while in Year 9 its 0.09
 * || Inflows || Outflows || Netflows || Discount Factor || Present value || Net Present Value ||
 * End of Year 0 ||  ||   ||   ||   ||   || -100 ||
 * EOY1 || 10 || 1 || 9 || 0.95 || 8.55 || -91.45 ||
 * EOY2 || 25 || 3 || 22 || 0.94 || 20.68 || -70.77 ||
 * EOY3 || 35 || 4 || 31 || 0.93 || 28.83 || -41.94 ||
 * EOY4 || 50 || 7 || 43 || 0.92 || 39.56 || -2.38 ||
 * EOY5 || 65 || 10 || 55 || 0.91 || 50.05 || 47.67 ||

//The// // Discount Factor exists because inflation reduces the value of money over time. eg $100 in 10 years time will not be able to buy you what $100 can now, so "money in the future is worth less than the same amount of money now". The Discount Factor will be given to you. //

PAY BACK By the end of Year 4 its not yet paid back, by the end of Year 5 its more than paid back. Our Pay Back Period is //4 years and ... months// At the end of Year4 $2.38 still needs to be paid off in Year5 each month the project earns a total of ($50.05/12 = __$4.18__) so ($2.38/$4.18) = 0.6 of a month The PAY BACK PERIOD for this investment is just under 4 years and 1 month, NOTE : 4y1m is the correct answer "using the Discounted Figures" - using the 'normal undiscounted' figures the Payback will be slightly quicker

AVERAGE RATE OF RETURN Formulae can be found on Loykie p235 // = (average yearly 'profit') / Initial Investment x 100 // __Numerator__ : (i) 8.55+20.68+28.83+39.56+50.05 = 147.8. (ii) $147.8 / 5 years. (iii) average profit per year = __$29.6__ //__Denominator__ :// initial investment $100 //x100// //Average Rate of Return// is 29.6% .* Note that we have used the discounted figures to calculate the ARR,

NET PRESENT VALUE Formulae can be found on Loykie p237 // = Aggregate Present Value - Initial Investment // $147.8 - $100 = $47.8