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TUFTS UNIVERSITY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ES 053 INTEGRATING ENGINEERING AND SYSTEMS Associate Professor Emeritus Stephen H. Levine Fall 2012

Lesson 5

Deciding Among Alternatives

Topics to be Covered Comparing PW’s, IRR’s, and the MARR : Real and actual dollar cash flows Depreciation and depreciation schedules : Before and after cash flows examples

One of the basic problems in engineering economics is deciding among alternatives, remembering that in many cases one of the alternatives is the do-nothing alternative. So let’s say you have several alternative projects or and you are making your decision based on rate of return. Then you will want to find out which of the alternatives has the best rate of return (IRR). Or maybe which one has the largest PW. The assumption is that the do-nothing alternative has a rate of return equal to the MARR, which is another way of looking at the MARR. (Actually, the MARR might be a little higher than do-nothing rate of return because of the existence of risk. How does that work?) The MARR, again, really is a measure of . Our next problem is one of comparing alternatives.

The Problem: The Advanced Technology Corporation (ATC), a multi-million dollar concern, is considering adding a new underwater mining robot to its product line. The decision as to whether to bring this new robot to production is dependent on its production cost. A significant part of the cost of producing this new robot is ATC’s need to obtain a specialized production machine from General Machine Company (GMC). GMC produces two models of this production machine, the Standard Model, which it will only sell, and the recently introduced Super Model, which it will only lease. Based on preliminary estimates ATC expects to be producing its new robot for 10 years, after which it will want to be rid of the production machine. Here are the details on the two options. They will introduce a number of new concepts which heavily impact cash flows and thus PW’s and IRR’s.

Option 1. Purchase a Standard Model production machine for $6,000,000. The government will allow ATC to fully depreciate this machine over 6 years, using the Straight Line depreciation method. The present salvage of a 10- year old machine of this type is estimated at $600,000. The Standard Model machine is expected to enable the production of robots generating $1,150,000 of before tax revenue in the first year, not for the purchase and annual maintenance cost of the

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production machine. While production levels of robots is expected to remain constant over the 10 year period this annual net revenue is expected to increase due to inflation at an annual rate of 3%. Annual maintenance cost for the production machine is expected to begin at $50,000 in year 1 and increase at 2% per year above the general annual inflation rate due to aging of the machine.

Option 2. Lease a Super Model production machine at $1,100,000 per year for the 10 years. To do so they must put down a $2,000,000 security deposit refundable when the lease is up. This machine is expected to generate $1,350,000 of before tax net revenue in the first year, not accounting for the leasing fee, and this will again increase at an annual rate of 3% due to inflation. The maintenance is all covered in the leasing contract. The leasing down payment is not deductible and the refund is not taxable.

The general annual inflation rate is expected to be 4% and the tax rate is 34%. ATC uses a real, after tax MARR = 7%.

Which, if either, option should ATC pursue?

Some Basic Concepts

Well, as we noted earlier, it is economics at least as much as technical capability that determines what actually get to produce. We should also note that as in the first problem many of the numbers are in fact estimates. We haven’t considered it yet but the sensitivity of our results and the decisions they lead to is an important aspect of any economic analysis.

There are a number of new concepts in this problem. They include (but as we shall see not limited to):

(1) inflation; (2) general inflation rate; (3) tax rate; (4) before and after tax cash flow; (6) depreciation; (7) Straight Line depreciation schedule; (8) real dollars and actual dollars (8) real, after tax, MARR.

What do we know about these? What do they have to do with evaluating the alternatives?

Inflation: Historically, have tended to rise over time. (As an example, my starting salary as an with a MS in 1964 was $9000/year, but my new Chevrolet was $2000.) But that means if you stick $1000 under the pillow for 10 years it is likely to have lost a lot of purchasing power. In addition, inflation is one more reason that a future payment may be worth less than a present payment. In evaluating cash flows inflation

es053 Lesson 5 - 2 needs to be taken into account.

General Inflation Rate: Different items inflate at different rates, and some may deflate while the rest inflate. Thus, while cars have increased in price, computers have decreased. The general inflation rate is a sort of average overt all types of . It is represented in things like the consumer price (CPI), an average over the products consumers typically buy. From Robert C. Sahr at Oregon State University we have the following table indexed to 2008.

Year CF Year CF Year CF Year CF 1854 0.039 1894 0.040 1934 0.063 1974 0.231 1855 0.041 1895 0.039 1935 0.064 1975 0.252 1856 0.040 1896 0.039 1936 0.065 1976 0.267 1857 0.041 1897 0.039 1937 0.068 1977 0.284 1858 0.039 1898 0.039 1938 0.066 1978 0.306 1859 0.039 1899 0.039 1939 0.065 1979 0.341 1860 0.039 1900 0.039 1940 0.066 1980 0.387 1861 0.041 1901 0.040 1941 0.069 1981 0.427 1862 0.047 1902 0.040 1942 0.076 1982 0.453 1863 0.059 1903 0.041 1943 0.081 1983 0.467 1864 0.074 1904 0.042 1944 0.083 1984 0.488 1865 0.077 1905 0.041 1945 0.084 1985 0.505 1866 0.075 1906 0.042 1946 0.092 1986 0.514 1867 0.069 1907 0.044 1947 0.105 1987 0.533 1868 0.067 1908 0.043 1948 0.113 1988 0.555 1869 0.064 1909 0.043 1949 0.112 1989 0.582 1870 0.061 1910 0.045 1950 0.113 1990 0.613 1871 0.057 1911 0.045 1951 0.122 1991 0.639 1872 0.057 1912 0.046 1952 0.124 1992 0.658 1873 0.056 1913 0.046 1953 0.125 1993 0.678 1874 0.053 1914 0.047 1954 0.126 1994 0.695 1875 0.052 1915 0.047 1955 0.126 1995 0.715 1876 0.050 1916 0.051 1956 0.128 1996 0.736 1877 0.049 1917 0.060 1957 0.132 1997 0.753 1878 0.047 1918 0.071 1958 0.136 1998 0.765 1879 0.047 1919 0.081 1959 0.137 1999 0.782 1880 0.048 1920 0.094 1960 0.139 2000 0.808 1881 0.048 1921 0.084 1961 0.140 2001 0.831 1882 0.048 1922 0.079 1962 0.142 2002 0.844 1883 0.047 1923 0.080 1963 0.144 2003 0.863 1884 0.046 1924 0.080 1964 0.145 2004 0.886 1885 0.045 1925 0.082 1965 0.148 2005 0.916 1886 0.044 1926 0.083 1966 0.152 2006 0.946 1887 0.045 1927 0.082 1967 0.157 2007 0.973 1888 0.045 1928 0.080 1968 0.163 2008 1.000 1889 0.043 1929 0.080 1969 0.172 2009 1.022 1890 0.043 1930 0.078 1970 0.182 2010 1.045 1891 0.043 1931 0.071 1971 0.190 2011 1.069 1892 0.043 1932 0.064 1972 0.196 2012 1.092 es053 Lesson 5 - 3

1893 0.042 1933 0.061 1973 0.208 2013 1.117

Tax Rate: “Nothing is sure but death and taxes” so we had better worry about how taxes affect cash flows, since you don’t get to keep all that net revenue (). Income tax is of course only one type of tax (Others?) but it is the only one that we will consider in this course. Tax policies can be quite complex but we will keep it simple; a certain fraction of taxable income.

Before and After Tax Cash Flow: The payment of taxes represents a cash flow so to get to the latter we will need to subtract the taxes from the former.

Depreciation: The value of many items such as cars and machinery decreases over time due to use, obsolescence, going out of style, and so on. When business equipment depreciates in value this is a type of economic loss to the business and the government recognized that this loss should be reflected in reducing taxable income. It also represents a reduction in the value of a business asset.

Straight Line Depreciation Schedule: Depreciation is spread over all or part of the lifetime of the item. Straight line depreciation means the item depreciates an equal amount each time interval. There are other more complex schedules that exist as well, but we are only interested in the basic concept and so will not consider them. If C is the initial cost of an asset, n is the number of intervals (years) over which it is to be depreciated, and S is its salvage value when fully depreciated, then using straight line depreciation its annual depreciation, d, is

C −S d = n and its book value after k years of depreciation is

Bk = C − k *d .

Real Dollars and Actual Dollars: According to my dictionary real means actual, but not in cash flow jargon. Real dollars are pegged to the price index of a specific year. Thus my $9000 salary in 1964 was $9000 actual dollars (i.e., I received a check for $750 each month) but in terms of buying power when referenced to the year 2008 would be (using the table) $9000/0.145 = $62,069 (and referenced to 2011 would be $62,069*1.069 = $66,352). Alternatively, $62,069 in 2008 is ‘really’ $9000 in 1964 dollars. [That 1964 Chevy II of mine would cost $14,745 in 2011 dollars – and it had no air-conditioning, no CD (or tape) player, no power assists, no cruise control, no nothin’!]

Real, After Tax MARR: Clearly, both inflation and taxes impact cash flows and therefore IRR. The MARR needs to take these factors into account.

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Taxes: Organizing a Systematic Approach to the Solution

When dealing with taxes there are lots of details to worry about here so the problem deserves a systematic approach. (Actually, all frequently encountered problems deserve a systematic approach, so that the next time you are faced with a similar problem you don’t have to waste time figuring out just what to do.) So let’s begin by developing some useful nomenclature. We will assume a time interval of one year, but any fixed interval will do.

R – gross revenue; E – operating expenses (do not include expenditures since these purchase capital assets); d – depreciation of capital assets; T – income taxes; t – effective tax rate (effective means there could be multiple taxes – federal, state, etc.)

We also want to develop two types of measures, income measures and cash flow measures, and make sure we understand the difference.

Income measures NIBT – Net Income Before Taxes (also called TI – Taxable Income) NIBT = R – (E + d) (Note: d is not a cash flow.) NIAT – Net Income After Taxes NIAT = NIBT – T Since T = t * NIBT NIAT = (1 – t) * NIBT

Cash Flow Measures BTCF – Before Tax Cash Flow BTCF = R – E (Note: d is not included.) = NIBT + d ATCF – After Tax Cash Flow ATCF = BTCF – T = (R – E) – t * (R – (E + d)) = (1 – t) * (R – E) + t * d (Note: all are cash flows including t * d.) Also, ATCF = NIBT + d – T = NIAT + d

Next, let’s develop our basic algorithm for going from BTCF to ATCF. 1. Given BTCF and d, calculate TI: TI = BTCF – d (Note: Capital expenditures are not deductible and salvage value is not taxable.) 2. Calculate T: T = t * TI 3. Determine ATCF

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ATCF = BTCF – T

Simple Tax Example Problem (but one with a slight twist)

Engineering Design Corporation (EDC) is considering the purchase and installation of a network of computer workstations for $90,000. The purpose of this system is to reduce EDC’s data processing costs. The estimated life of the system is 8 years at which time it will have an estimated salvage value of $18,000. EDC will use the Straight Line Method to schedule the depreciation of the system. EDC estimates that it will incur a $10,000 annual cost for maintaining the equipment. The tax rate is 40% and EDC uses an after tax MARR of 8%.

1. If the annual reduction in data processing costs is $25,000 should EDC purchase the equipment?

2. What is the minimum annual that EDC must realize to justify the purchase?

Part 1.

Simple Example Tax rate = 0.4 Annual Depreciation = ($90,000 - $18,000)/8 = $9000 Salvage not taxable

Let’s see how to organize the analysis. It is my experience that the more you separate the various cash flow streams the easier it is to understand what is happening

Clearly, at an annual savings of $25,000 this purchase is not justified since its IRR < MARR. Note that the purchase price of $90,000 is not taken as an expense and thus does not reduce taxable income because we have gained a capital asset of equal value. Likewise, the salvage does not add to the taxable income since we are giving up a capital asset of equal value.

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Part 2.

This time we can use Goal Seek to set the cell holding Annual Savings to the value that makes the IRR = 8.00%.

The required annual savings is $27,280.

Taking Inflation into Account

Let’s consider a very simple example, 6% annual inflation, and use the ATCF from our previous solution. We will convert that cash flow, which is presently in actual dollars (A$) into a real dollar (R$) cash flow with year 0 our reference year. To do that we need to deflate the future cash flows. For year N, with an annual inflation rate of M%

R$(N) = A$(N)/ (1+M%)N

It is just like discounting! In our example, therefore,

Quite the difference!

In Class Problem: (Early Development of the Taxation Department): With its superior knowledge of techniques the Calm Waters caveman tribe has conquered the neighboring Peaceful Sunset tribe. Calm Waters’ leader Og has

es053 Lesson 5 - 7 established the precedent that the victors should place the blame for the war on the vanquished and demand reparations. After consultation with his Department of Pillage he has formulated the following plan. It will require that at the end of each year for the next 5 years Peaceful Sunset deliver 15% of its cattle to Calm Waters. Research indicates that typically Peaceful Sunset has a herd of 100 cattle at each year’s end. Calm Waters’ tribal leaders have critiqued the plan and have two concerns and a question.

1. Concern 1: Delayed gratification – The tribe’s psychologists have noted that meat you expect to eat a year from now is not as immediately gratifying as meat eaten now. Displaying their tribe’s renowned mathematical acumen, they have concluded that each year’s delay until you eat the meat reduces your immediate gratification by 20%. 2. Concern 2: Shrinking cattle – The tribe’s veterinarians have noted the alarming trend that each year Peaceful Sunset’s cattle seem to be 15% smaller than the previous year.

In light of these concerns the tribal leaders have requested that Department of Pillage consider an alternative plan based on requiring that Peaceful Sunset immediately deliver 50 cattle.

How might Calm Water’s evaluate and compare these alternatives?

Back to ATC

Now let’s go back to ATC’s problem, which model to choose. First we will look at Option 1, the Standard Model.

and then we can look at Option 2, the Super Model.

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Both options are acceptable in terms of the MARR but clearly Option 2 is preferable. In this case both the IRR and PW favored Option 2, but they do not always agree. Why not? The answer lies in scale dependency. The IRR is scale independent; the PW is not.

Two Classic Cases of Hyper-Inflation

1. Weimar Germany in the 1920’s

Weimar Germany had greeted with total horror the financial punishment of Versailles. If Germany had paid off the sum of £6,600,000,000, she would have remained in debt to the Allies until 1987 !! However, by signing the Treaty of Versailles, she had agreed in principle to the issue of reparations and in 1921, Germany just about managed to pay its first installment of 2 billion gold marks. Weimar Germany was allowed to pay in kind (actual materials) as opposed to just cash. Most of this 2 billion was paid in coal, iron and wood.

In 1922, Weimar Germany simply could not manage to pay another installment. This the Allies did not believe - especially France where anger towards Germany still ran deep - and the German government was accused of trying to get out of her reparations responsibilities. This apparent refusal was only four years after the end of the war, and the attitude of the public towards Germany was still very hostile - and not just in France.

In 1922, French and Belgium troops invaded the Ruhr; Germany’s most valuable industrial area. The French and Belgium troops took over the iron and steel factories, coal mines and railways. Those Germans who lived in the Ruhr and were considered not to be co-operating were imprisoned. Food was taken. That this action by the French and Belgians broke the rules of the League of Nations - which both belonged to - was ignored by both countries. France was considered one of the League's most powerful members and here she was violating its own code of conduct.

Weimar’s government responded by ordering the workers in the Ruhr to go on strike and it ordered all people in the Ruhr to passively resist the French and Belgium soldiers. This meant that they were not to openly confront the French and Belgium soldiers, simply that

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they were not to help them in any way whatsoever. This lead to violence and over the next 8 months of the occupation, 132 people were killed and over 150,000 Ruhr Germans expelled from their homes.

The order for workers to go on a general strike may have been patriotic but it had disastrous consequences for Germany as a whole. The Ruhr was Germany’s richest economic area and produced a great deal of wealth for the country as a whole. The huge Krupps steelworks was there. By not producing any goods whatsoever, Germany’s started to suffer. The striking workers had to be paid and the people expelled from their homes had to be looked after. To do this, the government did the worst thing possible - it printed to cover the cost. This signalled to the outside world that Germany did not have enough money to pay for her day-to-day needs and whatever money may have been invested in Germany was removed by foreign investors.

Such a drop in confidence also caused a crisis in Weimar Germany itself when prices started to rise to match inflation. Very quickly, things got out of control and what is known as hyperinflation set in. Prices went up quicker than people could spend their money.

In 1922, a loaf of bread cost 163 marks.

By September 1923, this figure had reached 1,500,000 marks and at the peak of hyperinflation, November 1923, a loaf of bread cost 200,000,000,000 marks.

The impact of hyperinflation was huge : People were paid by the hour and rushed to pass money to loved ones so that it could be spent before its value meant it was worthless. People had to shop with wheel barrows full of money Bartering became common - exchanging something for something else but not accepting money for it. Bartering had been common in Medieval times! Pensioners on fixed incomes suffered as pensions became worthless. Restaurants did not print menus as by the time food arrived the price had gone up! The poor became even poorer and the winter of 1923 meant that many lived in freezing conditions burning furniture to get some heat. The very rich suffered least because they had sufficient contacts to get food etc. Most of the very rich were land owners and could produce food on their own estates. The group that suffered a great deal - proportional to their income - was the middle class. Their hard earned savings disappeared overnight. They did not have the wealth or land to fall back on as the rich had. Many middle class families had to sell family heirlooms to survive. It is not surprising that many of the middle class who suffered in 1923, were to turn to Hitler and the Nazi Party.

Hyperinflation proved to many that the old mark was of no use. Germany needed a new . In September 1923, Germany had a new chancellor, the very able Gustav Stresemann. He immediately called off passive resistance and ordered the workers in the Ruhr to go back to work. He knew that this was the only common sense approach to a

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crisis. The mark was replaced with the Rentenmark which was backed with American gold. In 1924, the Dawes Plan was announced. This plan, created by Charles Dawes, an American, set realistic targets for German reparation payments. For example, in 1924, the figure was set at £50 million as opposed to the £2 billion of 1922. The American government also loaned Germany $200 million.

This one action stabilized Weimar Germany and over the next five years, 25 million gold marks were invested in Germany. The economy quickly got back to strength, new factories were built, returned and things appeared to be returning to normal. Stresemann gave Germany a sense of purpose and the problems associated with hyperinflation seemed to disappear.

1924 to 1929 is known as the Golden Age of Weimar. Berlin became the city to go to if you had money, the Nazis were a small, noisy but unimportant party. Above all, Stresemann gave Germany strong leadership.

History Learning Site > Modern World > Weimar Germany > Hyper Inflation

2. Israel in the 1980’s

One of the most bizarre eras in Israel’s existence, certainly from a financial standpoint was the period of hyperinflation that Israel suffered in the early 1980’s. Like all countries in which inflation is rampant the name of the game is to part with the local currency as quickly as possible. Invest or spend! Don’t dawdle. It was similar to the children’s game “hot potato.” Don’t be left with shekels in your hand or bank account, when the music stops (i.e., when price increases go into effect). So, the populace would purchase dollars, invest in dollar denominated instruments, or in durable goods, like furniture, appliances and televisions, for example.

Rumors of price rises of 20% or more (sometimes a lot more) on food items would spread among the public and supermarkets would become total chaos, as the public would hoard goods from supermarket shelves. After all, what you don’t buy now will cost you at least 20% more tomorrow. The same applied to gasoline and other consumer goods. So, why not buy now?

One area in which absurdities reached extreme heights was housing, or more specifically mortgages. Before I made aliyah in 1978, I invested some money with Bank Tefahot, an Israeli mortgage bank. This gave me the option of receiving at a later date a secondary mortgage, equal to the amount of the initial investment, at a 5% fixed annual rate (in addition to my initial investment accrued with interest). When my wife and I purchased a condominium in Rishon LeZion in 1981, interest rates on mortgages were already at a 39% annual rate, a very high rate one might think. At a fixed 5% rate, we decided to take advantage of the cheap credit and took the secondary mortgage from Bank Tefahot.

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No one could foresee that the annual rate of inflation would soon exceed 800% a year. Fixed rate mortgage payments became laughably easy to make as inflation shot up to 800% a year. That is because salaries more or less kept pace with inflation, in a - price inflationary spiral, a typical phenomenon in high inflation .

The coup de grace came when I received a notice from Bank Tefahot canceling my secondary mortgage, because the cost of record-keeping it had become more costly than the value of our monthly payment. Yes, inflation had eaten away at the value of our monthly payment to such an extent that the mortgage bank wrote off the mortgage.

During this period, it seemed that Treasury Secretaries or Ministers, as they are referred to in Israel, were replaced, every few months. changed from Israeli Liras to Shekels and from Shekels to New Israeli Shekels. This latter change had the effect of truncating two or three zeros from the currency. So for example, 1000 Shekels would now be equal to ten new Shekels, in a futile attempt to stave off a complete loss of public confidence in the currency.

Eventually the powers that be exercised enough monetary discipline to bring inflation under control with the inflation rate falling to about 20% a year. In the 1990’s, the rate of inflation dropped even more and leveled off to that of many Western countries. But for a while, living through this period of hyperinflation, as a wage earner in Israel, was like a dog chasing his tale, trying to catch up but always coming up short and breathless.

The Israel Experience – Hyperinflation by Michael Rosenbloom ([email protected])

Homework Problems

Problem 1: Complete the In Class Problem Initial Investment - $140M Annual Gross Income - $80M in year 1 with 5% growth expected for 4 more years. Annual Cost = $40M in year 1 with increase at inflation rate for 4 more years. Income Tax Rate – 25% Annual Inflation Rate – 4% Tax incentive – 20% of annual net income is tax free in years 1-3. After tax real dollar MARR = 12%

Determine the PW and the IRR.

Problem 2: (Early Development of the Leadership Principle): With its superior knowledge of Operations Research techniques the Calm Waters caveman tribe has conquered the neighboring Peaceful Sunset tribe. Calm Waters’ leader Og has established the precedent that the victors should place the blame for the war on the vanquished and demand reparations. After consultation with his Department of Pillage he has formulated the following plan. It will require that at the end of each of the next 5 years Peaceful

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Sunset deliver 25 of its cattle to Calm Waters. Calm Waters can then slaughter the cattle for the tribe’s annual End-of-the-Year Barbecue Bash. By agreement with Peaceful Sunset the cattle that are delivered at the end of each year should weigh 500 ks* each.

True to the Calm Water’s credo, “More is Better, Most is Best”, an alternate plan has been suggested by the tribe’s Department of Gluttony. Noting that if the cows are allowed to graze in Calm Waters’ pastures they will increase their weight by 10% per year, they propose requiring an immediate delivery of 100 of those 500 ks cattle. At the end of each of the next 5 years 20 of the cattle can be slaughtered for the End-of-the-Year Barbecue Bash.

The tribe’s Department of Gratification estimates that each years delay in consuming the meat reduces the tribe’s immediate gratification by 12% (relative to the previous year). Og has long recognized that his maintaining the position of tribal leader depends significantly on providing that immediate gratification.

1. Develop a mathematical formulation useful to Og for evaluating both plans. What is his performance measure? 2. Based on this evaluation which plan should Og implement?

* - ks is the abbreviation for kilostones, a very early unit of weight

Problem 3: The DEF Company has bought a new machine for $200K and will be allowed to depreciate it over a 10 year period to $40K using a straight line schedule. a. Determine the machines book value for each year of its depreciation lifetime. b. Assume that in the absence of inflation the fully depreciated book value is a good estimate of the used machines value. What will its market value be if the annual inflation rate over this time period is 5%? (Note: if DEF sells it for more than $40K it will need to pay taxes on the difference and if it sells it for less it can take the difference as a loss.)

Problem 4: ABC is considering producing a product that they expect to generate an annual gross revenue of $1.9M in year 1 and increase at 4% per year over the following 9 years. The initial cost of the equipment required to produce the product is $10.0M and its expected salvage value after 10 years is $400K. The annual maintenance in year 1 should be $50K and increase at the general inflation rate. A major overhaul in year 5 is expected to cost $100K. Other costs associated with producing the product should total $200K in year 1 and grow at the general inflation rate. Given that the tax rate is 25% , straight line depreciation is used, and the general inflation rate is 3% per year:

a. What after tax, real dollar IRR can ABC expect to get from producing this product? b. If ABC’s after tax, real dollar MARR = 7% what is the minimum year 1 gross revenue ABC needs to make this production project acceptable, assuming the 4% annual increase as before?

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