When all future cash flows are expressed in

How do you convert a unit of inflated currency (e.g., a dollar) into a constant-value currency statement?

If a 3D printer increased in cost at exactly the inflation rate, what was the inflation rate if the printer costs exactly twice as much now as it did 10 years ago?

In an inflationary period, what is the difference between (a) inflated dollars and then-current future dollars, and (b) then-current future dollars and constant-value future dollars?

How many future dollars 10 years from now will have the same buying power as $10,000 today? The market interest rate is 12% per year and the inflation rate is 7% per year.

Determine todays purchasing power of $1,000,000 thirty years in the future, if if = 15% per year and f = 5% per year.

In an effort to reduce pipe breakage, water hammer, and product agitation, a French chemical company plans to install several chemically resistant pulsation dampeners. The cost of the dampeners today is 106,000, but the chemical company has to wait until a permit is approved for its bidirectional port-to-plant product pipeline. The permit approval process will take at least 2 years because of the time required for preparation of an environmental impact statement. Because of intense foreign competition, the manufacturer plans to increase the price only by the inflation rate of 3% each year. Determine the cost of the dampeners in 2 years in terms of (a) then-current euros, and (b) constant-value euros.

The lease cost for a specialized highway design software package is estimated to be $13,000 for each of years 1, 2, and 3 (future dollars). (a) Calculate the CV amount today (year 0) of each future cost estimate at the inflation rate of 6% per year. (b) Develop a spreadsheet and graph for inflation rates of 3%, 6%, and 8% per year that show the CV today

For many years, college cost (including tuition, fees, room, and board) increases have been higher than the inflation rate, averaging 5% to 8% per year. According to the College Boards Trends in College Pricing, the average total costs in 2015 dollars were $19,548 for students attending in-state 4-year public colleges and universities and $43,921 for students at 4-year private colleges and universities. Assume an additional $4000 per year for textbooks, supplies, transportation, and other expenses. Using a 7% per year inflation rate, (a) how much can a sophomore high-school student expect to spend on in-state tuition, fees, room, and board for the freshman year (3 years from now) at a 4-year public university, and (b) what is the estimated total cost for the second year at the university, if textbooks, supplies, etc. also increase at 7% per year?

The federal-level Pell Grant program provides financial aid to needy college students. The grant increases annually to account for inflation. The maximum total Pell Grant award increased from $5550 to $5,730 from 2013 to 2015. (a) What was the average inflation rate per year in this prior 2-year period? (b) Beginning in 2018, grants will no longer increase with inflation. What will be the maximum award starting in 2018 and thereafter, assuming the inflation rate in 2016 and 2017 is 2.5% per year?

According to NACEs April 2014 Salary Survey, engineering majors held 8 of the top 10 spots on the list of top-paid majors for the Class of 2014 bachelors degree graduates. Graduates in petroleum engineering were the highest paid at $93,500, earning $28,000 more than the next highest paid at $67,300. Civil engineering graduates were the tenth highest paid at $62,100. Assuming the starting salary of petroleum engineering graduates stays the same for the next 10 years, what annual increase in pay would be required for civil engineering graduates to receive the same starting salary as that of petroleum engineering graduates?

A UK-based life insurance company will pay a cash-value sum of 500,000 when the insured reaches the age of 65. The insured will be 65 years old 27 years from today. (a) Determine the cash value of the 500,000 in CV purchasing power, assuming inflation remains constant at 3% per year. (b) Write the spreadsheet single-cell function that displays the answer. (c) Convert your answer to U.S. dollars and euros using current exchange rates.

An engineer who is now 65 years old began planning for retirement 40 years ago. At that time, he thought that if he had $1 million when he retired, he would have more than enough money to live his remaining life in luxury. Assume the inflation rate over the 40-year time period averaged a constant 4% per year. (a) What is the CV purchasing power of his $1 million at age 65? (Hint: Use the day he started 40 years ago as the base year. (b) How many future dollars should he have accumulated over the 40years to have a CV purchasing power equal to $1 million at his current age of 65?

Jack has tracked the annual inflation rate (shown below) for a top-rated sportsman-level fishing outfit that he has always hoped to own. It cost $1000 ten years ago, but he could not afford it over the intervening years. (a) Estimate the cost now, which is the end of year 10. (b) Is the cost estimate the same using an average inflation rate of 5% per year over the 10-year period? Why or why not? Year Inflation Rate per Year 1, 3, 5, 7, 9 10% 2, 4, 6, 8, 10 0%

The Bureau of Labor Statistics has a website (www.bls.gov) that contains a Consumer Price Index inflation calculator that uses the averageCPI to adjust the purchasing power of money over different periods of time. The CPI index value has been calculated every year since 1913. The calculator indicated that $1 million in 1913 would have the same purchasing power as $23,930,909 in 2016. What was the average inflation rate over this 103-year time period?

The Bank of England has an inflation calculator website that uses the UK price index to show how the cost of goods and services has changed since 1750. The website reveals that something that cost 10,000 in 1920 cost 7984 in 1940. What was the average annual inflation rate over that 20-year time period in the early-to-mid 20th century?

Emissions of heat-trapping carbon dioxide (CO2) reached an all-time high of 36.9 gigatons in 2014, a 2.5% increase over 2013. The International Energy Agency said this further reduces the chance that the world could avoid a dangerous rise in global average temperature by 2020. (a) If the discharge of CO2 continues at the same 2.5% rate per year for the next 6 years, how many gigatons will be released in 2020, and (b) what will be the total percentage increase between 2014 and 2020?

In 2015, a retired person in the United States who received maximum social security benefits got $2699 per month, which represented a 1.7% cost of living adjustment (COLA) over 2014. (a) Determine the monthly benefit in 2018 if the COLA adjustments are 1.5%, 2.1%, and 2.7%, respectively, for the next 3 years. (b) Assuming the average annual inflation is 2.0% per year, determine if the monthly benefits in 2018 have more or less purchasing power in current-value terms assuming the 3 years of COLA adjustments above.

During periods of hyperinflation, prices increase rapidly over short periods of time. One of the worst cases of hyperinflation in history occurred in Zimbabwe in 2008 where prices doubled every day. If that rate continued for just 1 week, how much would a French baguette cost after 7 days if the cost at the beginning of the week was $1.25?

For years, Jake has practiced the buy now, pay later philosophy of money management. For example, he purchased a car 3 years ago with a 6-year (72 month) loan at 7% per year interest. He has refinanced the loan each year at a higher interest rate; 7.5% last year and 8.5% this year. With a serious recession anticipated in his line of work, he was told yesterday by his boss that his salary would be cut by 25% for the next 2 to 4 years. When Jake tried to refinance his car loan yet once again, the bank loan officer said that due to his multiple loan applications, his credit rating had been lowered significantly and that his current loan must be paid off in the next 6 months to recover his credit rating in the future. Provide Jake with some examples of what he could do to get his finances and credit rating in better order.

-, Inc., a high-tech company in San Diego, whose stock trades on the NYSE exchange, uses a MARR of 25% per year. If the chief financial officer (CFO) said the company expects to make a real rate of return of 20% per year on its investments over the next 3-year period, what is the company expecting the annual inflation rate to be over that time period?

Cellgene Biometrics, a small biotech company, uses a MARR of 40% per year when evaluating new investments. If the inflation rate is 9% per year, what will the real rate of return be, provided it realizes its optimistic MARR objective?

The new CEO of a high-tech incubator company wants to entice venture capitalists by promising a growth rate of 40% per year for at least 3 years. Therefore, the companys MARR was set at 40%. If this ROR was actually realized, but the CEO did not account for the observed 8% per year inflation rate, what was the real growth rate?

Calculate the inflation-adjusted interest rate when the annualized inflation rate is 7% per year and the real interest rate is 4% per year.

Because retail supermarket corporations operate on a low ROR, it is common to use a market MARR of about 3% per year. What real return rate is implied from a market interest rate of 3% per year when the annual inflation rate is 4% per year? Explain your answer.

Find the present worth of earthmoving equipment that has a first cost today of $150,000, an annual operating cost of $60,000, and a salvage value of 20% of the first cost after 5 years; these estimates being in future dollars. Assume the interest rate is 10% per year and that inflation has averaged 7% per year. Solve by hand and spreadsheet with inflation (a) not accounted for, and (b) accounted for.

Some of the following future cash flows have been expressed in then-current (future) dollars and others in CV dollars. Use an interest rate of 10% per year and an inflation rate of 6% per year. (a) Find the present worth. (b) Use a spreadsheet to find the PW value using one NPV function with all cash flows expressed as future dollars. Year Cash Flow, $ Expressed as 0 16,000 CV 3 40,000 Then-current 4 12,000 Then-current 7 26,000 CV

The company you work for is considering a new product line projected to have the net cash flows (NCF) shown. The values are in future dollars, which have been inflated by 5% per year. Because the plant manager is unsure how the present worth is calculated, he asked you to do it in two ways over the 4-year planning horizon: (1) using the companys market rate of 20% per year, and (2) converting all of the estimates into CV dollars and using the companys real rate. You said both ways will provide the same answer, but he asked you to show him the calculations. What is the present worth by method (1) and method (2)? Solve by hand and spreadsheet. Year 0 1 2 3 4 NCF, $1000 10,000 2000 5000 5000 5000

A regional infrastructure building and maintenance contractor must decide to buy a new compact horizontal directional drilling (HDD) machine now, or wait and buy it 2 years from now when a large pipeline contract will require the new equipment. The HDD machine will include an innovative pipeloader design and a maneuverable undercarriage system. The cost of the system is $68,000 if purchased now or an estimated $81,000 if purchased 2 years from now. At i = 10% per year and f = 5% per year, determine if the contractor should buy now or later (a) without any adjustment for inflation, and (b) with inflation considered.

Joan, the project manager, asks you to evaluate alternatives A and B on the basis of their PW values using a real interest rate of 10% per year and an inflation rate of 3% per year (a) without any adjustment for inflation, and (b) with inflation considered. Also, write the spreadsheet functions that will display the correct PW values. (c) Joan clearly wants alternative A to be selected. If inflation is steady at 3% per year, what real return i would machine A have to generate each year to make the choice between A and B indifferent? What is the required return with inflation considered? Machine A B First cost, $ 31,000 48,000 AOC, $ per year 28,000 19,000 Salvage, $ 5,000 7,000 Life, years 5 5

Compare the alternatives below on the basis of their capitalized costs with adjustments made for inflation. Use i =12% per year and f = 3% per year. Alternative X Y First cost, $ 18,500,000 9,000,000 AOC, $ per year 25,000 10,000 Salvage value, $ 105,000 82,000 Life, years 10

A grandfather is planning to leave his only granddaughter well off when she reaches the age of 25. He plans to deposit a lump sum now, which is her second birthday, such that she will have enough money to live comfortably without working. He wants her to have an amount that would have the same purchasing power as $2 million today. If he can invest the money now and earn an average market interest rate of 8% per year while the inflation rate averages 4% per year, what amount must he deposit?

A doctor is on contract to a medium-sized oil company to provide medical services at remotely located, widely separated refineries. The doctor is considering the purchase of a private plane to reduce the total travel time between refineries. The doctor can buy a used Learjet 31A now for $1.1 million or wait for a new very light jet (VLJ) that will be available 3 years from now. The cost of the VLJ will be $2.1 million, payable when the plane is delivered in 3 years. The doctor has asked you, his friend, to determine the present worth of the VLJ so that he can decide to buy the used Learjet now or wait for the VLJ. The MARR is 15% per year and the inflation rate is projected to be 3% per year. (a) What is the present worth of the VLJ with inflation considered? (b) Which plane should he buy?

A salesman from Industrial Water Services (IWS), who is trying to get his foot in the door of Westco Refining, offered electro-dialysis equipment for $2.5 million. This is $800,000 more than the price offered by a competing saleswoman from AG Enterprises. However, IWS said Westco wont have to pay for the equipment until the 2-year warranty runs out. IWS will also offer an extended 2-year warranty for $100,000, payable 2 years from now. If Westco does want the extended warranty, determine which offer is better using Westcos real return requirement of 15% per year and an assumed inflation rate of 3.5% per year.

As an innovative way to pay for various software packages that your company sells, a high-tech service company has offered to pay your company in any one of three ways: (1) pay $450,000 now; (2) pay $1.1 million 5 years from now; or (3) pay $200,000 now and $400,000 two years from now. You want to earn a real return of 10% per year and the inflation rate is 6% per year in the specialized software market. (a) Use PW analysis to determine which offer you should accept with inflation considered. (b) Determine the market return rates at which all three methods have the same PW value.

The company you work for signed a contract with a security firm to control access to company grounds and corporate offices. The contract amount was for $140,000 for the first year, renewable each year for up to a total of 5years at the same cost plus a percentage increase equal to the inflation rate for the preceding year. Your boss asked you to calculate the expected cost in the final year of the contract (year 5), assuming the inflation rate is 3% for the next 3years and 5% for the last one.

A plant manager is not sure whether he will get the approval to buy new equipment for automating an engine assembly line now or at some future time within the next 3 years. In order to have the money whenever he is given the go-ahead, he has asked you to tell him what the equipment is likely to cost in each of the next 3 years. The cost of the equipment today is $300,000, and the MARR is 15% per year. (a) How much will it cost at the end of years 1, 2, and 3 if the cost increases only by the inflation rate of 4% per year? (b) What case is this from the descriptions in Section 14.3?

An engineer planning for her sons college education made deposits into a separate high-risk brokerage account every time she earned extra money from side consulting jobs. The deposits and their timings are as follows: Year Deposit, $ 0 5,000 3 8,000 4 9,000 7 15,000 11 16,000 17 20,000 (a) If the account increased at 15% per year and inflation averaged 3% per year over the entire period, what was the purchasing power of the money in the account in terms of year zero CV dollars immediately after the last deposit in year 17? (b) Use a spreadsheet to recalculate the purchasing power if the account actually earned 6% per year and inflation was higher than expected at 4% per year. Compare the purchasing power with the total amount deposited over the 17 years.

The cost of constructing a roundabout (R/A) in a low-traffic residential neighborhood 5 years ago was $625,000. A civil engineer designing another R/A that is almost the same design estimates the cost today will be $740,000. If the cost had increased only by the inflation rate over the 5 years, determine the inflation rate per year.

An engineer deposits $10,000 into an account when the market interest rate is 10% per year and the inflation rate is 5% per year. If the account is left undisturbed for 5 years, (a) How much money will be in the account? (b) What will be the purchasing power in terms of todays dollars? (c) What is the real rate of return on the account?

Factors that increase costs and pricesespecially for materials and manufacturing costs sensitive to market, technology, and labor availabilitycan be considered separately using the real interest rate, i, the inflation rate, f, and additional increases that grow at a geometric rate, g (commonly due to maintenance and repair cost increases as machinery ages). The future amount is calculated based on a current estimate by using the relation: F = P(1 + i) n (1 + f ) n (1 + g) n = P[(1 + i) (1 + f ) (1 + g)]n The current cost to manufacture an electronic subcomponent is $145,000 per year. Provided the average annual rates for i, f, and g are 8%, 4%, and 3%, respectively, determine the equivalent future cost (a) in 3 years, and (b) in 8 years.

The Nobel Prize is administered by The Nobel Foundation, a private institution that was founded in 1900 based on the will of Alfred Nobel, the inventor of dynamite. In part, his will stated: The capital shall be invested by my executors in safe securities and shall constitute a fund, the interest on which shall be annually distributed in the form of prizes to those who, during the preceding year, shall have conferred the greatest benefit on mankind. The will further stated that the prizes were to be awarded in physics, chemistry, peace, physiology or medicine, and literature. In addition to a gold medal and a diploma, each recipient receives a substantial sum of money that depends on the Foundations income that year. The first Nobel Prize was awarded in 1901 in the amount of $150,000. In 1996, the award was $653,000; it was $1.03 million in 2014. (a) If the increase between 1996 and 2014 was strictly due to inflation, what was the average inflation rate per year during that 18-year period? (b) If the Foundation expects to invest money with a return of 5% above the inflation rate, how much will a laureate receive in 2020, provided the inflation rate averages 3% per year between 2014 and 2020?

To retire at a decent age and move to Hawaii, an engineer plans to trust her account to an investment firm that promises to make a real rate of return of 10% per year when the inflation rate is 4% per year. If the account currently is valued at $422,000 and she wants to retire in 15 years, how much (in then-current dollars) will have to be in the account for the realized rate of return to be a real 10% per year? Also, write a single-cell spreadsheet function to display the answer.

An offshore services company is considering the purchase of equipment that has a cost today of $96,000. Inflation is a concern. The manufacturer plans to raise the price exactly in accordance with the inflation rate that may be somewhere between 1% and 8% per year. Develop a graph of how much the equipment will cost 3 years from now in terms of both (a) CV, and (b) future dollars.

You just made an investment in an insurance policy that is guaranteed to pay you $1.8 million 20 years from now provided you live that long. What will be the purchasing power of that amount with respect to todays dollars if the market interest rate is 8% per year and the inflation rate stays at 3.8% per year over the 20-year period?

A top-of-the-line 3D printer costs $40,000 today. The manufacturer plans to raise the price so that a real rate of return of 5% per year is realized. In a period of 4% per year inflation, how much will the printer cost 3 years from now in terms of CV dollars?

Well-managed companies set aside money to pay for emergencies that inevitably arise in the course of doing business. A commercial solid-waste recycling and disposal company in Mexico City puts 0.5% of its after-tax income into such an account. (a) How much will the company have after 7 years if after-tax income averages $15.2 million and inflation and market interest rates are 5% per year and 9% per year, respectively? (b) What will be the buying power of that amount in todays dollars?

A company has been invited to invest $1 million in a partnership and receive a guaranteed total of $2.5 million after 4 years. By corporate policy, the MARR is always established at 4% above the real cost of capital. The real interest rate paid on capital is currently 10% per year and the inflation rate during the 4-year period is expected to average 3% per year. (a) Is the investment economically justified? (b) At what real interest rate on capital will the decision made above change?

Aquatech Microsystems spent $183,000 for a communications protocol to achieve interoperability among its utility systems. The company uses a real interest rate of 15% per year on such investments and a recovery period of 5 years. (a) What is the annual worth of the expenditure in future dollars at an inflation rate of 6% per year? (b) Write a single-cell spreadsheet function to display the correct AW value.

A DSL company has made an equipment investment of $40 million with the expectation that it will be recovered in 10 years. The company has a MARR based on a real rate of return of 12% per year. If inflation is 7% per year, how much must the company make each year (a) in constant-value dollars, and (b) in future dollars, to meet its expectation?

A European-based cattle genetics engineering research lab is planning for a major expenditure on research equipment. The lab needs $5 million of todays dollars so that it can make the acquisition 4 years from now. The inflation rate is steady at 5% per year. (a) How many future dollars will be needed when the equipment is purchased if purchasing power is maintained? (b) What is the required amount of the annual deposit into a fund that earns the market rate of 10% per year to ensure that the amount calculated in part (a) is accumulated? (c) Write a single-cell spreadsheet function that immediately displays the correct annual deposit required.

In wisely planning for your retirement, you invest $12,000 per year for 20 years into a 401-k investment account. (a) How much can you withdraw each year for 10 years, starting 1year after your last deposit, if you want a real return of 10% per year when the inflation rate averages 2.8% per year? (b) For a spreadsheet function challenge, write a single-cell function that displays the correct 10-year annual withdrawal amount directly

For a present sum of $750,000, what is the annual worth (in then-current dollars) in years 1 through 5 if the market interest rate is 10% per year and the inflation rate is 5% per year?

A recently graduated mechanical engineer wants to build a reserve fund as a safety net to pay his expenses in the unlikely event that an unexpected emergency arises. His aim is to have $45,000 developed over the next 3 years, with the proviso that the amount must have the same purchasing power as $45,000 today. If the expected market rate on investments is 8% per year and inflation is averaging 2% per year, find the annual amount necessary to meet his goal.

A multinational security software company is planning an overseas expansion that will cost $50 million of todays dollars 3 years from now. Due to a robust economy in Europe, the cost is expected to increase by 15% per year in each of the next 3 years. Assuming the inflation rate is 4% per year, determine the required annual deposit into a fund that earns the market rate of 10% per year to ensure that the amount needed in 3 years will be available. Also, write the spreadsheet function that displays the annual deposit directly.

(a) Calculate the perpetual equivalent annual worth in future dollars for years 1 through for income of $50,000 now and $5000 per year thereafter. Assume the market interest rate is 8% per year and inflation averages 4% per year. All amounts are quoted as future dollars. (b) If the amounts had been quoted in CV dollars, what is the annual worth in future dollars?

The two machines shown are being considered for a chip manufacturing operation. Assume the MARR is a real return of 12% per year and that the inflation rate is 7% per year. Which machine should be selected on the basis of an annual worth analysis if the estimates are in (a) constant-value dollars, and (b) future dollars? Solve by hand and using a spreadsheet. Machine A B First cost, $ 150,000 1,025,000 M&O, $ per year 70,000 5,000 Salvage value, $ 40,000 200,000 Life, years 5

For a real interest rate of 12% per year and an inflation rate of 7% per year, the market interest rate per year is closest to: (a) 5.7% (b) 7% (c) 12% (d) 19.8%

When all future cash flows are expressed in thencurrent dollars, the rate that should be used to find the present worth is the: (a) Real MARR (b) Inflation rate (c) Inflated interest rate (d) Real interest rate

In order to convert inflated dollars into constantvalue dollars, it is necessary to: (a) Divide by (1 + if ) n (b) Divide by (1 + f ) n (c) Divide by (1 + i) n (d) Multiply by (1 + f ) n

When the market interest rate is less than the real interest rate, then: (a) The inflated interest rate is higher than the real interest rate (b) The real interest rate is zero (c) A deflationary condition exists (d) An inflationary condition exists

The cost of a well-equipped F-150 truck was $29,350 three years ago. If the cost increased only by the inflation rate and the price today is $33,015, the inflation rate over the 3-year period was closest to: (a) 3% (b) 4% (c) 5% (d) 6%

If the market interest rate is 12% per year and the inflation rate is 5% per year, the number of future dollars in year 7 that will be equivalent to $2000 now is best represented by the equation: (a) Future dollar amount = 2000(1 + 0.198)7 (b) Future dollar amount = 2000/(1.198)

An investment of $1000 was made 25 years ago. The amount available 10 years from now at the market interest rate of 5% per year and an inflation rate of 2% per year is closest to: (a) $3085 (b) $5430 (c) $5515 (d ) $35,000

You expect to receive an inheritance of $50,000 six years from now. Its present worth at a real interest rate of 4% per year and an inflation rate of 3% per year is closest to: (a) $27,600 (b) $29,800 (c) $33,100 (d ) $50,000

For a real interest rate of 1% per month and an inflation rate of 1% per month, the nominal inflated interest rate per year is closest to: (a) 1% (b) 2% (c) 24% (d ) 24.12%

An industrial robot with a controller, teach pendants, and job-specific peripherals has an initial cost of $85,000 now, and the future cost will increase exactly by the inflation rate. The cost of a similar robot 3 years from now at a market interest rate of 10% per year and inflation rate of 4% per year is closest to: (a) $95,610 (b) $102,414 (c) $125,931 (d ) $127,261

Assume you save $6000 each year starting this year until your planned retirement 40 years from now. The buying power of the money in terms of todays dollars at the market interest rate of 10% per year and inflation rate of 5% per year is closest to: (a) $377,200 (b) $605,350 (c) $1,318,150 (d ) $2,655,550

What is the overall rate of return after 12 years?

If he decided to sell the stock or bond immediately after the fifth annual dividend, what is his minimum selling price to realize a 7% real return? Include an adjustment of 4% per year for inflation.

If Earl needed some money in the future, say, immediately after the fifth dividend payment, what would be the minimum selling price in future dollars, if he were only interested in recovering an amount that maintained the purchasing power of the original price?

As a follow-on to question 3, what happens to the selling price (in future dollars) 5 years after purchase, if Earl is willing to remove (net out) the future purchasing power of each of the dividends in the computation to determine the required selling price 5 years hence?

Earl plans to keep the stocks or bonds for 12 years, that is, until the bond matures. However, he wants to make the 7% per year real return and make up for the expected 4% per year inflation. For what amount must he sell the stocks after 12 years, or buy the bonds now, to ensure he realizes this return? Do these amounts seem reasonable to you, given your knowledge of the way that stocks and bonds are bought and sold?