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Assignment 6 EECE/CPEN 481 Instructor: Jeff Carmichael 1. Problem 1 (0.5 points) 2. Problem 2 (1.5 points) 3. Problem 3 (0.5 points) 4. Problem 4 5. Problem 5 (0.5 points) 6. Problem 6 (2 points) 7. Problem 7

1. Problem 1 Five years ago, when the relevant cost index was 105, a nuclear centrifuge cost $10,000,000. The centrifuge had a capacity of separating 4 litres of ionized solution per second. Today, a centrifuge with a capacity of 6.4 litres per second is needed, but the cost index now is 170. Assume a power- sizing exponent to reflect economies of scale, x, of 0.72, and use the power-sizing model. a. Determine the approximate cost of the larger new reactor, without adjusting for the cost index, meaning the cost in ‘five-years-ago dollars’. Round to the nearest hundred thousand dollars. b. Determine the approximate cost of the new reactor, expressed in today’s dollars. Round to the nearest hundred thousand dollars. 2. Problem 2 The provincial highway department is analyzing the reconstruction of a mountain road to Tofino. The vehicle traffic increases each year; hence the benefits to the motoring public also increase. Based on a traffic count, the benefits are projected as follows: Year End-of-Year Benefit 2028 $10,000 2029 $12,000 2030 $14,000 2031 $16,000 2032 $18,000 2033 $20,000 etc And so on, increasing $2,000 per year The reconstructed pavement will cost $230,000 in real dollars (inflation has already been accounted for), if it is installed in 2027. If it is installed in a future year after that, the cost will be higher: construction costs are expected to rise 7.5% per year. It will have a 15-year useful life. In each potential situation where you are considering beginning the project, the construction will always occur in one year, and the benefits will begin the following year. Assume a 5% discount rate. The reconstruction, if done at all, must be operational no later than 2033 (so, the last possible year of construction is 2032). Based on NPW analysis, should the project be done, and if so, in what year should it be constructed? 3. Problem 3 Sally lent a friend $10,000 at 15% interest, compounded annually. The loan will be repaid in five equal end-of-year payments. Sally expects the inflation rate to be 10%. After taking inflation into account, what rate of return is Sally receiving on the loan, rounded to the nearest tenth of a percent?

4. Problem 4 Pollution control equipment must be purchased to remove the suspended organic material from liquid being discharged from a vegetable packing plant. Two different pieces of equipment are available that would accomplish the task. A Filterco unit costs $5,000, will cost $1,300 per year to operate in the first year of operation, and has a five-year useful life. A Duro unit, on the other hand, costs $15,000, will cost $1,000 per year to operate in the first year of operation, but will have a 10- year useful life. The Duro unit will also have a salvage value of $500. Capital infrastructure costs are expected to rise at 8% per year due to inflation for the next 10 years. Therefore, when the Filterco unit needs to be replaced, the cost will be higher than the original purchase cost. Operating costs for both pieces of equipment are also expected to rise by 4% per year, due to increases in electricity costs. Assume you will borrow money to pay for the equipment, at a borrowing interest rate of 5% (which you should use as the discount rate). Based on NPW analysis, which piece of pollution control equipment should be purchased? Show your calculations, and round each NPW to the nearest dollar. 5. Problem 5 The table below contains information about the (fictional) professors’ salary index (PSI). Year PSI % increase from previous year 2012 82 3.22% 2013 87 6.00 2014 94 a 2015 b 5.90 2016 104 c 2017 108 d 2018 e 4.87 2019 118 3.80 (a) Calculate the unknown quantities a, b, c, d and e in the table. Round the PSI to whole numbers, and the % increase in PSI to two decimal places (hundredths of a percent). (b) What is the base year of the PSI? How did you determine it? (c) Given the data for the PSI, calculate the average annual price increases in salaries paid to professors for two separate periods: between 2012 and 2017, and between 2015 and 2019. In each case, round to one decimal point.

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6. Problem 6 A couple in Regina, Saskatchewan, must decide whether it is more economical to buy a home or to continue to rent. The couple rents a one-bedroom duplex for $460 a month plus $100 per month for basic utilities. Rent is expected to rise 2.5% each year, and utilities are expected to rise 5% each year. Rent and utilities costs only rise at the end of each year. So in year 1, for example, the rent will be $460 each and every month. But the rent will be higher in year 2, and so on. The couple is considering buying a home that costs $94,000. A local mortgage company will provide a loan that requires a down payment of 5%. If they buy the house, the realtor will also charge a sales commission of 5% of the value of the purchase, payable immediately. The couple would select a 25- year fixed-rate mortgage with an 7% interest rate. It is estimated that the basic utilities, home insurance, and maintenance costs will be $300 each month, and will rise 4% every year (but will only rise once per year, at the end of the year). The home is expected to appreciate in value 3.5% a year. If they buy a home, assume they will sell it in 15 years. (a) Choose a discount rate to apply for net present worth analysis. Justify your decision to choose this discount rate. (b) Analyze both options using net present worth analysis, using an annual time step (rounded to the nearest dollar). Which alternative should the couple select? (c) The problem is missing a piece of information that you would need to properly assess the options. What is it, and why is it necessary? 7. Problem 7 Craps is a popular casino gambling game that uses two (six-sided) dice. One of the many bets available is the “Hard-way 8”, which occurs if both dice come up fours when rolled. If a “hard-way 8” is rolled before a 7 is rolled or any other combination that adds to 8 is rolled, a $1 bet will typically win the player $9 (and they will get their original $1 bet back as well). If any other total number is rolled, the bet neither wins nor loses. What is the expected return for such a $1 bet, if you assume the gambler will keep playing until they either win or lose? Round to the nearest cent.

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