Engineering Economic Analysis

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Assignment 5 EECE/CPEN 481 Instructor: Jeff Carmichael

Selected problems covering material on measuring environmental benefits, inflation, and price changes, drawing in part on material from the textbook (Engineering Economic Analysis: Fourth Canadian Edition).

Point values for the problems are listed below.

1. Problem 1: 2 pts (2x value) 2. Problem 2: 1 pt 3. Problem 3: 1 pt 4. Problem 4: 1 pt 5. Problem 5: 1 pt 6. Problem 6: 2 pts (2x value)

Assignment 5 Solutions 1. Based on Problem 8-22 What methods might you use for estimating the value of the benefits for each of the following? In each case, give two examples of methods that could apply, and describe the steps involved for that exact situation. In each case, give one example of a method that would NOT work well, and describe why. (a) An hour of reduced commuting time (b) The conversion of 15 kilometers of unused railway tracks near a city of 300,000 into a new bike path (c) A reduction in annual flood risks from the Mississippi River for St. Louis by 5% (d) The creation of a new national park in the Okanagan region of BC (e) Saving a human life #1 (8-22) (a) A first approximation would use the ‘wage benefit’ method: calculate the average value of an hour of a commuter’s time, based on the average hourly income of people living in the area, and multiply this by the number of commuters using the route. But a more thorough analysis would also attempt to estimate the value of the fuel saved, based on the average fuel consumption of a commuter vehicle, and the health-related value of the corresponding reduction in pollution (through dose-response methods of estimating reduced hospital/doctor visits connected to pollution). Contingent valuation method could also be used. (b) Among the benefits we might expect from this conversion are increased revenue from tourism; reduced pollution due to reduced commuting; improvement in public health; and increased quality of life for the citizens.

Hedonic methods might be useful (did similar areas see an increase in property values when a track was converted?). Comparison with other areas might also be possible to seek parallel effects that increased tourism (‘travel cost’). As above, the health-related value of reductions in pollution due to less driving and more cycling might also be possible to measure (through traffic surveys, and dose-response methods of estimating reduced hospital/doctor visits connected to pollution). Contingent valuation method could also be used. (c) We can get historical data on the cost of flooding (relocation and replacement costs) in St Louis over the past 50 years, and make adjustments up to the present day, adjusting for inflation, population and business growth, and the growth of property values in the area to come up with an estimate of what damage from a new flood today (or in the future, if we have inflation and property value forecasts) might be. We can then compare the cost of flood reduction with the benefit of a reduced chance of flood damage. Benefits will be 5% of the anticipated flood damage. Notice that this method relies on historical data on flood risk, which won’t be able to address changes in future flood risks associated with, for example, climate change. Those changes would need to be accounted for as well. Contingent valuation method could also be used, but wouldn’t be a great choice, at least not as the main method to get an estimate. d) Travel cost method is the most likely method to use. Data on travel costs to visit other national parks, adjusted for similarities and differences, could be used to estimate the value of a possible new park. There may also be hedonic price impacts: homes near a national park might be worth more than homes far away. Contingent valuation method could also be used. e) This implies that we are seeking this value for a generic human life, that is, we want to put a value on the lives of unidentified individuals who we expect to save (or endanger) as a result of a particular policy. Techniques used include observations of avoidance behaviour (people pay more to live further from noise or risky areas that harm life) or wage or income differentials (people are paid more to do riskier jobs). These methods are often used to estimate the statistical value of a human life. Contingent valuation method could also be used.

2. Based on Problem 14-24 Assume your salary is $55,000 in 2020 and is expected to be $110,000 in 2050. Inflation is expected to average 1.8% a year during that time. (a) What will the annual average market rate of your salary increase be during that period, rounded to the one decimal place? (b) What will the annual average real rate of salary increase be, adjusted to account for inflation, rounded to one decimal place? (c) What would your salary in 2050 be, if your salary increased at the rate of inflation? Round your answers to the nearest dollar. #2 solution: Determine the market rate and then back out the real interest rate. a) $110,000 = $55,000 (F/P, i%, 30) (1 + i)30 = $110,000/$55,000 = 2 b) i = 2.1/30 – 1 = 0.0234 = 2.3% c) i’ = (i – f)/(1 + f) = (0.0234 – 0.018)/(1 + 0.018) = 0.0053 = 0.5% Future salary if only inflationary increases: 55,000 * (1+.018)^30 = $93,928

3. Based on Problem 14-41 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 $6,000, will cost $1,200 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. Neither unit is expected to have any salvage value.

Equipment 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 each year, but only 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. #3 solution: Cost of Filterco = $6,000, Life = 5 years Cost of Duro = $15,000, Life = 10 years Equipment (capital) inflation = 8% Operating inflation = 4% You need to choose an analysis period. The best choice will be 10 years. You can either buy one Duro unit, or buy a Filterco unit now and replace it in five years.

5% borrowing cost (discount rate) Filterco: Cost of replacement Filterco unit 5 years from now = capital cost (F/P, i%, 5) = 6,000 (F/P, 5%, 5) = 9,126 Converting all values to present day P: Initial capital: 6,000 (no conversion).

Replacement capital:: P = F (P/F, 5%, 5) = 6,908 Annual operating cost A=1,200, g=4%, i=5%. P = A (P/A, g=4%, 5%, 10) = 1,200 (9.126) = 10,951 Total: 6,000 + 6,908 + 10,951 = $23,859 Duro: Converting all values to present day P: Initial capital $15,.000 (no conversion) Annual operating cost: A=$1,000, g=4%, i=5%. P = A (P/A, g=4%, 5%, 10) =1,000 (9.126) = 9,126 $15,000 +9,126 = $24,126 Filterco has a lower NPW: buy that unit.

4. Based on Problem 14-57 The table below contains information about the (fictional) professors’ salary index (PSI).

Year

PSI

2012 2013 2014 2015 2016 2017 2018 2019

82 87 94 b 104 108 e 118

% increase from previous year 3.22% 6.00 a 5.90 c d 4.87 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. #4 solution: (a) Unknown quantities are calculated as follows: a. % change = [(94 − 87)/87] x 100% = 8.05% b. PSI = 94 (1.085) = 100 c. % change = (104 − 100)/100 = 4.47% d. % change = (108 − 104)/104 = 3.85% e. PSI = 108 (1.0487) = 113 (b) The base year is 2015. This is the year in which the index has a value of 100. (c) i. PSI (2012) = 82 PSI (2017) = 108 h = 5 years i* = ? i* = (108/82)0.2 − 1 = 5.7% ii. PSI (2015) = 100 PSI (2019) = 118 n = 4 years i* = ? i* = (118/100)0.25 − 1 = 4.2%

5. Based on Problem 14-59 General price inflation is estimated to be 2.2% for the next five years, 3% in the five years after that, and 3.8% in the following five years. Suppose you invest $10,000 today and will earn 4.6% interest per year, compounding the interest annually for those 15 years. (a) How much money will be in your investment account in 15 years, rounded to the nearest dollar? (b)What will the real value of that investment be in 15 years, adjusting for the nasty bite of inflation? (c) What will the real average annual growth rate of your investment be, over the 15 years (rounded to one decimal place)? #5 solution: Actual Dollars: F = $10,000 (F/P, 4.6%, 15) = $19,632 Real Dollars:

Year 1−5 6−10 11−15

Inflation 2.2% 3.0% 3.8%

R$ in today’s base = $19,632 (P/F, 2.2%, 5) (P/F, 3.0%, 5) (P/F, 3.8%, 5) = $12,605 Thus, the real growth in purchasing power has been: $12,605 = $10,000 (1 + i*)15 i * = 1.6%

6. Based on Problem 14-71 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 $120 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 (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? #6 solution: (a) Choose a discount rate Best value among all the interest rates given is the borrowing cost, which is the most common lowest value we would use. The only other plausible alternative would be the MARR (which isn’t given), which might be the interest they could earn on their continued savings (the avoided closing costs and down payment).

7% (b) NPW analyses Alternative 1: Rent Rent increases at 2.5%/yr and utilities increase at 5% / year. Use borrowing cost (7%) as discount rate: most indicative rate given.

Rent starts at $5,520 per year, and utilities start at $1,440 per year.

NPW = (5520)((P/A1, , g=2.5%, 7%, 15) + (1,440)(P/A, g=5%, 7%, 15) = ($76,023)

Alternative 2: Buy a House $4,700 down payment plus $4,700 sales commission for a cash requirement of $9,400. That leaves $89,300 to borrow.

Mortgage interest rate per month = 7%/12 = 0.583% n = 25 years × 12 = 300 payments.

Monthly mortgage payment (A): A = (94,000 – 4,700)(A/P, 0.583%, 300) = $631/mo = $7,574 / yr Utility/insurance / maintenance costs start at $300 x 12 = $3,600 in year 1, and rise at 4% per year. The geometric series present worth formula can be used.

Appreciation in value and sale of house: House value appreciates at 3.5% per year for 15 years, and is sold at end of 15th year. Revenue on sale is then: $94,000 * (1+.035)^15 = $157,483 Need to subtract the remaining balance on the mortgage of $54,359. Net revenue = $103,124 of “salvage value”.

Discounted value of net revenue from sale of house = $37,377 So the present worth of all expenses and revenues is PW = $9,400 + (3,600)((P/A1, , g=4%, 7%, 10) + (7,574)(P/A, 7%, 10) + (103,124) (P/F, 7%, 15) = ($73,820) So renting is better (cheaper) than buying the house.