Ultimate Writer

5

This assignment asks you to come up with a simplified version of a costing exercise for your chosen project.

You must include (10% for each, except Point 11 which is considered part of the other points):

1. Costs in (at least) three time categories: the start of the project, the middle of the project and the end of the project. A time category may consist of more than one time period (and probably will) – for example, the middle of your project may be 10 years long. These costs should be listed in a table similar to those seen in the European Commission Textbook.

2. At least three different types of cost ‘elements’: present costs, future costs and annuities (regular payments). If your project involves buying a machine immediately (present cost), paying maintenance costs once a year for the 10 years you own the machine (annuity) and then selling the machine for scrap at the end of 10 years (future cost), then you have everything you need.

3. Two different discount rates: an appropriate MARR for financial and profit calculations, and a social discount rate to use when evaluating the discount rate from the point of view of society. You may wish to use the Ramsey equation for the social discount rate.

4. A calculation of the present value of costs using the MARR, and using the social discount rate. It may be convenient to have these as separate rows on your cost table (see sample answer).

	Time Period
	0	1	2	3	4	Total
	Start	Middle	End
Item 1
Item 2
Item 3
Total
PV @ MARR
PV @ SDR
MARR		per period
SDR		per period

5. At least one example of top-down macro-costing.

6. At least one example of bottom-up micro-costing.

7. At least one shadow wage calculation, with an explanation of the methods used and choices made.

8. At least one non-wage shadow price calculation, with an explanation of the methods used and choices made.

9. Short statement and explanation of all assumptions and estimates made. (This can be its own section, or integrated into other sections.)

10. All sources used, cited in APA format.

11. Appropriate adjustments made for inflation, if necessary.

Sample Project: Selling chewing gum for charity.

Chenguang (晨光) is a university student living in BC, with a demanding job that encourages overtime work. Due to her work, she is only able to attend lectures on Mondays (she keeps up with her courses by getting notes from her classmates and submitting assignments online).

Chenguang wants to raise money for charity by selling chewing gum to her fellow students over a one-week period. On Sunday, she will buy the gum and print out pamphlets. On Monday morning, she will give a ten-minute presentation in each of her three lectures.

From Tuesday to Thursday, she will sell chewing gum from 5:00 PM to 7:00 PM. On Friday she will sell chewing gum from 7:00 PM to 10:00 PM. This is time she would normally be working (and earning overtime pay). On Saturday, she will sell chewing gum from 9:00 AM to 5:00 PM. This will be done by paying her room-mate $20 to take her regularly scheduled work shift. The money will be paid on Sunday morning, once the shift has been successfully completed.

On Sunday, Chenguang will also transfer money to the charity for the amount of money that she raised by selling chewing gum.

I. Summary Table

II. Discount Rates

II.A. Finding the MARR

Since Chenguang is a university student, the interest rate on student loans was considered appropriate.

According to Student Aid BC[footnoteRef:1], most student loans are an integrated combination of Canada student loans and BC student loans. The BC portion of the loan charges ‘prime interest’, while the Canada portion of the loan charges ‘prime interest’ plus 2.5% per year. [1: Manage your debt [Web page]. (n.d.). Retrieved from https://studentaidbc.ca/plan/debt ]

I don’t know what Chenguang’s mix of Canada and BC loan portions is, so I’ve assumed that each portion contributes 50%. This assumption may be revised later if necessary.

As of October 18, 2017, Canada’s prime interest rate was 3.20% per year[footnoteRef:2]. This means that the BC portion will charge 3.20% a year, and the Canada portion will charge 5.70% a year. [2: Bank of Canada. Daily Digest [Web page]. Retrieved from http://www.bankofcanada.ca/rates/daily-digest/ on October 22, 2017.]

All together, the interest rate on a student loan with this mix will be

a year

Our project uses days as its time period, not years. Assume there are 365 days in a year. Then, at a daily interest rate of i, over the course of a year $1 becomes $1 x (1 + i)365. Over the same time period, at an interest rate of 4.45% a year, $1 becomes $1 x (1 + 4.45%). Therefore, we can find the daily interest rate we seek by setting

Therefore, in per day terms, our MARR = 0.011929% per day.

III.B. Finding the Social Discount Rate

According to Annex II of European Commission (2015), it is common to estimate the social discount rate using the formula

where SDR = Social Discount Rate p = pure time preference, e = elasticity of marginal utility of consumption and g is expected per-capita consumption growth,

Both European Commission (2015) and Paulden, Galvanni, Chakraborty, Kudinga, & McCabe (2016) agree that there is no consensus on whether the pure time preference term should be zero or non-zero. As a compromise, I am using the Stern Review value reported in European Commission (2015) of 0.1%. This is very low, but not quite zero.

Evans (2005) calculated the elasticity of marginal utility of consumption for Canada as lying between 1.25 and 1.3. I will use the average of these values, setting e = 1.275. I assume that the values calculated for Canada in 2005 continue to be valid into the future.

Finally, European Commission (2015) points out that real per capita GDP growth is often used as a proxy for g. Using Statistics Canada data on British Columbia’s real GDP[footnoteRef:3] and population[footnoteRef:4], I calculate an average yearly growth rate in real GDP of 1.81% for the years between 2011 and 2015 (the last for which real GDP statistics are available). My g is therefore 1.81%. [3: http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/econ50-eng.htm ] [4: http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/demo02a-eng.htm ]

In per-year terms, the social discount rate is p + eg = 0.1% + 1.275 x 1.81% = 2.41%.

Assuming 365 days in a year, in per-day terms,

Once we have the daily MARR and SDR, the present value of costs in Day t are just the total costs in Day t multiplied by (P/F,r,t) = 1/(1 + r)t using the appropriate r (MARR or SDR).

If you’re feeling fancy and you have a cost that repeats from Day 1 to Day N, you can also find its present worth by multiplying the repeated cost by (P/A,r,N).

III. E-mail Costs (Macro-Costing)

Before anything else, Chenguang must send an e-mail to her professor, asking for permission to give a 10-minute presentation in class.

I assume Chenguang spends half an hour composing and sending the e-mail on Sunday (Day 0 of the project). Her professor spends five minutes replying on the following Thursday (Day 3).

I further assume that the income earned by Chenguang and the professor are good measures of the opportunity cost of their time when writing and replying to the e-mail.

Chenguang’s job pays her minimum wage. In BC, the minimum wage is $11.35 per hour (Correia, 2017). Assuming other costs are negligible, and that the student pays no income tax, Chenguang’s cost of writing the e-mail is therefore $11.35/2 = $5.68 on Day 0.

What about the professor’s costs? According to Statistics Canada[footnoteRef:5], for the 2016/2017 academic year, the average university instructor in Canada earned $98,400. According to the Inflation Calculator web site[footnoteRef:6], which uses data from Statistics Canada, BC’s CPI was 120.7 in 2016 and 123.5 in 2017. If instructor salaries went up at the rate of inflation, then the average salary for the 2017/2018 academic year should be $98,400 x 123.5 / 120.7 = $100,682.68 [5: http://www.statcan.gc.ca/daily-quotidien/170425/dq170425b-eng.htm ] [6: http://inflationcalculator.ca/british-columbia/ ]

We need to pro-rate 5 minutes of this yearly salary. There are 252 working days in BC in from September 1, 2017 to September 1, 2018[footnoteRef:7]. Assuming that a professor works 8 hours each of these days, and knowing there are 60 minutes in each hour, this means there are 120,960 working minutes in the year between September 2017 and September 2018. The cost of 1 minute of professor time is therefore $100,682.68/120,960 = $0.83, and the cost of 5 minutes is therefore 5 x $0.83 = $4.16. This cost is incurred on Day 3. [7: http://www.workingdays.ca/British%20Columbia.htm ]

IV. Presentation (Macro-Costing)

I assume there are two costs to the presentation: half an hour spent planning the presentation on Sunday, and 10 minutes of class time to give the presentation on Monday.

Assuming the minimum wage she earns at work is a reasonable measure of the opportunity cost of her time on Sunday, the cost of preparing the presentation is $11.35/2 = $5.68. This is incurred on Sunday, Day 6.

Assume there are 60 students in Chenguang’s class, that students attend an average of 12.5 hours of lectures per week (5 courses per term, 3 lectures per course per week, 50 minutes per lecture), and that there are 26 teaching weeks in a university year.

Then, there are 26 x 12.5 x 60 = 19,500 minutes of lecture per year.

According to Statistics Canada[footnoteRef:8], average tuition in BC for the 2016/2017 academic year was $5,534. According to the Inflation Calculator web site, BC’s CPI was 120.7 in 2016 and 123.5 in 2017. If tuition went up at the rate of inflation, then average tuition for the 2017/2018 academic year should be $5,534 x 123.5 / 120.7 = $5,662.38 [8: https://www.statcan.gc.ca/daily-quotidien/160907/cg-a001-eng.htm ]

Assume tuition only pays for lectures. On average, lectures cost $5,662.38/19,500 = $0.29 per minute, per student. Since there are 60 students in the class, the cost of the presentation is 10 x $0.29 = $17.42. This is paid on Monday, Day 7 of the project.

V. Fliers (Micro-Costing)

Fliers are made using a printer, printer ink and paper. I will assume that Chenguang owns an HP ENVY 4520 printer, and uses HP 63 black ink cartridges and standard 20 lb. (75 g/m2) letter-sized paper.

In 2017, there is no import tariff[footnoteRef:9] on either black ink (321511 Printer Ink – Black) or letter-sized 75 g/m2 paper (480256 Paper, Fine,<=10% Fib Mech/Chem-Mec Proc, Sht <=435X297Mm,>=40 G/M²<=150G/M², Uncoated). I therefore assume the Standard Conversion Factor for the shadow prices of these products is 1. [9: Customs Tariff, http://www.cbsa-asfc.gc.ca/trade-commerce/tariff-tarif/menu-eng.html ]

I used amazon.ca as a source of price data[footnoteRef:10], and assumed that Chenguang bought her paper and ink at advertised list prices, with free (or Prime) shipping. [10: I also checked amazon.com to make sure there were no drastic differences in the prices of the same product.]

In particular, I assumed she bought 1,500 sheets of Amazon Basics paper[footnoteRef:11] for $18.99 ($0.013 per sheet) and re-manufactured high-yield HP 63 XL cartridges[footnoteRef:12] by the pair, paying $28.66. Since each XL cartridge can print 480 sheets of paper, assuming the re-manufactured cartridges have the same yield, this implies an ink cost of $0.03 per sheet. [11: https://www.amazon.ca/AmazonBasics-Bright-Multipurpose-Copy-Paper/dp/B01FV0F75G/ ] [12: https://www.amazon.ca/Novajet-Cartridge-Replacement-DeskJet-OfficeJet/dp/B01KJHNDZC/ ]

This means a cost per flyer of about $0.04. I assume that Chenguang chooses to print 1 flier for every 10 students in the class and every 10 pieces of gum (see below). There are 60 classmates and 380 pieces of gum, so she will print 44 flyers at a cost of 44 x $0.04 = $1.87. (Difference in calculation due to Excel using full precision and my reporting rounded numbers.)

I assume that the student spends half an hour looking up flyer designs online and setting them up to work with her printer. Since her opportunity cost is assumed to be equal to the minimum wage, this costs $11.35 / 2 = $5.68.

I assume electrical, printer depreciation and other costs are negligible.

The total cost of the flyers is $5.68 + $1.87 = $7.55, paid on Sunday, Day 6 of the project.

VI. Gum (Shadow Price, SCF)

I assume that Chenguang plans to buy and sell original-flavour, double-twist tie Dubble Bubble gum, and that she can buy it at the price at which it is sold on amazon.ca without having to pay for shipping.

Dubble Bubble can be bought in packs of 340[footnoteRef:13] for $45.97, 380[footnoteRef:14] for $54.79 or 1 lb.[footnoteRef:15] for 16.99 (there are about 72 units[footnoteRef:16] per lb.). This implies per-unit costs of $0.14 and $0.24 for the 1-lb. bag. I assume Chenguang buys the 380-count bucket, and intends to sell all the units while charging $0.25 per Dubble Bubble. [13: https://www.amazon.ca/Dubble-Bubble-Gum-53-9-Ounce/dp/B00300CWEE/ ] [14: https://www.amazon.ca/Dubble-Bubble-Bubblegum-380ct-Tub/dp/B000NMCOYK/ ] [15: https://www.amazon.ca/Original-Dubble-Bubble-Gum-1lbs/dp/B00T3X5IYI/ ] [16: https://www.sweetfactory.com/original-dubble-bubble-bubblegum-wrapped-1-lb-bag/ ]

To find the shadow price of 380 pieces of Dubble Bubble, we will multiply its market price by a Shadow Conversion Factor (SCF) found using the formulas from Annex III of European Commission (2015).

According to European Commission (2015), in cases such as this one where there is only an import tariff and no export tariffs or subsidies, the SCF can be calculated as

where M = value of imports, X = value of exports and TM = value of the import tariff collected, which for ad valorem tariffs can be calculated as tM x M, where tM is the % tariff on M.

According to the Customs Tariff Archive[footnoteRef:17], the import tariff on category 170410 Chewing Gum (With or Without Sugar Coating) has been constant at 9.5% from 2007 to 2017. [17: Customs Tariff Archive, http://www.cbsa-asfc.gc.ca/trade-commerce/tariff-tarif/archive-eng.html (2017 tariffs also available on the main site)]

I collected information on M and X from 2007 to 2016 for 170410 Chewing Gum (With or Without Sugar Coating) from Trade Data Online and used it to calculate SCF for each year. The SCF I finally used was the average of these, and equal to about 0.9855.

The shadow price of 380 pieces of Dubble Bubble is therefore

paid on Sunday (Day 6)

170410 Chewing Gum (With or Without Sugar Coating), $thousands
Year	M	X	Import Tariff	Tm	SCF
2007	21078	68802	9.50%	2002.41	0.978
2008	12744	55974	9.50%	1210.68	0.983
2009	10688	61368	9.50%	1015.36	0.986
2010	8774	59718	9.50%	833.53	0.988
2011	9687	56313	9.50%	920.27	0.986
2012	10785	58951	9.50%	1024.58	0.986
2013	10812	63463	9.50%	1027.14	0.986
2014	11108	72180	9.50%	1055.26	0.987
2015	12352	78301	9.50%	1173.44	0.987
2016	12829	82553	9.50%	1218.76	0.987
2017			9.50%
				AVERAGE	0.9855

VII. Cost of Selling (Shadow Wage)

I will ignore any transport costs or costs of renting a room or table to sell the gum in. The transport cost assumption may be justified if the student works, studies and lives on and very near campus. Assuming a zero shadow cost of renting the space is more problematic, and this assumption should be challenged in the sensitivity analysis.

Our student works at a job that encourages overtime and pays the BC minimum wage of $11.35 per hour. According to BC law[footnoteRef:18], employers must pay 1.5 times this wage for hours of work exceeding 8 and less than 12, and twice that rate for hours of work exceeding 12. [18: https://www2.gov.bc.ca/gov/content/employment-business/employment-standards-advice/employment-standards/factsheets/hours-of-work-and-overtime ]

Assume our student normally works from 9 to 7 Tuesday – Thursday, 9 to 10 Friday and 9 to 5 Saturday. Her scheduled gum selling times are 5 to 7 Tuesday – Thursday, 7 to 10 Friday and 9 to 5 Saturday. If these schedule hours include travel and set-up time, and she works her regular hours otherwise, then the costs to her are as follows:

Student normally works…	From	Gum sale	Cost	Dollars
10 hours Tuesday	9 to 7	5 to 7	2 x 1.5	34.05
10 hours Wednesday	9 to 7	5 to 7	2 x 1.5	34.05
10 hours Thursday	9 to 7	5 to 7	2 x 1.5	34.05
13 hours Friday	9 to 10	7 to 10	2 x 1.5 + 1 x 2	56.75
8 hours Saturday	9 to 5	9 to 5	8 x 1	90.8

VIII. Fees (Future Costs)

On Sunday, Day 13 of the project, the student must pay 2 fees: Chenguang must pay her room-mate $20 for having taken her shift on Saturday, and she must transfer to the charity the amount she earned by selling bubble gum. She plans to sell 380 pieces at $0.25 each, so this will be a transfer of $95. I assume this can be done via smartphone in a matter of seconds, so that the shadow wage may be ignored.

References

Correia, C. (2017, August 15). B.C. to boost minimum wage by 50 cents to $11.35. CBC News. Retrieved rom http://www.cbc.ca/news/canada/british-columbia/bc-minimum-wage-september-2017-1.4248636

European Commission Directorate-General for Regional and Urban Policy. (2015). Guide to Cost-Benefit Analysis of Investment Projects: Economic appraisal tool for Cohesion Policy 2014 – 2020. Retrieved from http://ec.europa.eu/regional_policy/en/information/publications/guides/2014/guide-to-cost-benefit-analysis-of-investment-projects-for-cohesion-policy-2014-2020

Paulden, M., Galvanni, V., Chakraborty, S., Kudinga, B. & McCabe, C. (2016). Discounting and the Evaluation of Health Care Programs. Retrieved from https://www.cadth.ca/sites/default/files/pdf/CP0008_Economic_Evaluation_Guidelines_Discount_Rate_Report.pdf