Year 10 GENERAL MATHEMATICS

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1 Year 10 GENERAL MATHEMATICS UNIT 2, TOPIC 3 - Part 1 Percentages and Ratios A lot of financial transaction use percentages and/or ratios to calculate the amount owed. When you borrow money for a certain period of time from a bank or financial institution by taking a loan or mortgage, you must repay the original amount borrowed plus an extra amount called the interest. Similarly, if you lend money for a certain period of time to a bank or financial institution, you are expected to be rewarded by eventually getting your money back plus the interest. There are two common ways that interests are calculated, they are known as Simple Interest and Compound Interest. NOTE: All questions for Part 1 are included in this booklet. Page 1 of 27

2 Table of Contents Year 10 GENERAL MATHEMATICS... 1 UNIT 2, TOPIC Part 1 Percentages and Ratios... 1 Table of Contents A Percentage Change... 3 Calculating percentage change... 3 Exercise 8A B Financial applications of ratios and percentages... 6 Shares and currency... 6 Share dividends... 6 Percentage dividends... 6 The price- to- earnings ratio... 7 Mark- ups and discounts... 7 Goods and services tax... 7 Exercise 8B Applications of percentage change... 8 Year 10 GENERAL MATHEMATICS UNIT 2, TOPIC Part 2 Interest, Purchase options and Depreciation A Simple interest applications The simple interest formula Using a CAS calculator to calculate Simple Interest B Compound Interest, Inflation And Appreciation Compound Interest The formula for Compound Interest is: Inflation Appreciation C Personal loans and Effective Interest Using a calculator finance solver Effective rate of interest D Depreciation Flat- rate depreciation Reducing- balance depreciation Unit cost depreciation Page 2 of 27

3 8A Percentage Change Percentages can be used to give an indication of the amount of change that has taken place, which makes them very useful for comparison purposes. Percentages are frequently used in comments in the media. For example, a company might report that its profits have fallen by 6% over the previous year. The percentage change is found by taking the actual amount of change that has occurred and expressing it as a percentage of the starting value. Example 1 - The price of petrol was $1.40 per litre but has now risen to $1.65 per litre. What is the percentage change in the price of petrol? Calculating percentage change In the business world percentages are often used to determine the final selling value of an item. For example, during a sale period a store might decide to advertise 25% off everything rather than specify actual prices in a brochure. At other times, when decisions are being made about the financial returns needed in order for a business to remain viable, the total production cost plus a percentage might be used. In either case, the required selling price can be obtained through multiplying by an appropriate percentage. Consider the situation of reducing the price of an item by 18% when it would normally sell for $500. The reduced selling price can be found by evaluating the amount of the reduction and then subtracting it from the original value as shown in the following calculations: Reduction of 18%:!"!"" 500 = $90 Reduced selling price: $500 $90 = $410 The selling price can also be obtained with a one- step calculation of!" 500 = $410.!"" Page 3 of 27

4 In other words, reducing the price by 18% is the same as multiplying by 82% or (100 18)%. To reduce something by x%, multiply by (100 x)%. Conversely, to increase something by x%, multiply by (100 + x)% Example 2 - Increase $160 by 15%. When a large number of values are being considered in a problem involving percentages, spreadsheets or other technologies can be useful to help carry out most of the associated calculations. For example, a spreadsheet can be set up so that entering the original price of an item will automatically calculate several different percentage increases for comparison. On a CAS Exercise 8A Question 1 If the price of bananas was $2.65 per kg, calculate the percentage change (increase or decrease) if the price is now: a $3.25 per kg b $4.15 per kg c $1.95 per kg d $2.28 per kg. Question 2 Calculate the percentage change in the following situations. a A discount voucher of 4 cents per litre was used on petrol advertised at $1.48 per litre. b A trade- in of $5200 was applied to a car originally selling for $ c A shop owner purchases confectionary from the manufacturer for $6.50 per kg and sells it for 75 cents per 50 grams. d A piece of silverware has a price tag of $168 at a market, but the seller is bartered down and sells it for $147. Question 3 The price of a bottle of wine was originally $ After it received an award for wine of the year, the price was increased by 12.25%. Twelve months later the price was reduced by 15.5%. a What is the final price of a bottle of this wine? b What is the percentage change of the final price from the original price? Page 4 of 27

5 Y10 General Maths FINANCIAL ARITHMETIC Question 4 A mobile phone is sold for $ If this represents a 15% reduction from the RRP, what was the original price? Question 5 A car yard offers three different vehicles for sale. The first car was originally priced at $18,750 and is now on sale for $14,991. The second car was originally priced at $12,250 and is now priced $9999, and the third car was originally priced at $23,990 and is now priced $19,888. Which represents the largest percentage reduction? Question 6 The following table shows the changes in property prices in the major capital cities of Australia over a five- year period. a) When comparing the median house prices for the five capital cities over this $525,000 $929,842 time period, which city had the largest Sydney: Melbourne: $505,000 $688,000 percentage change and by how much? Perth: $465,000 $535,000 b) In the same time period, which city had Brisbane: $435,000 $475,000 the smallest percentage change? Question 7 A power company claims that if you install solar panels for $1800, you will make this money back in savings on your electricity bill in 2 years. If you usually pay $250 per month, by what percentage will your bill be reduced if their claims are correct? Question 8 A house originally purchased for $ is sold at a later date for $ a What is the percentage change in the value of the house over this time period? b The new buyer pays a deposit of 15% and borrows the rest from a bank. They are required to pay the bank 5% of the total borrowed each year. If they purchased the house as an investment, how much should they charge in rent per month in order to fully cover their bank payments? Question 9 The following table shows the changes in an individual s salary over several years. Use CAS or a spreadsheet to answer these questions. a Enter the information in your CAS calculator or spreadsheet and use it to evaluate the percentage change of each salary from the previous year. b What entry is required in cell C3 in order to calculate the percentage change from the previous year? Question 10 A population of possums in a particular area, N, changes every month according to the rule N = 1.55M 18, where M is the number of possums the previous month. The number of possums at the end of December is 65. Use CAS to: a construct a table and draw a graph of the number of possums over the next 6 months b evaluate the percentage change in each of the next 6 months. Page 5 of 27

6 8B Financial applications of ratios and percentages Shares and currency Share dividends Many people earn a second income through investments such as shares, seeking to make a profit through buying and selling shares in the stock market. Speculators attempt to buy shares when they are low in value and sell them when they are high in value, whereas other investors will keep their shares in a company for a longer period of time in the hope that they continue to gradually rise in value. When you purchase shares you are effectively becoming a part- owner of a company, which means you are entitled to a portion of any profits that are made. This is known as a dividend. To calculate a dividend, the profit shared is divided by the total number of shares in the company Example 3 Calculate the dividend payable for a company with 2,500,000 shares when $ of its annual profit is distributed to the shareholders? Percentage dividends Shares in different company can vary drastically in price, from cents up to hundreds of dollars for a single share. As a company becomes more successful the share price will rise, and as a company becomes less successful the share price will fall. An important factor that investors look at when deciding where to invest is the percentage dividend of a company. The percentage dividend is calculated by dividing the dividend per share by the share price per share. Percentage dividend = dividend per share share price per share Example 4 Calculate the percentage dividend of a share that costs $13.45 with a dividend per share of $0.45. Give your answer correct to 2 decimal places. Page 6 of 27

7 The price- to- earnings ratio The price- to- earnings ratio (P/E ratio) is another way of comparing shares by looking at the current share price and the annual dividend. It is calculated by dividing the current share price by the dividend per share, giving an indication of how much shares cost per dollar of profit. Price to earnings ratio = share price per share dividend per share Example 5 Calculate the price- to- earnings ratio for a company whose current share price is $3.25 and has a dividend of 15 cents. Give your answer correct to 2 decimal places. Mark- ups and discounts In the business world profits needs to be made, otherwise companies may be unable to continue their operations. When deciding on how much to charge customers, businesses have to take into account all of the costs they incur in providing their services. If their costs increase, they must mark up their own charges in order to remain viable. For example, any businesses that rely on the delivery of materials by road transport is susceptible to fluctuations in fuel prices, and they will take these into account when pricing their services. If fuel prices increase, they will need to increase their charges, but if fuel prices decrease, they might consider introducing discounts. Example 6 A transport company adjusts their charges as the price of petrol changes. By what percentage, do their fuel costs change if the price per litre of petrol increases from $1.36 to $1.42? Goods and services tax In Australia we have a 10% tax that is charged on most purchases, known as a goods and services tax (or GST). Some essential items, such as medicine, education and certain types of food, are exempt from GST, but for all other goods GST is added to the cost of items bought or services paid for. If a price is quoted as being inclusive of GST, the amount of GST paid can be evaluated by dividing the price by 1.1 Example 7 Calculate the amount of GST included in an item purchased for a total of $ Page 7 of 27

8 Exercise 8B Applications of percentage change Question 1. Calculate the dividend payable per share for a company with: a) 32,220,600 shares, when $1,995,000 of its annual profit is distributed to the shareholders b) 44,676,211 shares, when $5,966,000 of its annual profit is distributed to the shareholders c) 263,450 shares, when $8,298,675 of its annual profit is distributed to the shareholders. Question 2. How many shares are in a company that declares a dividend of: a) 28.6 cents per share when $1,045,600 of its annual profit is distributed? b) $2.34 cents per share when $3,265,340 of its annual profit is distributed? c) $16.62 cents per share when $9,853,000 of its annual profit is distributed? Question 3. Alexandra is having trouble deciding which of the following companies to invest in. She wants to choose the company with the highest percentage dividend. Calculate the percentage dividend for each company to find out which Alexandra should choose. a) A clothing company with a share price of $9.45 and a dividend of 45 cents b) A mining company with a share price of $53.20 and a dividend of $1.55 c) A financial company with a share price of $33.47 and a dividend of $1.22 d) A technology company with a share price of $7.22 and a dividend of 41 cents e) An electrical company with a share price of $28.50 and a dividend of $1.13 Question 4. Correct to 2 decimal places, calculate the price- to- earnings ratio for a company with: a) a current share price of $12.50 and a dividend of 25 cents b) a current share price of $43.25 and a dividend of $1.24 c) a current share price of $79.92 and a dividend of $3.32 d) a current share price of $ and a dividend of $7.64. Question 5. Calculate the current share price for a company with: a) a price- to- earnings ratio of 22.4 and a dividend of 68 cents b) a price- to- earnings ratio of 36.8 and a dividend of 81 cents c) a price- to- earnings ratio of 17.6 and a dividend of $1.56 d) a price- to- earnings ratio of 11.9 and a dividend of $3.42. Question 6. A coffee shop adjusts its charges as the price of electricity changes. By what percentage does its power cost change if the price of electricity increases from: a) 88 cents to 94 cents per kwh? b) 92 cents to $1.06 per kwh? Question 7. An electrical goods department store charges $50 plus n cents per km for delivery of its products, where n = the number of cents over $1.20 of the price per litre of petrol. What will be the percentage increase in the total delivery charge for a distance of 25 km when the petrol price changes from $1.45 to $1.52 per litre? Question 8. Two companies are competing for the same job. Company A quotes a total of $5575 inclusive of GST. Company B quotes $5800 plus GST, but offers a 10% reduction on the total price for payment in cash. Which is the cheaper offer, and by how much? Question 9. A plumber quotes his clients the cost of any parts required plus $74.50 per hour for his labour, and then adds on the required GST. a How much does he quote for a job that requires $250 in parts and should take 4 hours to complete? b If the job ends up being faster than he first thought, and he ends up charging the client for only 3 hours labour, what percentage discount on the original quote does this represent? Page 8 of 27

9 Question 10. A boat is purchased during a sale for a cash payment of $2698. a) If it had been discounted by 15%, and then a further $895 was taken off for a trade- in, what was the original price? b) What is the percentage change between the original price and the cash payment? Question 11. A carpet company offers a trade discount of 12.5% to a builder for supplying the floor coverings on a new housing estate. a) If the builder spends $32 250, how much was the carpet before the discount was applied? b) If the builder charges his customers a total of $35,000, what percentage discount have they received? Question 12. The Australian government is considering raising the GST tax from 10% to 12.5% in order to raise funds and cut the budget deficit. The following shopping bill lists all items exclusive of GST. Calculate the amount by which this shopping bill would increase if the rise in GST did go through. Note: GST must be paid on all of the items in this bill. litres of soft drink $2.80 Bottle of shampoo $7.60 Large bag of pretzels $5.30 Box of chocolate $8.35 Frozen lasagne $ tins of dog food $3.50 Question 13. The following table shows the mark- ups and discounts applied by a clothing store. Item Cost price Normal retail price (255% mark- up) Standard discount (12.5% mark- down of normal retail price) January sale (32.25% mark- down of normal retail price) Stocktake sale (55% mark- down of normal retail price) Socks $1.85 Shirts $12.35 Trousers $22.25 Skirts $24.45 Jackets $32.05 Ties $5.65 Jumpers $19.95 Use a CAS calculator to answer these questions. a) Enter the information in your CAS or spreadsheet and use it to evaluate the normal retail prices and discount prices for each column as indicated. b) What entry is required in cell F5 in order to calculate the marked- down price? c) What would be the percentage change between the standard discount price and the stocktake sale price of a jacket? Page 9 of 27

10 Year 10 GENERAL MATHEMATICS UNIT 2, TOPIC 3 - Part 2 Interest, Purchase options and Depreciation When you borrow money for a certain period of time from a bank or financial institution by taking a loan or mortgage, you must repay the original amount borrowed plus an extra amount called the interest. Similarly, if you lend money for a certain period of time to a bank or financial institution, you are expected to be rewarded by eventually getting your money back plus the interest. There are two common ways that interests are calculated, they are known as Simple Interest and Compound Interest. Questions Chapter 9 Financial arithmetic 9A: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12 9B: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18 9C: In Notes 9D: 1, 2, 3, 6, 7, 8, 9, 10, 11, 14, 15, 16, 19 Page 10 of 27

11 9A Simple interest applications The simple interest formula When you invest money and receive a return on your investment, the amount of money you receive on top of your original investment is known as the interest. Similarly, when you take out a loan, the additional amount that you pay back on top of the loan value is known as the interest. Interest is usually calculated as a percentage of the amount that is borrowed or invested, which is known as the principal. Simple interest involves a calculation based on the original amount borrowed or invested; as a result, the amount of simple interest for a particular loan is constant. For this reason simple interest is often called flat rate interest. It is important to remember that the rate and the time must be compatible. For example, if the rate is per annum (yearly, abbreviated p.a. ), the time must also be in years. The value of a simple interest investment can be evaluated by adding the total interest at any point in time to the value of the principal. Example: John borrows $5000 from a bank to buy his first car. The bank lends him over a period of 5 years with an interest rate of 7.8% per year. Using simple interest. Year Principal Interest Interest Accumulation Using a CAS calculator to calculate Simple Interest On a calculator Page enter the following Then press ENTER for the interest after 1 year On the next line type the following ans Then press ENTER for the interest after 2 years Press ENTER again for the interest after 3 years and continue to press ENTER a 4 and 5 time. Page 11 of 27

12 In summary, Simple Interest is calculated by!"! Simple Interest is calculated by the formula = S. I. =!"" Where I = the amount of interest earned ($) P = Principal amount of money borrowed or invested ($) r = Rate of the interest per year or per annum (pa) (%) T = Term - borrowed or investment period At the end of the borrowing or investing period, the total amount of money repay or reward is calculated as followed. A = P + I Where A = Total Amount repay or reward ($) P = Principal ($) I = Simple Interest ($) Example 8: Calculate the amount of simple interest, I, earned and the total amount, A, at the end of the term if: (a) $ is invested for 5 years at 9.5% p.a. Using a CAS calculator On a calculator Page enter the following Then press ENTER for the interest after 1 year On the next line type the following ans Page 12 of 27

13 Then press ENTER for the interest after 2 years Press ENTER again for the interest after 3 years and continue to press ENTER a 4 th and 5 th time. Now add the interest to the Principal to find the Total Amount A = P + I $17,700 = $5,700 + $12,000 (b) $2500 is invested for 3 months at 4.5% p.a. Example 9: Lily is saving for a new computer. How long, to the nearest month, will it take her to earn $650 simple interest on $8375 that is invested at 6.25% p.a.? Page 13 of 27

14 Example 10: After comparing investment options from a variety of institutions, Lynda and Jason decided to invest their $ in State Government bonds at 7.75% p.a. The investment is for 5 years and the interest is paid semi- annually (every six months). Calculate how much interest: (a) They receive in every payment (b) Will be received in total Page 14 of 27

15 9B Compound Interest, Inflation And Appreciation Compound Interest When dealing with Simple Interest, the interest amount is the same for every year over the loan period. On the other hand Compound Interest is calculated as followed: Example: John invests $5000 in a bank account to save up to buy his first car. The bank offers him a compound interest rate of 7.8% per year. How much will John have in the bank after 5 years We can do this a number of ways: 1. Manually: Year Principal Interest Total (P+I) 2. CAS Spreadsheet Label columns and enter original value Put the interest equation in cell b1 Add the interest to the principal Fill down the amount (note: dash means it is waiting for the corresponding b cells to be filled first) Page 15 of 27

16 Filling down the interest The answer in cell a6 gives the total amount after 5 years (the start of the 6 th year) 3. CAS calculator recursion On a calculator page enter 5000 and press enter On the next line enter the following ans!""!"" +!.!!"" press enter (Note the CAS will auto insert Ans in this case because it is at the start of the evaluation) This formula is read as Principal amount X (100% of the Principal + 7.8% of the Principal) The result given is the amount after 1 year a Principal of $5000 plus 7.8% of $5000 = $5390. Now press enter repeatedly till you have covered the entire 5- year period. The Total after 5 years is $ Sometimes you may need to use a formula due the large number of compoundings. This is shown in the example below. The formula for Compound Interest is: A = P 1 + r%! = P 1 + r 100 Where A = the amount at the end of n compounding period ($) P = principal ($) r = rate of interest per period (%) n = number of compounding periods! Page 16 of 27

17 Example 4: Tamara has $ to invest for 3 years. She considers the following options: All the investments are equally secure. Advise Tamara which option to take. i. A term deposit at 5.25% p.a. compounded annually ii. Shares paying a dividend rate of 5.08% p.a. compounded quarterly iii. A building society paying a return of 5.4% p.a. compounded monthly iv. A business venture with guaranteed return of 7.3% p.a. compounded daily. Page 17 of 27

18 Inflation One of the measures of how an economy is performing is the rate of inflation. Inflation is the rise in prices within an economy and is generally measured as a percentage. In Australia this percentage is called the Consumer Price Index (CPI). By looking at the inflation rate we can estimate what the cost of various goods and services will be at some time in the future. To estimate the future price of an item one year ahead, we increase the price of an item by the rate of inflation. Example 5: The cost of a new car is $ If the inflation rate is 6%, estimate the price of the car after one year. When calculating the future cost of an item several years ahead, the method of calculation is the same as for compound interest. This is because we are adding a percentage of the cost to the cost each year. Example 6: The cost of a wide- screen high- definition plasma television is $4999. If the average inflation rate is 4%, estimate the cost of the television after five years (to the nearest dollar). On a CAS Inflation causes prices to rise and therefore money loses its value; that is, the amount we able to purchase decreases. Page 18 of 27

19 Appreciation A similar calculation can be made to anticipate the future value of collectable items, such as stamp collections, memorabilia from special occasions, land, paintings and antiques. This type of item increases in value over time if it becomes rare, and rises at a rate much greater than inflation. The amount by which an item grows in value over time is known as appreciation. Example 7: Mr Ly purchases a rare stamp for $360. It is anticipated that the value of the stamp will rise 9% per year. Calculate the value of the stamp after 15 years, correct to the nearest $10. If the difference between the amounts received for an asset is greater than the amount originally paid for the asset, a capital gain is obtained. When a capital gain or profit occurs as a result of selling certain assets such as shares and investment properties, then a capital gains tax must be paid to the Australian Taxation Office. Example 8: Alex and James bought a house for $ in an area where house prices rise (appreciate) on average 4% per year. They decided to hold on to their house until its value is at least $ How many years should Alex and James wait until they sell their current house? (answer to the nearest year). Using CAS nsolve( Page 19 of 27

20 9C Personal loans and Effective Interest Personal loans require regular payments to be made at set intervals. Interest and fees associated with setting up the loan are factored into the repayments. The most common method of calculating interest on personal loans is a reducing interest method, in which interest is calculated on the amount still owing rather than the entire amount borrowed. Using a calculator finance solver Problems involving reducing balance loans can be easily solved using a calculator s Finance Solver. The calculator will show the following fields: N I% PV Pmt FV P/Y C/Y Here N represents total number of repayments. For example, if repayments are made monthly over 2 years, N = 12 2 = 24. I (%) represents interest rate per year. PV stands for present value. This is the value of the loan. (If you borrowed the money from the bank, enter the value of your loan as a positive number.) Pmt represents the amount of each payment. (If you are repaying the loan to the bank, enter the amount of payment as negative number.) FV stands for future value, that is, the value of you loan at some stage in the future. If you wish to repay your loan in full, FV = 0. P/Y means number of payments per year. If for example, you pay monthly, P/Y = 12. C/Y is the number of compounding periods per year. The finance solver can be used to find any one of the above values, provided that all other values are known. To find the unknown value, fill in all known values, place the cursor where the entry for the unknown value should be and press ENTER. Page 20 of 27

21 Example 13 - A person has borrowed $900 from a bank at 15% p.a., calculated on a reducing monthly balance. If he agrees to repay $150 per month, calculate: a) The number of monthly repayments needed to repay the loan b) The total amount repaid c) The amount of interest paid. Page 21 of 27

22 Effective rate of interest Previously we have looked at paying off a loan at a set interest rate, however we have found the amount of interest paid would vary with different compounding terms (daily, weekly, monthly, etc.). The effective annual interest rate is used to compare the annual interest between loans with these different compounding terms. To calculate the effective annual interest rate, use the formula: r!" = 1 + i n! 1 Where: r = the effective annual interest rate; i = the nominal rate, as a decimal; n = the number of compounding periods per year For a loan of $100 at 10% p.a. compounding quarterly over 2 years. The effective annual interest rate is: r!" = 1 + i n! 1 r!" = ! 1 r!" = or r!" = 10.38% Example - Jason decides to borrow money for a holiday. If a personal loan is taken over 4 years with equal quarterly repayments compounding at 12% p.a., calculate the effective annual rate of interest (correct to 1 decimal place) Page 22 of 27

23 9C Exercise Page 23 of 27

24 9D Depreciation Depreciation means that items reduce in value from the time they are acquired. The price for which an item was originally bought is called the purchase price of the item. The portion of the purchase price an item loses in value is called its depreciation. The value of an item at any given time is called its book value. This information may be summarised by the following formula: Book value = Purchase price depreciation V = P D Flat- rate depreciation Flat- rate depreciation means that an item loses value by the same amount each year. This amount is often given as a percentage of the purchase price. Over several years the amount of depreciation is given by the formula: D = PrT 100 Where D = amount of depreciation P = Purchase price r = percentage rate of depreciation T = number of years Since V = P D Therefore V = P PrT 100 Page 24 of 27

25 Example 14: A company car purchased for $ depreciates at 12% per annum by flat- rate depreciation. (a) Calculate the book value of the car after 3 years. (b) Calculate the total depreciation over the first 6 years. (c) How long will it take until the car reaches its scrap value of $4500? Page 25 of 27

26 Reducing- balance depreciation We have just observed the similarity in calculating flat- rate depreciation and simple interest. Both are percentages of a fixed amount. The difference, however, is that interest is added to the principal, whereas depreciation reduces the cost of an asset. The reducing- balance method, can be compared with compound interest. Both are characterised by applying a fixed percentage to an amount that changes at the beginning of each time period. As the book value of an asset declines, so does depreciation. Compared with straight- line depreciation, in which the item s value decreases by the same amount each time period, reducing- balance depreciation decreases by a smaller amount each year. The formula for the book value of an asset that depreciates under the reducing- balance method is: V = P 1 r 100! Where V = book value of depreciated item ($) P = purchase price ($) r = allowed annual rate of depreciation (%) n = number of years Example 15: A construction company purchased a new Crane for $ It depreciates at 12% per annum reducing- balance. (a) Calculate the book value of the Crane after 3 years. (b) Calculate the total depreciation over the first 5 years of service. (c) After how many years does the Crane have a value below $20 000? Page 26 of 27

27 Unit cost depreciation Unit cost depreciation usually applies to machinery which performs some repetitive task. Every time the machine completes one task its value decreases by a unit cost. If we buy a coffee maker for $1000 (purchase price) and expect to trade it in later for $200 (scrap value), it will depreciate by $800 over its lifetime. If we expect it to produce 4000 cups of coffee, then its unit cost (cost of 1 cup of coffee) is equal to!""!""" = $0.20 That is, the machine s value falls by 20 cents every time it produces a coffee. We need to know: purchase price scrap value unit cost = number of repetitions expected Depreciation = unit cost no. of times used Example 16: Calculate the book value of an $8900 photocopier with a scrap value of $150, if it has an expected life of photocopies and has been used times. Page 27 of 27