BUIL1149 PROPERTY ECONOMICS
PROBLEM SHEET # 6 (MICRO MODULE)
(SOLUTIONS TO ASTERISKED PROBLEMS)
Note: This problem sheet will not be covered in tutorials. Instead a solution sheet will be posted in the on-line class-room which will provide solutions to each problem. It is also expected that students will employ the HP-10B2 calculator (used in omgt1113 Property Concepts) to solve all of the financial problems appearing in this problem sheet.
Q1*
An investor in residential real estate is planning to build and hold a property for a period of 5 years. She will pay $500,000 up-front at the inception of the project with all monies totally financed out of her own financial resources which if left in the bank would have earned a fixed annual compounding rate of 8%.The investor anticipates that the net cash flow generated from the property will be $6,000 per year and the property will sell for $710,000 at the end of the 5th year.
(a)Sketch a time-line of the cash flows associated with this Investment
(b)Determine the Net Present Value (NPV) of the proposed Investment
The key strokes on the HP-10B2 required to obtain this solution are as
follows:
(c)Determine the Internal Rate of Return (IRR) of the Investment
An internal rate of return IRR = 8.3144% ensures that the future cash flows associated with the investment when discounted by IRR equal the initial capital outlay K
The key strokes on the HP-10B2 required to obtain this solution are as follows:
Q2*, [#]
The wage rate a small tiling firm has to pay its tilers and the output it can produce(measured in square feet of laid tiles) varies with the number of workers as follows (all figures are hourly):
Wage Rate (AFCL)
Total output (TPPL) / $15
10 / $20
22 / $25
32 / $30
40 / $35
46 / $40
50 / $45
52 / $50
52
Assume that output sells at $10 per square foot of laid tiles.
(a)Copy the table and add additional rows for Total Factor Cost of labour TFCL, Marginal Factor Cost of Labour MFCL, Total Revenue Product of Labour TRPL and Marginal Revenue Product of Labour MRPL. Put the figures for MFCL and MRPL in the spaces between the columns.
(b)How many tilers will the firm employ in order to maximise profits?
Up to 5 tilers because the 5th tiler brings in $60 of additional revenue and the extra cost of labour is $55
(c)What will be its hourly wage bill at this level of employment?
5 tilers per hr. x $35 / tiler-hr = $175
(d)How much hourly revenue will it earn at this level of employment?
TRPL = $460 at an activity level of 5tilers per hr.
(e)Assuming that the firm faces other (fixed) costs of $30 per hour, how much hourly profit will it make?
Profit = TRPL – TFCL – Total Fixed Cost = $460 – $175 – $30 = $255
(f)Assume that the workers now formed a union and that the firm agreed to pay the negotiated wage rate to all employees. What is the maximum to which the hourly wage rate could rise without causing the firm to try to reduce employment below that in (b) above?
A shade less than $60 (which equals MRPL at the firm’s profit-maximising employment level). Up to 5 workers per hour will be profitable to employ because each will be contributing no less than $60 of additional revenue. At a wage which is a shade less than $60, it does not pay the firm to reduce the number of tilers employed per hour as the firm will suffer fall in revenue than are greater than the saviungs in wage costs.
(g)What would be the firm’s hourly profit now?
Total cost is a shade below $330 (i.e. A tad below $300 in wages plus $30 in fixed costs) Total revenue product remains unchanged at $460 so that the firm makes a profit just a little less than $130
Q3*
In the following diagram
Let S represent the fixed annual supply of cultivable land
Required
(a)In the first instance suppose that the land is only suitable for the cultivation of potatoes and the demand for this land to grow potatoes is given by DP. If the market for this land is competitive on both the demand and supply side determine the equilibrium market rent. Also indicate what area on this diagrameconomists would refer to as economic rent.
(b)If all the land were held by one landowner that is able to engage in price discrimination of the 1st degree, what would the economic rent now be given by?
(c)Suppose that at some later date, farmers learn that this land is also suitable for the cultivation of turnips. In the above diagram DT denotes the demand for this land to grow turnips. What now will be the economic rent if as in (b) all the land is held by a perfectly price discriminating landlord. Also indicate how much land will be used for turnip and potato cultivation
Q4*
Aaron does all the bookkeeping for his wife Carmen’s Project Management Consultancy Firm. At the moment Aaron implements a time-consuming paper based accounting system that occupies him up to 20 hours a fort-night. He is currently investigating the economic viability of buying a computer for Carmen’s Business along with a printer and “Mind Your on Business (MYOB)” - an accounting software product that may be tailored to handle all book-keeping tasks including the generation of quarterly BAS activity statements. For each hour of released time from the arduous paper-based book-keeping tasks, Aaron hopes he will be able to do the housework and child-minding and cooking which presently is done by Gretel (the family governess) at the rate of $30 per hour.
The relevant data that Aaron has been able to assemble for his decision-making are as follows:
Item
Computer$2500
Printer$400
Software$1500
Software Training$250
Fortnightly Time Savings on Book-keeping5 hours
Finally, the source of funds for this capital investment is the family company’s retained earnings currently sitting in a cash management account which earns 6.5% pa or .25% per fortnight.
Required:
If the life of the computer, software and printer is 3 years (or 26 x 3 = 78 fortnights) determine whether Aaron’s proposal to bring Carmen’s Home office into the 20th century is economically viable.
The initial outlay is:
K = - $4650 = - [$2500 + $400 + $1500 + $250}
The fortnightly savings due to Carmen not having to be paid is:$150 = 5 x $30 and the fortnightly interest rate is 6.5% ÷ 26 = .0025
Hence:
The key strokes on the HP-10B2 required to obtain this solution are as follows:
Q5*
Anita’s kindly Uncle Leonardo da Vinci recently passed way at the age of 85 and bequeathed her a large NSW pastoral lease property that has 10 years to run. Not being a farm girl, Anita has recently applied for and received ministerial approval to transfer the lease.
For the remaining lease-term, suppose that $10000 is payable at the end of each year and the net annual takings (before lease payments) are reasonably expected to be around $100,000 per annum. For simplicity also assume net annual takings eventuate at the end of each year when farm produce is sold and all non-rental expenses of running the farm are incurred.
Required:
(a)What is the present value of the lease payments as well as the net annual takings (before lease payments) if the appropriate discount rate is 10%?
The present value of the lease payments PV1is given by:
And the present value of the net annual takings PV2 is given by:
(b)What is the most that Anita could possibly expect for the leased property if she were to transfer it to another farmer?
The most that Anita could possibly expect (call it PV3) would be given by the difference between PV2 and PV1: That is:
PV3 = PV2 – PV1 = 614456.71 – 61445.67 = 553011.04
Alternatively, PV3 may be obtained as follows:
(c)What is the magnitude of the error in (b) if perpetuity formulae were used to generate the values required in (a).
If perpetuity formulae were used to obtainPV1, PV2 and PV3 would be given by:
PV3 = PV2 – PV1 =
The error is quite substantial and amounts to:
Error = 900000 – 553011.04 = 346988.96
Moral of Story: Even though it may be tempting to use simple formulae because theyare simple, they do notalways apply. So when you work in the real-world make sure you know when to use and when not to use formulae in your financial tool-kit.
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[#]This problem has been adapted from Question 3 appearing in Sloman J & Norris K Principles of Economics, Ch 8, p. 208