Assignment 3 - 2012

Due date(s):	01 October 2012
(PDF)	Assignment questions
Link	[{{{questions_link}}} Download questions]
Link	[{{{solutions_link}}} Assignment solutions]
Other instructions	Tutorial date: 24 September 2012

<rst> <rst-options: 'toc' = False/> <rst-options: 'reset-figures' = False/>

Assignment objectives

=========

.. question::

What annual amount of actual dollars must parents save at 6% interest, compounded annually, to give them an annual payment of $15,000 per year, for 5 years, starting 15 full years from now? This is money for their child's university tuition. They will put this amount of money in an RESP for the child. However, the parents do not want a cheque for $15,000 starting in the 16th year from now, rather they would like each $15,000 payment to have the equivalent purchasing power of $15,000 in today's money, so use an inflation rate of university tuition, the so-called "cost of learning index" of 5% to escalate the value of money they would like to receive.

.. question::

A small 10 MW power plant is operating at 7,000 hours utilization per year, producing power sold to the grid at a flat rate of $0.04 per kWh. Use a period duration of 1 month, but let the effective time value of money rate be 10% per annum. What is the present value of all revenues over a 10 year time frame? How does this present value compare to the NPV calculated in assignment 2 using a period duration of 1 year. .. question:: Show the book value and amounts written off each year as depreciation for a capital expense of :math:`P =` $400,000. The lifetime is expected to be :math:`n=6` years with a salvage value of :math:`S =` $30,000. Use the (a) straight-line method, (b) declining balance method and (c) double-declining balance method. You will need an equation we have not learned in class: if one can estimate a salvage value, then use :math:`d = 1- \sqrt[\displaystyle n]{\displaystyle \frac{S}{P}}` for the declining balance methods. But if :math:`S=0`, then use :math:`d=\displaystyle \frac{1}{n}`. The double-declining methods use double the value of this :math:`d`. For straight line methods, the rate :math:`d = \displaystyle \frac{P-S}{n} \cdot \displaystyle \frac{1}{P}`. Plot the book value of the investment over time; superimpose book value from all 3 methods from :math:`n=0` to :math:`n=9`. .. question:: Evaluate the NPV and DCFRR for the following case: a company purchases a second-hand distillation column at a cost of $250; site preparation is $20, engineering planning, safety and hazard analysis $20, and installation is $100 and lasts a year. Once completed, we expect to operate the column for 10 years. The salvage value is expected to be $0 in the final year.

Based on today's rates we could make a net revenue of $75 per year in today's money, but we will inflate the revenue by 5% per year, based on market trends for the product. Also major maintenance is expected in the 6th year of full operation, at a cost of $100, (also estimated in today's dollars, so use an inflation rate of 5% to inflate it to future dollars).

The company's MARR is 15%, which does not include the effect of inflation. All figures are in $1000's of dollars.

Calculate the NPV (shown as a plot over time, overlay plots from both cases below) and DCFRR for the following two cases:

* No depreciation and no taxes payable (i.e. the way we have learned so far in the course) * Take depreciation on the straight line method and corporate taxes at 30%.

Comment on the difference in results and whether the investment is worthwhile in either case. What factors would you alter in a sensitivity analysis?

.. question::

You are operating a subsidiary company in Brazil and investigating the production of a speciality chemical which is currently being imported. Annual production capacity would be 10000 tonnes. Specialized reactors, but with a capacity of 20000 tonnes are available from Germany at a cost of € 5 million (EUR). The cost of the reactors would be about 20% of the entire equipment cost required for producing the chemical; the rest would be due to raw material processing equipment, storage, separation units, utilities, and ancillaries. These units could all be sourced locally.

Installation would be about 40% of the equipment cost. You have a quotation of BRL 35 million for local engineering and site preparation. Royalties are payable to a Canadian company that is licensing the necessary patents, know-how and flow sheet. This license fee is CAD 35 per tonne produced and must be paid quarterly.

It is expected that all expenses to build and start the plant will be evenly spread over 24 months, with regular production starting in the 25th month. The Brazilian market demand is expected to be about 7000 tonnes per year when the plant starts producing, increasing at a rate of 3% per year. The expected price would be BRL 12 per kilogram when you start producing, but you plan to raise that price by 8% per year.

The main raw material can be obtained very cheaply in Brazil, which is why you are building the plant here. The cost is BRL 1500 per tonne of final product, with expected increases of about 7% per year. Other raw materials required are BRL 1200 per tonne final product, with a similar annual increase expected. Other costs are expected to be around BRL 400 per tonne final product, increasing by 8% per year. Salaries and other labour costs are estimated at BRL 15 million per year, increasing at 7% per year.

Working capital costs to get started: catalysts, supplies, etc will be ignored for this question.

Corporate income taxes in Brazil can be assumed similar to Canada: 35% per annum (you should verify if this is true though), depreciation is allowed on the declining balance method. Assume that 10% of the capital expenditure can be recovered as salvage (don't inflate or deflate, just use 10% of the total CAPEX), and the plant life is 12 years, once starting production.

The main aim is to calculate the (a) payback time using discounted cash flows, (b) NPV and (c) DCFRR for this investment. Several intermediate steps will be required however. NPV should be reported as a plot of NPV over time.

.. raw:: latex

\vspace{0.3cm} \hrule \center{END}

</rst>