Foundations of finance

Question 1 (50 marks).

You are an architect.  You are designing for your client, the rectangular courtyard of a
large  mansion.    The  total  area  of  the  courtyard  must  be  200  square  metres.    The
client  has  asked  that  the  courtyard  should  have  the  largest  rectangular  lawn  in  the
middle.  The client also wants a paved and tiled border area all round the edge of the
lawn.  The tiled area must be 1 meter wide on the east and west sides, 2 meters wide
on the north side and 1.5 meters on the south side.

i)  What  should  the  length l, and  the  width w,  of  the  rectangular  courtyard
be,  so  that  the  lawn  area  in the middle  of  the  courtyard  is the largest
possible?
ii)  What is the largest surface area of the lawn?

Explain, in words all the reasons and steps you took to reach your answer.

Min 2 m
Min 1.5
m
Min 1 m
Min 1 m
l
w

Question 2 (50 marks).

You  work  for  a  major  mobile  phone  company  as  a  communications  manager  in
charge  of transmissions.    The  company  has  one  million  transmission  locations  in
Europe.  Each location has two vertical towers, one six feet high and one fifteen feet
high.    The  two  towers  have  to  be  twenty  feet  apart.   The  two  towers  need  to  be
connected  to  each  other  via  an  expensive  communications  cable.    The  connecting
cable is attached to the top of each tower and must be connected to one junction box
on  the  ground.  The  junction  box  needs  to  be  located  between  the  two  towers.  The
cost  of  the  cable  connecting  the  6  ft  tower  to  the  junction  box  is  £0.5  million per
metre  while  for  the  cable  connecting  the  15  ft  tower  to  the  junction  box  costs  £0.75
million per metre.

The diagram below should clarify the picture.

6 feet
Tower
15 feet
Tower
20 feet
Junction  Box
Connecting
Cable

i)  What is the minimum total cost of both the connecting cables?

ii)  Where should the junction box be located to minimise the total cost?

Here  too,  please  explain,  in  words  all  the  reasons  and  steps  you  took to  reach  your
answer.
So  that  you  know  that  the  learning  outcomes  on  the  module  are
effectively covered and do relate to this coursework, here is a mapping.

1.  Apply basic mathematical techniques and tools used in modern finance.

Questions 1, 2, 3.

2.  Describe and evaluate measures of risk aversion using expected utility theory.

3.  Understand the concept of efficient frontiers when choosing to invest in risky
assets.

4.  Evaluate choices using the net present value approach.

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