Advanced Corporate Finance & Theory FNCE5000

RESEARCH PROJECT
This Project is to be completed individually.

PART A – MONTE CARLO ANALYSIS
Background
You are the CFO of Blue-Sky Mining, a gold miner. Your company has just
spent $10 million on exploration and appraisal drilling to identify a new
200,000 ounce (estimated) gold resource. You now have to determine the
viability of mining the resource at an expected rate of 50,000 ounces per
year for 4 years.
You decide to construct a 4 period (i.e. 4 year) Monte Carlo valuation of the
project according to the following details.
1) The price of gold ($/ounce) follows a lognormal random walk (where
parameter 0.12 G ? ? is the volatility):
2
0 1 $1000 , exp 0.05 , ~ (0,1)
2
G
t t Gt t G G G z z N
?
? ?
?? ? ?
? ? ?? ? ? ? ?
?? ? ?
.
2) The gold production cost ($/ounce) also follows a lognormal random
walk correlated with the price of gold (where parameter 0.12 C ? ? is the
volatility, and parameter ? ? 0.18 is the correlation coefficient):
? ? ? ? 2
2
0 1 $900 , exp 0.05 1 ,
2
~ (0,1).
C
t t C t t
t
C C C z y
y N
?
? ? ? ?
?? ? ?
? ? ?? ? ? ? ? ? ?
?? ? ?
3) Annual gold production is a lognormal random variable (where
parameter 0.05 Q ? ? is the uncertainty):
2
50000exp , ~ (0,1) .
2
Q
t Qt t Q x x N
?
?
? ?
? ?? ? ?
?? ??
4) An ad valorem royalty (tax) of 2.5% is charged on annual gold
production in excess of 2,500 ounces based on the average gold price for
the year:
? ? 1 0.025max 2500,0 ( ) ,
2
t t
t t
R Q G G ? ?
? ?
where the max??? function works as per Microsoft Excel so that:
? ? , if
max ,
, if
A A B
A B
B B A
? ?
? ? ? ?
.
5) Annual operating profit is:
0 ( ) , 0. t t t t t ? ? Q G ?C ? R ? ?
6) An operating loss can be carried forward one year as a corporate tax
shield. Corporate tax is charged at a rate of 30% against positive
operating profit after deduction of any carry forward loss. Therefore
annual cash flow is:
? ? 1 1 IF 0 , , IF 0 , (1 0.3) , 0.3max 0 , , t t t t t t t t CF ? ? ? ??? ? ? ??? ? ? ? ? ? ? ?? ????
where the IF??? function works as per Microsoft Excel so that:
? ? , if is true
IF , ,
, if is false
A logical statement
logical statement A B
B logical statement
?
??
?
.
7) The discrete annual discount rate is e0.05 ?1 ? 5.13%.
8) The simulation will use 20,000 random (and uncorrelated) realisations of
each of 1 1 1 x , y , z , 2 2 2 x , y , z , 3 3 3 x , y , z , 4 4 4 x , y , z .
Question A1 (5 marks)
Each period there are 3 sources of uncertainty: , , t t t G C Q. Nevertheless,
based on the background assumptions, you expect: t G to grow at 5.13% per
year, t C to grow at 5.13% per year; and t Q to stay constant at 50,000 each
year. Using expected values for , , t t t G C Q, what is the present value of the
project (PV*)?
Question A2 (5 marks)
Now, incorporating the simulated Monte Carlo uncertainty, what is the
present value of the project (PVMC)? How does it compare with PV*?
Investigate what happens to the relative difference between PVMC and PV*
when you increase the margin between 0 G and 0 C (e.g. what happens as
you decrease 0 C but keep 0 G constant)? Provide a discussion that explains:
? why PVMC and PV* are different; and, more generally,
? the circumstances under which it is important to recognise
uncertainty in capital budgeting.
Question A3 (5 marks)
The levels of uncertainty of , , t t t G C Q are determined by the parameters
, , G C Q ? ? ? . Investigate how the relative difference between PVMC and PV*
changes as you vary the parameters , , G C Q ? ? ? (e.g. try variously setting the
parameters to zero or doubling them). Summarise and explain your findings.
Question A4 (5 marks)
What is the expected rate of taxation of annual operating profit each year?
Why is different to 30%?
PART B – REAL OPTION TO ABANDON
Background
You now decide to incorporate into your Monte Carlo valuation the real
option to abandon the gold mine after 2 years. The abandon decision will be
based on the margin between 2 G and 2 C . Specifically, taking into account
the royalty rate of 2.5%, you will abandon the project at year 2 if:
0.975G2 ? C2 ? 0 . The decision to abandon does not affect the years 1 and 2
cash flows (i.e. 1 CF and 2 CF will not change), but if you do abandon the
project, then the years 3 and 4 cash flows will be zero (i.e. if
2 2 0.975G ? C ? 0 , then 3 CF ? 0 and 4 CF ? 0 ).
Question B1 (5 marks)
With the real option to abandon the gold mine, what is the present value of
the project (PVRO)? What then is the value of the real option to abandon (i.e.
PVRO – PVMC)? What is the probability you will abandon?
Question B2 (5 marks)
Investigate how the value of the real option to abandon (i.e. PVRO – PVMC)
changes as you vary the margin between 0 G and 0 C (e.g. what happens
when you increase or decrease 0 C but keep 0 G constant)? Provide a
discussion that explains:
? why PVMC and PVRO are different; and, more generally,
? the circumstances where real options are particularly valuable.
Question B3 (5 marks)
The levels of uncertainty of , , t t t G C Q are determined by the parameters
, , G C Q ? ? ? . Investigate how the value of the real option to abandon (i.e.
PVRO – PVMC) changes as you vary the parameters , , G C Q ? ? ? (e.g. try
variously setting the parameters to zero or doubling them). Summarise and
explain your findings.
END OF PROJECT

Advanced Corporate Finance & Theory FNCE5000

RESEARCH PROJECT
This Project is to be completed individually.

PART A – MONTE CARLO ANALYSIS
Background
You are the CFO of Blue-Sky Mining, a gold miner. Your company has just
spent $10 million on exploration and appraisal drilling to identify a new
200,000 ounce (estimated) gold resource. You now have to determine the
viability of mining the resource at an expected rate of 50,000 ounces per
year for 4 years.
You decide to construct a 4 period (i.e. 4 year) Monte Carlo valuation of the
project according to the following details.
1) The price of gold ($/ounce) follows a lognormal random walk (where
parameter 0.12 G ? ? is the volatility):
2
0 1 $1000 , exp 0.05 , ~ (0,1)
2
G
t t Gt t G G G z z N
?
? ?
?? ? ?
? ? ?? ? ? ? ?
?? ? ?
.
2) The gold production cost ($/ounce) also follows a lognormal random
walk correlated with the price of gold (where parameter 0.12 C ? ? is the
volatility, and parameter ? ? 0.18 is the correlation coefficient):
? ? ? ? 2
2
0 1 $900 , exp 0.05 1 ,
2
~ (0,1).
C
t t C t t
t
C C C z y
y N
?
? ? ? ?
?? ? ?
? ? ?? ? ? ? ? ? ?
?? ? ?
3) Annual gold production is a lognormal random variable (where
parameter 0.05 Q ? ? is the uncertainty):
2
50000exp , ~ (0,1) .
2
Q
t Qt t Q x x N
?
?
? ?
? ?? ? ?
?? ??
4) An ad valorem royalty (tax) of 2.5% is charged on annual gold
production in excess of 2,500 ounces based on the average gold price for
the year:
? ? 1 0.025max 2500,0 ( ) ,
2
t t
t t
R Q G G ? ?
? ?
where the max??? function works as per Microsoft Excel so that:
? ? , if
max ,
, if
A A B
A B
B B A
? ?
? ? ? ?
.
5) Annual operating profit is:
0 ( ) , 0. t t t t t ? ? Q G ?C ? R ? ?
6) An operating loss can be carried forward one year as a corporate tax
shield. Corporate tax is charged at a rate of 30% against positive
operating profit after deduction of any carry forward loss. Therefore
annual cash flow is:
? ? 1 1 IF 0 , , IF 0 , (1 0.3) , 0.3max 0 , , t t t t t t t t CF ? ? ? ??? ? ? ??? ? ? ? ? ? ? ?? ????
where the IF??? function works as per Microsoft Excel so that:
? ? , if is true
IF , ,
, if is false
A logical statement
logical statement A B
B logical statement
?
??
?
.
7) The discrete annual discount rate is e0.05 ?1 ? 5.13%.
8) The simulation will use 20,000 random (and uncorrelated) realisations of
each of 1 1 1 x , y , z , 2 2 2 x , y , z , 3 3 3 x , y , z , 4 4 4 x , y , z .
Question A1 (5 marks)
Each period there are 3 sources of uncertainty: , , t t t G C Q. Nevertheless,
based on the background assumptions, you expect: t G to grow at 5.13% per
year, t C to grow at 5.13% per year; and t Q to stay constant at 50,000 each
year. Using expected values for , , t t t G C Q, what is the present value of the
project (PV*)?
Question A2 (5 marks)
Now, incorporating the simulated Monte Carlo uncertainty, what is the
present value of the project (PVMC)? How does it compare with PV*?
Investigate what happens to the relative difference between PVMC and PV*
when you increase the margin between 0 G and 0 C (e.g. what happens as
you decrease 0 C but keep 0 G constant)? Provide a discussion that explains:
? why PVMC and PV* are different; and, more generally,
? the circumstances under which it is important to recognise
uncertainty in capital budgeting.
Question A3 (5 marks)
The levels of uncertainty of , , t t t G C Q are determined by the parameters
, , G C Q ? ? ? . Investigate how the relative difference between PVMC and PV*
changes as you vary the parameters , , G C Q ? ? ? (e.g. try variously setting the
parameters to zero or doubling them). Summarise and explain your findings.
Question A4 (5 marks)
What is the expected rate of taxation of annual operating profit each year?
Why is different to 30%?
PART B – REAL OPTION TO ABANDON
Background
You now decide to incorporate into your Monte Carlo valuation the real
option to abandon the gold mine after 2 years. The abandon decision will be
based on the margin between 2 G and 2 C . Specifically, taking into account
the royalty rate of 2.5%, you will abandon the project at year 2 if:
0.975G2 ? C2 ? 0 . The decision to abandon does not affect the years 1 and 2
cash flows (i.e. 1 CF and 2 CF will not change), but if you do abandon the
project, then the years 3 and 4 cash flows will be zero (i.e. if
2 2 0.975G ? C ? 0 , then 3 CF ? 0 and 4 CF ? 0 ).
Question B1 (5 marks)
With the real option to abandon the gold mine, what is the present value of
the project (PVRO)? What then is the value of the real option to abandon (i.e.
PVRO – PVMC)? What is the probability you will abandon?
Question B2 (5 marks)
Investigate how the value of the real option to abandon (i.e. PVRO – PVMC)
changes as you vary the margin between 0 G and 0 C (e.g. what happens
when you increase or decrease 0 C but keep 0 G constant)? Provide a
discussion that explains:
? why PVMC and PVRO are different; and, more generally,
? the circumstances where real options are particularly valuable.
Question B3 (5 marks)
The levels of uncertainty of , , t t t G C Q are determined by the parameters
, , G C Q ? ? ? . Investigate how the value of the real option to abandon (i.e.
PVRO – PVMC) changes as you vary the parameters , , G C Q ? ? ? (e.g. try
variously setting the parameters to zero or doubling them). Summarise and
explain your findings.
END OF PROJECT