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