Dealing With Uncertainty
An apartment priced at HKD 5M
After 30% down payment, mortgage = 3.5M
To be repaid by 20 years or 240 months
Interest rate is HIBOR+0.7%
In April 2011, HIBOR=0.25%, monthly payment is
Alternatives with Different Lives
You can invest $100 in a project
After one year, you can withdraw from the project and
You can also choose to stay on the project. Then after
another year, you will re
Sequential Decisions Over Time
Previously in handling uncertainties
We assume a single decision is to be made at the beginning
Sometimes, we need to make several decisions
sequentially over time
The outcome of each decision may be random
The goal is
Payback Period Method
A typical project has cash outflows in the beginning
periods, then followed by cash inflows
The (simple) payback period () is the earliest time
period when the accumulative cash inflow is no less
than the ac
Increasing Speed of Exponential Functions
The story of A Grain of Rice
F(t) = 2t-1
One dollar today is more valuable
than one dollar tomorrow
Capital and Interest
You deposit $1,000 to the bank, and after one year,
Compound interest is the eighth wonder of the world. He who
understands it, earns it . he who doesn't . pays it
Compound interest is the most powerful force in the universe.
Compound interest is the greatest mathematical discovery of
Starting from today (25/2/2016), we make a
monthly investment to a project for $10K per month
The value of the project will increase by 1% per
How much is the value of our investment after one
year (on 25/2/2017)?
Suppose no investment
Applications of Money-Time
Evaluating An Engineering Project
Your friend owes you $10,000.
He can pay you $10,000 today
He also suggests an option of paying you $10,500 after one year
How about $10,400 or $10,600?
How to evaluate the o
Do I have to use the interest factor notation in
No. You can do calculation in any way you feel
comfortable, as long as the final result is correct.
However, if you make a mistake
Can I use a financial calculator or Excel?
Concepts of Cost
What is cost?
Mr. Li bought a movie ticket on the Internet at the
price of HK$65.
Before going to the theater, he read some movie
surveys and found that the movie was
The transportation will cost HK$14 if Mr. Li goes
Cost reduction is important in profit maximization
Profit = Revenue - Cost
Cost reduction can be achieved in project design
Identify the design variable that is the primary cost
Develop the expression for the cost in t