Project Management –
Part I (Finance)
The Time Value of Money
• We refer to a series of cash flows lasting several periods
as a stream of cash flows. We can represent a stream of
cash flows on a timeline, a linear representation of the
timing of the expected cash flows.
The Three Rules of Time Travel
• 1) It is only possible to compare or combine values at the
same point in time. A dollar today and a dollar in one year
are not equivalent.
• To compare or combine cash flows that occur at different
points in time, you first need to convert the cash flows into
the same units or move them to the same point in time.
• 2) To move a cash flow forward in time, you must
compound it. (compound interest)
• FV = C * (1+r) * (1+r) * … * (1+r) = C(1+r)^n
An initial deposit of $1000, %10, 2-year
period
The Three Rules of Time Travel
• 3) Moving Cash flows back in time
• Present Value of a Cash Flow
• PV = C / (1+r)^n
The Time Value of Money
• Megan wants to buy a designer handbag and plans to
earn the money babysitting. Suppose the interest rate is
6% and she is willing to wait one year to purchase the
bag. How much babysitting money (to the nearest whole
dollar) will she need to earn today to buy the bag for $400
one year from now?
The Time Value of Money
• Johnny and Darren both earn $100 working on their
respective neighbors' big farms. Johnny puts his $100 in
the piggy bank that his parents gave him to encourage
him to save. Darren puts his money in a savings account
his parents set up for him. The savings account pays 3%
interest. They both take their money out after 5 years.
How much more money does Darren have than Johnny?
The Time Value of Money
• Rondo is in the market for a new car. He has narrowed his
search down to 2 models. Model A costs $32,000 and
Model B costs $28,000. With both cars he plans to pay
cash and own them for 4 years before trading in for a new
car. His research indicates that the trade in value for
Model A after 4 years is 60% of the initial purchase price,
while the trade in value for Model B is 45%. The interest
rate is 5%. For simplicity assume that operating and
maintenance costs for the models are identical. Which
model is the better decision and how much "cheaper" is it
than the alternative?
The Time Value of Money
• Christine is a new homebuyer. She wants to make sure
that she incorporates the cost of maintenance into her
decision. She estimates that routine repairs and
maintenance on the home she is considering will be
$1,590 in the first year (one year from now). Due to the
increasing age of the home, she expects that
maintenance costs will increase 6% annually. The interest
rate is 5%. If she plans to be in the home for 10 years,
what is the present value of all future maintenance? (Note
that maintenance costs will change annually, and starts
one year from now and she plans to do the last one
before selling her house.)
Annuities
• An annuity is a stream of N equal cash flows paid at
regular intervals. The difference between an annuity and a
perpetuity is that an annuity ends after some fixed number
of payments. Most car loans, mortgages, and some bonds
are annuities. We represent the cash flows of an annuity
on a timeline as follows.
Annuities
• Future Value of the annuity
(1 + 𝑖)𝑛 − 1
𝐹𝑉 = 𝐶 ∙
𝑖
• Present Value of the annuity
1 − (1 + 𝑖)−𝑛
𝑃𝑉 = 𝐶 ∙
𝑖
Annuities
• You are about to purchase a new car and have two
options to pay for it. You can pay $20,000 in cash
immediately, or you can get a loan that requires you to
pay $500 each month for the next 48 months (four years).
If the monthly interest rate you earn on your cash is 0,5
%, which option should you take?
• 𝑃𝑉 48 𝑝𝑒𝑟𝑖𝑜𝑑 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 𝑜𝑓 $500 = $500 ∙
1
0.005
1−