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foundations of finance 1
💳 textbook readings
*use the key concepts list on the group*
lecture 1: welcome and introduction
this module
develops core concepts and theoretical models of modern finance theory
shows how these concepts and models can be applied to analysis of corporate
financial decisions
if you work in finance you will use course content directly.
lecture 2.1: future values
the time value of money
the basic problem:
foundations of finance 1 1
, any investment project or financial instrument involves cash flows at different
times - some now, some perhaps in 10 years’ time
how do we compare these?
people are impatient and would rather have $100 today, rather than the promise
of $100 in a year
people need to be rewarded for giving up access to their money during the life of
an investment.
key concept: the present value of a future cash flow
what is the promise of $100 in 1 year worth today?
key concept: the future value of a current investment
how much will $100 that we have now be worth to us in 1 year?
example: time value of money 3
rules of comparing cash flows
rule 1 (comparing and combining values): It is only possible to compare of
combine (add or subtract) values at the same point in time
future values
rule 2: (moving cash flows forward in time): to move a cash flow forward, we
must compound it (at the appropriate rate)
compounding is when we increase the cash flow as we take it forward into the
future, to account its anticipated growth
simple case: we have $100 today and interest rate is 10% per year.
in 1 years’ time: 100(1.10)^1 = $110
in 2 years’ time: 100(1.10)^2 = $121
note that, the value is $121, this is because we’re receiving interest on
interest
foundations of finance 1 2
, generalising, it is possible to calculate future value with cash flow, number of
periods, and interest rate
general formula:
where
difficult case: assume you receive a flow of $1000, each for 3 years, starting
today (t=0)
what is FV at t=3? (at 10% rate)
cash flow at t=0 needs to be compounded forward by 3 periods, cash flow at t=1
by 2, and cash flow at t=2 by 1
Total future value: $1331 + $1210 + $1100 = 3461
lecture 2.2 present values
rule 3: (moving cash flows back in time): we must discount it back to the
appropriate rate
basic concept: $1 today is worth more than $1 a year later
discounting is when we decrease the value of a future cash flow as we work out
what it’s worth in the present, to take account of the fact that we have to wait for it.
foundations of finance 1 3
, when we go forward in time, we talk about an interest rate, and use that calculate
future values of current cash flows
when we go backward in time, we talk about an discount rate, and use that
calculate present values of future cash flows
both have same symbol r in formulas
simple case: we expect to receive $110 in 1 years time and discount rate is
10% per year. what is it worth today?
110/(1.10)^1 = $100
reverse it
generalising, the formula to covert a single future cashflow into a present value is:
where
note: the denominator is called the discount factor
it moves a cash flow back from a distinct future time point back to the present
calculate present value of a future cashflow at time t in the future by multiplying it
by the discount factor for time t
note: if there are multiple cash flows at a time, apply different discount factor to
each future cash flow, because they take place at different times
foundations of finance 1 4
foundations of finance 1
💳 textbook readings
*use the key concepts list on the group*
lecture 1: welcome and introduction
this module
develops core concepts and theoretical models of modern finance theory
shows how these concepts and models can be applied to analysis of corporate
financial decisions
if you work in finance you will use course content directly.
lecture 2.1: future values
the time value of money
the basic problem:
foundations of finance 1 1
, any investment project or financial instrument involves cash flows at different
times - some now, some perhaps in 10 years’ time
how do we compare these?
people are impatient and would rather have $100 today, rather than the promise
of $100 in a year
people need to be rewarded for giving up access to their money during the life of
an investment.
key concept: the present value of a future cash flow
what is the promise of $100 in 1 year worth today?
key concept: the future value of a current investment
how much will $100 that we have now be worth to us in 1 year?
example: time value of money 3
rules of comparing cash flows
rule 1 (comparing and combining values): It is only possible to compare of
combine (add or subtract) values at the same point in time
future values
rule 2: (moving cash flows forward in time): to move a cash flow forward, we
must compound it (at the appropriate rate)
compounding is when we increase the cash flow as we take it forward into the
future, to account its anticipated growth
simple case: we have $100 today and interest rate is 10% per year.
in 1 years’ time: 100(1.10)^1 = $110
in 2 years’ time: 100(1.10)^2 = $121
note that, the value is $121, this is because we’re receiving interest on
interest
foundations of finance 1 2
, generalising, it is possible to calculate future value with cash flow, number of
periods, and interest rate
general formula:
where
difficult case: assume you receive a flow of $1000, each for 3 years, starting
today (t=0)
what is FV at t=3? (at 10% rate)
cash flow at t=0 needs to be compounded forward by 3 periods, cash flow at t=1
by 2, and cash flow at t=2 by 1
Total future value: $1331 + $1210 + $1100 = 3461
lecture 2.2 present values
rule 3: (moving cash flows back in time): we must discount it back to the
appropriate rate
basic concept: $1 today is worth more than $1 a year later
discounting is when we decrease the value of a future cash flow as we work out
what it’s worth in the present, to take account of the fact that we have to wait for it.
foundations of finance 1 3
, when we go forward in time, we talk about an interest rate, and use that calculate
future values of current cash flows
when we go backward in time, we talk about an discount rate, and use that
calculate present values of future cash flows
both have same symbol r in formulas
simple case: we expect to receive $110 in 1 years time and discount rate is
10% per year. what is it worth today?
110/(1.10)^1 = $100
reverse it
generalising, the formula to covert a single future cashflow into a present value is:
where
note: the denominator is called the discount factor
it moves a cash flow back from a distinct future time point back to the present
calculate present value of a future cashflow at time t in the future by multiplying it
by the discount factor for time t
note: if there are multiple cash flows at a time, apply different discount factor to
each future cash flow, because they take place at different times
foundations of finance 1 4
