finance final 1

people with money but no ideas/time

investors

people with ideas but not enough money

companies

projects go into

retained earnings or taxes or coupon payments, dividends, & stock repurchases

Finance decisions inside a business enterprise are

all about answering the question:

Is it worth it?

Finance decisions inside a business enterprise are to main objective is to make individuals and their businesses better off (i.e., to

create or preserve the economic value of assets)

What defines “worth it”?

Benefits of some activity or investment > costs of that activity or investment.

Cash flow coming in > cash flow going out.

In other words: time value of money (which depends on time, rates of return, and risks

What is Corporate Finance NOT?

investors or financial institutions and markets

What is time value

A dollar in our hand today is worth more – has more

value – than a dollar promised in the future.

What is time value?

A dollar in our hand today is worth more – has more

value – than a dollar promised in the future.

Why is this so?

Inflation – reduces purchasing power.

Uncertainty – future is uncertain (risk).

Lost opportunity – time entails opportunity cost

Why do we invest our money?

Holding cash is ___. Inflation erodes the_______

tricky, buying power of our cash.

Why do we invest our money?

By lending (investing) our money, we hope to earn a

return on that money.

Why do we invest our money?

The rate of return that we earn ideally is higher

enough than the

rate of inflation to overcome our

propensity for current consumption

When investing our money, is it i or r ?

It just depends on the “point of view”…

r =____ = ____

rate of return, lender’s view (income)

i =_________ = _______

interest rate, borrower’s view (expense)

opportunity cost – When

considering any activity, the value of the next best available alternative.

opportunity cost - It’s the value of

what you give up to do something.

For much of what we do in finance, opportunity cost is

the

interest rate – or some other rate of return – we give up by taking some action.

Sometimes opportunity cost is the

“lost” opportunity of the next best alternative

Interest

Can be ________ or________

charged (interest on your mortgage), earned (interest on a 2-year CD)

simple interest – ___amount charged

same, each period, based on the original principle.

compound interest – interest is ___ on

_____

earned/charged, principle + existing interest.

compound interest –This is

interest on top of interest.

value at end of period 2- value at end of period 1

interest earned

Mechanics of Compound Interest- In each year, you start with a _____ – your savings have been increased by the __________. So, your interest income also is _____

greater balance, previous year’s interest,higher.

The _____the interest rate, the ___your savings grow. A few percentage points

added to the compound interest rate can _______-

higher, faster , dramatically affect the future balance.

FV =

$1,000 × (1 + r)^n

PV =

the present value of the lump sum today

NPER =

number of time periods.

Rate = the ______ (or rate of return) expressed in

the same_________ (e.g., yearly, monthly,

weekly, etc.).

interest rate, time domain as NPER

PMT = the

amount of periodic cash flows, if any.

payment, used when we have a stream of level (same)

cash flows.

We need to be mindful of the SIGN of the cash flow.

Cash inflow versus Cash Outflow.

Excel functions solve equations similar to 0 =

FV = PV(1+rate)nper

PV(1+rate)^nper (excel)

= fv(rate, nper,, pv)

standard compound interest formula:

A=P(1+r/n)^nt

A=P(1+r/n)^nt

A is the final amount you will have at the end.

• P is your principal investment

• r is the annual interest rate expressed as a decimal

• n is the number of times the interest compounds per year

• t is the term of the CD in years

Present value (PV) excel =

PV(rate, nper,, fv)

present value =______ calculation

FV / (1 + r)^n

Finding PV is about reducing value out

from future to

now. Divide.

Finding PV is about reducing

value out from future to

now. Divide.

This ___________ – a most

important idea for finance.

reducing value is also

called discounting

“r” is measuring______. It’s an______

risk and lost opportunity _, interest

rate or rate of return.

Finding FV is about

increasing value out to the future. Multiply.

Present values are calculated using__________.

compound interest.

PVs decline when ________. The longer you have to wait for your money, ______

FV cash payments are delayed, the less it is worth today.

Present value is

bringing money back

FV is the

future cashflow and the future value of a lump sum.

r is called the

discount rate.

is the discount factor.

1 / (1 + r)n

Present Value

Value of a

future cashflow

Discount Factor

Present value of a $1 future payment

Discount Rate

Interest rate used to compute present value of a future cash flow

Practical Uses

Retirement Savings Goal…

Investment Comparison…

Grad School, Wedding, Travel, Home Purchase, etc. …

money grows to what amount in the future?, Which has a higher FV?,, How much it will cost in the future due to effects of inflation.

Discounted Cash Flow (DCF)

Method of calculating

present value by discounting future cash flows.

Discounted Cash Flow (DCF)

Discount each cash flow, then

sum (add) them up.

Discount Factor = ___= ____

DF, PV of $1

DF =

1/ (1 + r )^t

Discount factors can be used to

compute the present value of any cash flow.

PVs decline when the_________-. Your future money is ________

discount rate is higher, worth less today.

rate (r) =

(FV / PV)^1/n - 1

time (n) =

ln(FV / PV)/ ln(1 + r)

future value and ____- can find each other

rate

present value and ____- can find each other

time

The Rule of 72

Used to estimate the

number of years required to double a sum of money at a given rate of interest.

By dividing the rate of interest into 72, a

good estimate of the

period required to double your money can be calculated.

The Rule of 72 =

72 / r

Organizing inputs using a _____. To find the future value of a stream of cash

flows, calculate the - future value of Stream of Cash Flows

timeline, future value of each flow and then add them up.

We treat each cash flow

as a__________ over the _____ with the investment rate

of 6%- future value of Stream of Cash Flows

Then we _____________ to get the ________at the end of three years.

lump sum and calculate its FV, relevant number of years, sum up the

compounded values, accumulated value of deposits

To find the present value of a stream of cash flows, calculate the

present value of each flow and then add them up

present value of each flow

Each period’s__________ by the rate of 6%. The________over the two-year period determines_

The present value of the two- year series of cash flows is the

future cash flow is discounted, sum of the discounted values , today’s worth or present value.

amount you need to invest today to generate that future stream.

Using the NPV function: NPV(rate, values())

• Note that this

expects only future cash flows!

NPV function:

NPV(rate, values())

Also note that NPV requires that the i_________, but_____________ like the Excel TVM functions. Also needs ___________-

interest rate be the same for all the periods, DOESN’T require a negative

and a positive, contiguous streams (no breaks, use 0 if a time period has time period has no cash flow)

Spreadsheets can help you in making Finance decisions by

incorporating the _________. It is an extremely useful tool for ______

worth of money in relation to time, investment bankers and financial analysts.

excel=PV

(rate, nper, pmt, [fv],[type])

excel=FV

(rate, nper, pmt, [pv],[type])

excel =NPER

(rate, pmt, pv, [fv],[type])

excel=RATE

(nper, pmt, pv, [fv],[type],[guess])

excel=PMT

(rate, nper, pv, [fv],[type])

TVM Terminology

PV

• Present Value

• Today’s Value

• Discounted Value

TVM Terminology

NPER

• Number of periods

• Time: year, month, week

• t, n

TVM Terminology

FV

• Future Value

• Value tomorrow

• Value out in time

• Inflation adjusted value

TVM Terminology

Rate

• Interest rate (i)

• Discount rate (r)l

• Required rate of return

• Cost of capital

TVM Terminology

PMT

• Amount of recurring payment

• Level (unchanging) amount

• An annual annuity

In Excel for Finance, future payments can either be

periodic constant payments or a lump sum amount at the end of the investment period, or both a periodic constant payment and a lump sum.

=PV(rate, nper, pmt, [fv],[type])

=PV(interest rate, number of periods, periodic payment, initial amount)

=PV(rate, nper, pmt, [fv],[type])

rate –

nper –

pmt –____ If this is omitted, make sure you

provide Excel with a FV.

[fv] –_____This is an optional argument.

[type] – __

Interest rate per period., Total number of compounding periods., Annuity amount per period.. Future value of the investment. , It is 0 if the annuity is received at the end of the compounding

period and 1 if it received at the beginning of the compounding period. This is an optional argument and by default, its value is set to 0.

The RATE function in Excel can be used to find the

interest rate

for discounting the future value of the investment in present

value calculation.

The syntax of the RATE function is :

=RATE (nper, pmt, pv, [fv],[type],[guess])

The last argument of this function is “guess”. It is an optimal

argument that is used to provide Excel with an

estimate of what

the rate could be. If omitted, the default value will be 10%.

The PMT function calculates thd

periodic

payment against an investment or a loan at a constant

interest rate for a specified period of time.

Value of an Annuity

Annuity payment streams involve equal, periodic outflows

and inflows.

Examples of an annuity stream include

rent, lease, mortgage, car loan, and retirement annuity payments.

Annuity vs Annuity Due: ________is the difference.

timing of the payment

_______________(mortgage and loan payments) is known as an ordinary annuity.

An annuity stream starting at the end of each period

_______________(rent and insurance payments) is an annuity due.

An annuity stream beginning at the start of each period

To find the present value of an ordinary annuity, you could

value each cash

flow at the end of each period by the discount rate and then sum them.

ordinary annuity / (1+discount rate) ^ year

Present Value of an Annuity

the present value of a series of equal periodic cash flows

across time for a finite period

Present Value of an Annuity formula

pv = pmt * (1-(1/(1+r)^n)))/r

Present Value of an Annuity formula excel

PV(Rate, Nper, Pmt, FV, Type)

Practical applications of an present value of an annuity include figuring out the

Present Value of an Annuity formula

nest egg needed prior to retirement, or the lump sum needed for college

expenses.