slide thuyết trình TIME VALUE OF MONEY AND DCF MODEL

Nguyễn Thị Thu Trang 1LECTURE CONTENT • Part 1: Time value of money • Present value and future value of cash flows.. Nguyễn Thị Thu Trang 2OBJECTIVE LEARNING Explain what the time value

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TIME VALUE OF

MONEY

AND DCF MODEL

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ThS Nguyễn Thị Thu Trang 1

LECTURE CONTENT

• Part 1: Time value of money

• Present value and future value of cash flows.

• Part 2: Discounted cash flow valuation model

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OBJECTIVE LEARNING

Explain what the time value of money is and why it is so important in thefield of finance.

Explain the concept of future value, including the meaning of the termsprincipal, simple interest and compound interest, and use the

future value formula to make business decisions.

Explain the concept of present value, how it relates to future value, anduse the present value formula to make business decisions.

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TIME VALUE OF MONEY

Opportunity cost

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CF s at different times are not

Which asset would you rather own?

$1,000 now or next year?

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Put two CFs in comparable terms.

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I SINGLE CASH FLOW FORMULA

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I SIMPLE INTEREST

1 _1 10% 1 2

3 1

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• ‘Interest on interest’- interest earned on reinvestment of previously earned interest.

The interest in each

Principal and the

interest you previously earned.

COMPOUND INTEREST

period is earned using both the original

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ThS Nguyễn Thị Thu Trang

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FuturG value ($)

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Grovvth of $ 1 00 Oíiglnal amount at 1 0% per year Red

shaded area represents the portion of the total that results

from compoundlng of Inlerest

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CHANGING THE COMPOUNDING PERIOD

compounding)

depending on the nature of the asset

■ Bonds generally pay interest semi-annually.

■ Banks pay often pay interest on a monthly basis.

1 The annual interest rate (i) must be converted to a ‘periodic’ rate (i/m).

2 The number of periods in years (t) must be converted to a total number

of compounding periods (t*m).

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CHANGING THE COMPOUNDING PERIOD

• When the interest is compounded more than once per year:

• FV formula: FVt = PV(1 + -^)t2m

• PV formula: PV = 7*

(1+1)t»m

2 Example 1: A lump sum of $100 is invested for a period of three years

with an annual interest rate of 10%.What will its value be 3 years time?

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TIME VALUE - EXAMPLES

• Suppose you need $10,000 in one year for the down payment on a new car If you can earn 7% annually, how much do you need to invest today?

• Suppose you had a relative deposit $10

at 5.5% interest 200 years ago How much would the investment be worth today?

• You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today What is the implied rate of interest?

• You want to purchase a new car, and you are willing to pay $20,000 If you can invest

at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?

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DIFFERENT TYPES OF CASH FLOWS

Annuity: a level (equal sized) stream of cash flows for a fixed time

■ Ordinary Annuity : an annuity for which the cash flows occur at the ending of

each period

4 _5

■ Annuity Due : an annuity for which the cash flows occur at the beginning of

each period (the first payment occurs immediately)

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FUTURE VALUE OF AN ORDINARY ANNUITY

CF/(1+Ỉ) n-1 CF/(1+i) n -

1

CF CF/(1+i) 1 -

CF/(1+i) 2

-CF

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PVA = CF ~l-(l+i)~n ~

i

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I ORDINARY ANNUITY - EXAMPLE

save $300 each month If the interest rate is 3% per year, payablemonthly, how much can Maria save after 2 years?

much car can you afford if interest rates are 6% compoundedmonthly?

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FVADUE = FVA t (1 + r) = CF (1 + r)

f - 1

FUTURE VALUE OF AN ANNUITY DUE

Time

0 r%1 2 3 4 5

• There are 5 payments, but the first payment occurs immediately.

• This is the same as each CF of an ordinary annuity of (5) payments earns one

year interest more.

• In general term, the formula for the FV of an annuity due is:

Annuity due value = Ordinary annuity value x (1+r)

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PRESENT VALUE OF AN ANNUITY DUE

Annuity due value = Ordinary annuity value x (1+r)

PVADUE = PVA(1 + r) = CF (1 + r)

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ANNUITY DUE - EXAMPLE

money received each year at the 10% annual compound interest

savings account, the first deposit occur immediately Ask how much

money you will have at the end of the third year?

starting today, with a final payment to be made at the beginning of

Year 6 If the interest rate is 7% per year, what is the present value

of these cash flows?

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PRESENT VALUE OF A PERPETUITY

i(1 + 0 n

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-ThS Nguyễn Thị Thu Trang 20

i

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FUTURE VALUE OF MULTIPLE CASH

FLOWS

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FLOWS

2345 Time

7%

Q1:You deposit$100 inYear 1,

$200 in Year 2 and $300 in Year 3.

How much will you have in 3 years

with 7% interest per annum.

Q2: How much will it be in 5 years

if you don’t add additional cash?

$100

Solution 1

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FLOWS

5 1 -1 -1 -i -1 -1

Q1:You deposit$100 inYear 1,

$200 in Year 2 and $300 in Year 3.

How much will you have in 3 years

with 7% interest per annum.

Q2: How much will it be in 5 years

if you don’t add additional cash?

$343.47

$245.01

► $131.08

$719.56

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PRESENT VALUE OF MULTIPLE CASH

FLOWS

You are offered an

investment that will pay

$200 in Yr 1, $400 in Yr

2, $600 in Yr 3 and $800

at the end of Yr 4.You

can earn 12% on similar

investments What is the

most you should pay for

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FUTURE VALUE AND PV OF MULTIPLE CASH FLOWS

I

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Case study: we have cash

flows generated through the

years below, calculate the

PV and FV of this cash

flow, indicating the

discount rate of 7%.

How much will it be in 7

years if you don’t add

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Effective Annual Rates of Interest

• A reasonable question to ask in the above example is “what is the

effective annual rate of interest on that investment?”

• FV3 = 100x(1 + ^)2x3 = 100x(1.05)6=$134

• The Effective Annual Rate (EAR) of interest is the annual rate that

would give us the same end-of-investment wealth after 3 years:

• 100 x (1+EAR)3 = $134

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Effective Annual Rates of Interest

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The Discounted Cash Flow Model - DCF

• The discounted cash flow model is built on the basis of the concept ofmonetary price and the relationship between profit and risk (will bedetailed in the following chapters)

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Asset valuation, including tangible assets and financial assets, to decide whether to buy or sell the property.

Analyze, evaluate and make decisions

on whether or not to invest in an

whether to buy or rent a fixed asset.

Analyze, evaluate and decide whether

or not to buy a business.

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CF(1+i) 0

I Ị - „ CF(1+i) n- < n-1 > = CF(1+i) * 1

L—————————————— _

- $114.49=100(1.07) 2

I

628.49(1.07) 2 —►[ $719.56

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FV at Year 5

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