slide thuyết trình TIME VALUE OF MONEY AND DCF MODEL

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TIME VALUE OF

MONEY

AND DCF MODEL

“I think being in love with life is a key to eternal youth.”

—Doug Hutchison

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ThS Nguyễn Thị Thu Trang

download by : skknchat@gmail.com

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LECTURE CONTENT

• Part 1: Time value of money

• The importance of time value of money.

• Single cash flow formula.

• Simple interest and compound interest.

• Present value and future value of cash flows.

• Part 2: Discounted cash flow valuation model

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

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TIME VALUE OF MONEY

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CFs at different times are not directly

$1,000 now or next year?

Put two CFs in comparable terms.

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SINGLE CASH FLOW FORMULA

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SIMPLE INTEREST

Time 0

$10 0

• The interest in each period is earned only using the original principal.

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and the interest you previously earned.

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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:

• The more frequent the compounding, the more money accumulates.

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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

§ Annuity Due : an annuity for which the cash flows occur at the beginning of each period

(the first payment occurs immediately)

CF forever

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FUTURE VALUE OF AN ORDINARY ANNUITY

Time 0 i% 1 2 … n-1 n

CF(1+i)n-n = CF(1+i)0CF(1+i)n-(n-1) = CF(1+i)1

…

CF(1+i)n-2CF(1+i)n-1

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PRESENT VALUE OF AN ORDINARY ANNUITY

Time 0i %1 2 … n-1 n

CF/(1+i)1CF/(1+i)2

… CF/(1+i)n-1CF/(1+i)n

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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% compounded

monthly?

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FUTURE VALUE OF AN ANNUITY DUE

Time

• 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

Time

Annuity due value = Ordinary annuity value x (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?

today, with a final payment to be made at the beginning of Year 6 If theinterest rate is 7% per year, what is the present value of these cash

flows?

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PRESENT VALUE OF A PERPETUITY

• We have present value of normal cash flows.

• Using to valuate preference stock.

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FUTURE VALUE OF MULTIPLE CASH FLOWS

Time 0

• Q1:You deposit $100 in Year 1, $100 $200

$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?

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FUTURE VALUE OF MULTIPLE CASH FLOWS

Time 0 7%

• Q1:You deposit $100 in Year 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

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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

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 additional cash?

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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?”

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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 of

monetary price and the relationship between profit and risk (will be

detailed 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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