slide thuyết trình TIME VALUE OF MONEY AND DCF MODEL

• Single cash flow formula.. • Present value and future value of cash flows.. • Part 2: Discounted cash flow valuation model... the concept of present value, how it relates to future val

TIME VALUE OF MONEY

AND DCF MODEL

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

—Doug Hutchison

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

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

Explain

TIME VALUE OF MONEY

Which asset would you rather own?

$1,000 now or next year?

Put two CFs in comparable terms.

SINGLE CASH FLOW FORMULA

COMPOUND INTEREST

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

earned interest.

• The interest in each period is earned using both the original

principal and the interest you previously earned.

SIMPLE

INTEREST VS

COMPOUND

INTEREST

CHANGING THE COMPOUNDING PERIOD

• So far it has been assumed that the cash flows are yearly (annual

compounding)

• There are however many possible compounding periods that occurdepending on the nature of the asset

• Thus, how does this affect FV and PV calculations?

• Steps:

of compounding periods (t*m).

CHANGING THE COMPOUNDING PERIOD

• FV formula: 𝐅𝐕𝐭 = 𝐏𝐕(𝟏 + 𝐦𝐢 )𝐭∗𝐦

• PV formula: 𝐏𝐕 = 𝐅𝐕𝐭

(𝟏)𝐦𝐢 ) 𝐭∗𝐦

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

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?

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

each period (the first payment occurs immediately)

• Perpetuity: an annuity in which the cash flows continue perpetually

1 CF

CF CF

CF CF

1 CF

FUTURE VALUE OF AN ORDINARY ANNUITY

PRESENT VALUE OF AN ORDINARY ANNUITY

ORDINARY ANNUITY - EXAMPLE

Ø Starting with her next monthly salary payment, Maria intends tosave $300 each month If the interest rate is 3% per year, payablemonthly, how much can Maria save after 2 years?

ØIf you can afford a $2,000 monthly car payment for 2 years, how

much car can you afford if interest rates are 6% compounded

monthly?

FUTURE VALUE OF AN ANNUITY DUE

year interest more.

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

1 CF

PRESENT VALUE OF AN ANNUITY DUE

• There are 5 payments, and the first payment occurs immediately

• This is $CF today plus an ordinary annuity of (5-1) payments.

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

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

1 CF

ANNUITY DUE - EXAMPLE

• Suppose you rent a house for $12,000 a year and deposit all the

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?

• Kathy’s uncle promised her an allowance of $1,000 per year,

starting today, with a final payment to be made at the beginning ofYear 6 If the interest rate is 7% per year, what is the present value

of these cash flows?

PRESENT VALUE OF A PERPETUITY

• A perpetuity is the cash flow with inflows or outflows incurred forever.

• We have present value of normal cash flows.

• Using to valuate preference stock.

FUTURE VALUE OF MULTIPLE CASH FLOWS

• 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 additional cash?

FUTURE VALUE OF MULTIPLE CASH FLOWS

• 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 additional cash?

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

this one?

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?

Year Cash Flow

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?”

Effective Annual Rates of Interest

• FV3 = 100 x (1 + EAR)3 = $134

• (1 + EAR)"= %")%## = 1.34

• EAR = 1.34!" − 1 = 0.1025 = 10.25%

• So, investing at 10.25 % compounded annually is the same as

investing at 10% compounded semiannually

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)

DCF MODEL

APPLICATION

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 investment project

Analyzing, evaluating and deciding whether to buy or rent a fixed asset

Analyze, evaluate and decide whether

or not to buy a business.