CORPORATE FINANCE

CHAPTER 3 : TIME VALUE OF MONEY

Chapter Outline
01 FUTURE VALUE

02 PRESENT VALUE

03 ANNUITY

04 COMPOUNDING PERIODS

05 SIMPLIFICATIONS
Imagine…!!!

Which would you prefer – RM 1,000

today or RM 1,000 in 5 years?

Obviously RM 1,000 today

You already recognize that there is
TIME VALUE OF MONEY
01. FUTURE VALUE
FUTURE VALUE (FV) is the value of a current asset at a specified date in the future based
on an assumed rate of growth

Formula :

C0 =Cash to be invested at period 0

FV = C0 x (1+r)t r
t
= Interest rate per period
= number of periods
1. Simple Interest
Future Value = Current Value ( 1 + (Interest Rate x Number of Years

$170 $100 .07 10

FOR
7% 10
$100 Years
2. Compound Interest
10
Number
Future Current (( 1 + Interest ) Of years
Value = )
Value Rate

196.72 $100 .07

FOR
$100 7% 10
Years
 PRACTISE
Mr. Kent has put RM 500 in a savings account on
Maybank. The account earns 7%, compounded
annually. How much Mr. Kent have at the end of three
years?

FV = C0 x (1+r)t
= RM 500 x (1+0.07) 3
= RM 612.52
02. PRESENT VALUE
PRESENT VALUE (PV) is the current value of a future sum money or stream of cash flows
given a specified rate of return.

PV also referred to as discounted value

Formula :

FV = Future Value
PV = FV / (1+r)t r
t
= Interest rate per period
= number of periods
 PRACTISE 1
How much would an investor need to lend today so that
she could receive $1 two years from today, interest rate of
9%.

PV = FV / (1+r)t
= $1 / ( 1+ 0.09) 2
= $1 / (1.1881)
= $ 0.84

Note : The process calculating the present value of a

future cash flow is called discounting
 PRACTISE 2
Billy will receive $20,000 three years from now. He can
earned 8% on his investment. What is the present value
of his future cash flow?

PV = FV / (1+r)t
= $20,000 / ( 1+ 0.08) 3
= $20,000 / (1.259)
= $ 15,87
03. ANNUITY
Annuity is a level stream of regular payments that lasts for fixed number
of periods.

1
1−
1+𝑟 𝑡
𝑃𝑉 = 𝐶
𝑟
 PRACTISE
Linh Dang has just won the state lottery, paying $50,000 a
year for 20 years. He is to receive first payment from now.
If the interest rate is 8 percent, what is the present value
of the lottery?
1
1−
1+𝑟 𝑡
𝑃𝑉 = 𝐶
𝑟
1
1− 20
1 + 0.08
𝑃𝑉 = $ 50,000 𝑥
.08
= $ 50,000 x 9.8181
= $ 490,905
We can also provide a formula for the future value of an annuity:

𝟏+𝒓 𝒕−𝟏
𝑭𝑽 = 𝑪
𝒓

Example:
Suppose you put $3,000 per year into CleverAds Corp. The account pays 6 percent
interest per year. How much will you have when you retire 30 years?
1+𝑟 𝑡−1
𝐹𝑉 = 𝐶
𝑟
1+𝑟 𝑡 −1
𝐹𝑉 = 𝐶
𝑟
1+1,06 30 −1
= $3,000
.06
= $3,000 x 79.0582
= $237,174.56

Means that you will have close to a quarter million dollars in the account
Tricks in Annuity

DELAYED ANNUITY
The first payment is not paid immediately. 01

Annuity Due
02 The payment is due immediately at the
beginning of each period

Infrequent Annuity
The payments occurring less frequently than 03
once a year

04 Equating Present Value of

Two Annuities
Example Delayed Annuity
Alvin will receive a- four year annuity of $500 per year,
beginning at date 6. If the interest rate is 10 percent, what is
the present value of her annuity?

0 1 2 3 4 5 6 7 8 9 10
$500 $500 $500 $500
$984.13 $ 1,584.95

Step 1: Calculate Present value of annuity

1
1−
1.10 4
𝑃𝑉 = $500 𝑥
.10
= $500 x 3.1699
= $ 1,584.95
So that $ 1,584.95 represent the present value at date 5

Step 2 : Discount present value of the annuity back to date 0 :

PV = FV / (1+r)t
= $1,584.95 / 1.10 5
= $ 984.13
and $ 984.13 represent the present value on date 0
Example Annuity Due

Insurance
Car Payment
Mortgages

Imagine : You rent a house and the landlord require payment upon the
start of a new month continuously.
Growing Annuity
Growing annuity is a finite/ limited number of growing cash
flows.
Formula :

𝟏 𝟏 𝟏+𝒈 𝑻
𝑷𝑽 = 𝑪 − 𝒙
𝒓−𝒈 𝒓−𝒈 𝟏+𝒓

𝟏+𝒈 𝑻
𝟏− 𝟏+𝒓
=C
𝒓−𝒈
04. COMPOUNDING
Compounding is refers to the increasing value of an asset due to the interest earned on both a
principal and accumulated interest.
Formula :

Annual percentage rate (APR) is the synonym of stated

annual interest rate (r)
Example
What is the end year wealth if Alpha start saving money in the
bank with 24 percent rate with monthly $1 investment ?

0.2412
𝐴 = $1 x 1 +
12

= $1 x 1.02 12

= $1.2682
 Effective Annual Rate (EAR)
Formula :

SAR / r = stated annual interest rate

n = number of compounding per periods
 Example
If the stated annual rate of interest 7 percent, is
compounded quarterly. What is effective annual rate ?

𝑆𝐴𝑅𝑛
EAR = 1 + -1
𝑛
0.084
EAR = 1 + -1
4
= .0824
= 8.24 %
 Compounding over Many Years
Future Value with Compounding Future Value with Compounding
 05. SIMPLIFICATION
PERPETUITY is a constant stream of
𝐶
𝑃𝑉 =
cash flows without end 𝑟
Formula for Present Value of
Perpetuity:
𝐶 𝐶 𝐶
𝑃𝑉 = + 2
+ 3
+ ….
1+𝑟 1+𝑟 1+𝑟

𝑪
Growing Perpetuity is a series of periodic payments that grow at a 𝑷𝑽 =
proportionate rate and rare received for an infinite amount of time 𝒓−𝒈
PV = Present Value of growing perpetuity
C = Cash flow to be received one period
r = Discount rate
g = Rate of growth per period
Thank you