Accounting and Finance Management

1. Joseph Winthrop B. Godoy
Reporter
Thursday, September 15, 2016
Time Value of Money
Master in Management Technology
Batch 36
Accounting and Financial Management

3. • The amount of money is not the only thing
that matters…
• What also matters is when you have to get
(from investment) or when you have to give (to
investment) the money
• Whenever we talk about money, we can also
talk about its value or growth (+/-) over time.
Money is a manageable variable amount that
can increase or decrease over a constant
future Timeline. -jwbgodoy
Introduction

4. Parable of the Talents
Mat 25:14-30 (14) "At that time God's kingdom will also be like a
man leaving home to travel to another place for a visit. Before he
left, he talked with his servants. He told his servants to take care
of his things while he was gone. (15) He decided how much
each servant would be able to care for. The man gave one
servant five bags of money (five talents). He gave another servant
two bags(two talents). And he gave a third servant one bag(one
talent). Then he left. (16) The servant who got five bags went
quickly to invest the money. Those five bags of money earned
five more. (17) It was the same with the servant who had two
bags. That servant invested the money and earned two more.
(18) But the servant who got one bag of money went away and
dug a hole in the ground. Then he hid his master's money in the
hole.

5. Parable of the Talents
(19) "After a long time the master came home. He asked the
servants what they did with his money. (20) The servant who
got five bags brought that amount and five more bags of money
to the master. The servant said, 'Master, you trusted me to care
for five bags of money. So I used them to earn five more.' (21)
"The master answered, 'You did right. You are a good servant
who can be trusted. You did well with that small amount of
money. So I will let you care for much greater things. Come and
share my happiness with me.' (22) "Then the servant who got
two bags of money came to the master. The servant said,
'Master, you gave me two bags of money to care for. So I used
your two bags to earn two more.'

6. Parable of the Talents
(23) "The master answered, 'You did right. You are a good
servant who can be trusted. You did well with a small amount of
money. So I will let you care for much greater things. Come and
share my happiness with me.' (24) "Then the servant who got
one bag of money came to the master. The servant said,
'Master, I knew you were a very hard man. You harvest what you
did not plant. You gather crops where you did not put any seed.
(25) So I was afraid. I went and hid your money in the ground.
Here is the one bag of money you gave me.' (26) "The master
answered, 'You are a bad (wicked) and lazy servant! You say you
knew that I harvest what I did not plant and that I gather crops
where I did not put any seed.

7. Parable of the Talents
(27) So you should have put my money in the bank. Then, when
I came home, I would get my money back. And I would also get
the interest that my money earned.' (28) "So the master told his
other servants, 'Take the one bag of money from that servant
and give it to the servant who has ten bags. (29) Everyone who
uses what they have will get more. They will have much more
than they need. But people who do not use what they have will
have everything taken away from them.' (30) Then the master
said, 'Throw that useless servant outside into the darkness,
where people will cry and grind their teeth with pain.'

8. 1 bag of money =

12. Reporter’s Objectives:
1) Understanding the definition of Time Value of
money or TVM
2) Knowing the Components of Time Value of
Money
3) How to Answer the Question in TVM with
different methods
4) TVM Formulas & Computations
5) Compounding vs. Discounting
6) Time Line, Annuity & Perpetuity
7) Application of Time Value of Money

13. Understanding the TVM
 What is TVM or Time Value of Money?
 It is one of the most important concept of Financial
Management. The worth of a unit money is going to be
changed in the future.
 It refers to the fact that ₱1 in hand today is worth more
than ₱1 promised at some time in the future
 The reason for the differential is that ₱1 today can be
invested to earn a return called interest (Simple or
Compounded interest)
 Compounding and Discounting form the basis for the
valuation process used in financial management

15. Invest for
as long as
possible
Invest as
much as
possible, as
often as
possible
Invest at the
highest
interest rate
possible

18. How to Answer the Question

24. Interest
Principal
InterestInterestInterest
Time Line

25. Simple Interest

26. = FV
PV x [ 1+(i x N) ] = FV
I=(PV)(i)(N) = PxRxT
FV = PV + I = Future Value
= PV + PV(R)(T)
= PV [1 + (R)(T)]

27. Compound Interest

29. How compound interest works
(Basic Compounding)
• The table shows the ending wealth that an investor
could have accumulated by the end of 1998 had he
invested ₱1,000 in 1938
• Cumulative Wealth (₱ 000s)
1938 1948 1958 1968 1978 1988 1998
Share of Stocks 1,091 2,103 10,128 27,639 51,038 193,038 485,068
Bonds 1,056 1,434 1,623 2,084 3,691 10,480 37,720
Treasury Bills 1,006 1,058 1,244 1,893 3,678 11,489 23,253
Phil. Stocks Exchange1,344 2,651 15,602 44,804 66,815 303,322 2,260,431

33. Example of Simple vs.
Compounding Interest
Example: ₱100 invested for 30 years
at an annual interest rate of 8%
Simple Interest: ₱340.00
Annual Compounded Interest:
₱1,006.27
As we can see, if we translate this
same “compound vs. simple” approach
to a larger principal amount, the
difference between the two can be end
up being very different.
FV= PV (1+i)N
FV= PV [1 + (R)(T) ]

34. Compound and Discounting
Compounding method is used to know the future value of
present money
Discounting is a way to compute the present value of future
money

35. Present(₱)Past(₱) Future(₱)
M(1+i)-n M(1+i)+n
M
Compounding & Discounting
Discounting Compounding
Time Line

36. Compound and Discounting Variables
P = current cash flow
F = future cash flow
PV = Present Value of a future cash flow(s)
FV = Future Value of a cash flow(s)
A = the amount of annuity
i = the stated (or nominal) interest rate
I = amount of interest
r = the effective period rate of return
n = # of periods under consideration
m = # of compounding periods per year

39. Compounding Formula
Fn = P(1 + r)n or FV = PV(1 + r)n
• The equations represent the
compounding relationship that is the
basis for determining equivalent future
and present values of cash flows
• Compounding – the process of
converting present values of cash
flows into their future value
equivalents
 To find the Future Value (FV) of a
certain Present Value (PV)

41. Discounting Formula
PV = __FV _ or PV = FV(1 + r)-
n
(1 + r)n
• Discounting – the process of
converting future values of cash
flows into their present value
equivalents
 To find the Past Value of a certain
Present Value

47. PV=$100 FV=$ ???
Future Value

48. Given: PV = $100 i = 10% = 0.10 N = 5 years
Required: FV or Future Value
Solution : FV = PV x (1 + i)N
Future Value Formula

50. (Discounting Formula)

51. PV =

53. ______
____
___________

56. Annuity Formulas
• Future Value of an annuity
FV = 𝑨
𝟏+𝒓 𝒏−𝟏
𝒓
• Present Value of annuity
PV = 𝑨
𝟏−
𝟏
𝟏+𝒓 𝒏
𝒓
= 𝑨
𝟏+𝒓 𝒏−𝟏
𝒓 𝟏+𝒓 𝒏

57. Varying Compound Periods
Any time period can be chosen for
compounding
Effective interest rate – actual
interest rate earned after adjusting
the nominal interest rate for the
number of compounding periods

58. Varying Compound Periods
• Effective annual rate formula
𝒓 𝒂𝒏𝒏𝒖𝒂𝒍 = 𝟏 +
𝒊
𝒎
𝒎
− 𝟏
• Effective period rate formula
𝒓 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 = 𝟏 +
𝒊
𝒎
𝒎
𝒇
− 𝟏

59. Cash Flows Across Time Periods
To determine the present and future values
associated with multiple cash flows that are paid
through time, the following process is used:
1. Choose a point in time as the basis for
economic comparison
2. Shift cash flows that occur at different times
into equivalent amounts at the chosen point in
time through compounding or discounting
3. Add or subtract all of these equivalent cash
flows to obtain a net total

62. PV=$272.32
x (i=5%)
$285.94
- 100.00
------------
$185.94
x (i=5%)
$195.23
- 100.00
------------
$ 95.23
x (i=5%)
$ 100.00
- 100.00
------------
$ 00.00
FV=$315.24

69. Annuity Due
• Annuity due - payments are made at the
beginning of each period
Example: leasing arrangements
• To compensate for the payment made at
the beginning of the time period, multiply
the future or present value annuities
factors by (1 +r) to shift them by one
period

70. Amortization of Term Loans
• Compounding and discounting are found in
debt financing
• Under term loans or mortgages, borrower
repays original debt in equal installments
consist of two portions:
1. Interest
2. Principle

71. Amortization of Term Loans
• Common computational problems with
term loans or mortgages include:
1. What effective interest rate is being charged?
2. Given the effective interest rate, what amount of
regular payments have to be made over a given
time period, or what is the duration over which
payments have to take place given the amount?
3. Given a set of repayments over time, what portion
• represents interest on principle?
• represents repayment of principle?

72. Repayment Schedules for Term Loan
and Mortgages
• Most loans are not repaid on an annual basis
• Loans can have monthly, bi-monthly or weekly
repayment schedules
• In the Philippines, interest on mortgages is
compounded monthly in other country Canada
semi-annually posing a problem in calculating
the effective period interest rate

77. • Exist when an annuity is to be paid in perpetuity
• Present value of Perpetuity
• Example: Lifetime Savings Calculator (see Excel File)
𝑜𝑟 𝑃𝑉 =
𝐴
𝑟

78. Time Value of Money Application
1. Mortgages
1. Annualized Growth Rates
1. Example: If a company’s earnings were ₱100 Million 5 yrs. ago, and
are ₱200 Million today, the annualized 5-year growth rate could be
found by: Growth Rate (g) = (FV/PV)1/N – 1 =
(200,000,000/100,000,000)1/5 – 1 = 0.1487=14.87%
2. Monthly Mortgage Payments
1. Example: A 30-year loan with monthly compounding (so N=30*12=360
years), and a rate of 6% (so r=0.06/12=0.005), we first calculate the PV
Annuity factor: PV Annuity Factor = (1- (1/(1+r)N)/r = (1-
(1/(1.005)360)/0.005 = 166.7916
2. With a loan of ₱250,000, the monthly payment in this example would
be ₱250,000/166.7916, or ₱1,498,.88 a month

79. Time Value of Money Application
2. Retirement Savings
1. Savings and retirement planning are sometimes more complicated,
as there are various life-cycles stages that result in assumptions for
uneven cash inflows and outflows. Problems of this nature often
involve more than one computations of the basic time value
formulas; thus the emphasis on drawing a timeline is sound advice,
and a worthwhile habit to adopt even when solving problems that
appear to be relatively simple.

80. 1. Given the actual amount of money you have now in your pocket:
2. Compute the FV with simple interest of 5% per year up to year 2036 and
compare the FV with compounded interest of 7.1773462% every year up to
2026.
3. Then, add your FV to the PV of Jowin’s savings account that pays 3%
interest rate compounded annually which will grow its value in 5 years
amounting to ₱ 4,579.13
4. With that computed amount available, we decided to donate 50% of our
money to a charitable institution, How much is to be given to the
charitable institution?
5. If you subtract your actual money from the remaining amount and invest it
up to 2020 with annual interest rate of 10% compounded quarterly, solve
for the maturity value of the investment and the interest earned.
Bonus: Five (5) Lessons you learned from the Parable of the Talents
Note: Your 5 answers must be at least 1 to 3 words only
Seatwork

81. TVM Formulas:
1. Simple Interest: I = P(R)(T) F = P + P(R)(T) =P(1+RT)
2. Compounding and Discounting:
Future Value: a) Single Cash Flow: FV = PV (1+i)N
b) Annuity: FV = A[(1+r)n - 1) / r ]
Present Value: a) Single Cash Flow: PV = FV (1+i)-N
b) Annuity: PV = A[{1-
[1/(1+r)n]}/r(1+r)n ]
PV = A[(1+r)n - 1)/r(1+r)n ]
3. Varying Compound Periods
• Effective annual rate formula
• Effective period rate formula
11 






m
m
i
annualr
11 






f
m
m
i
effectiver

82. Solutions
1. ₱ 100.00 (my actual money)
2. Simple Interest: FV = PV + PV(R)(T) =PV(1+RT)
FV=100(1+.05*20) = 100(1+1) = ₱200 (Ans)
Compounded Interest: FV = PV (1+i)N = 100(1+0.718) 10 =₱200. 05(Ans)
3. ₱200 + PV = Ans. Given: FV=4,579.13 i=3% N=5yrs PV=FV/(1+i)N =
4,579.13/(1+0.03)5 = 3949.997 = 3950.00 ; ₱200+PV = ₱ 4,150.00 (Ans)
4. M = 4,150 – 4,150*50% = 4,150-2,075 = ₱ 2,075.00 (Ans)
5. Mymoney = (2,075-100) = ₱ 1,975.00 FV=PV[1+ (i/m)]tm ; PV=1975;
i=10% m=4 (qtrly); t=2020-2016=4yrs ; FV = 1975[1+(0.1/4)]4(4)
Maturity Value = ₱ 2,931.90 (Ans)
Interest Earned = FV – PV = 8,720.12-1,975 = ₱ 956.90 (Ans)
Bonus: 5 Lessons learned from the Parable of the Talents
1. Be Good
2. Be Faithful
3. Responsible steward (manager)
4. Use Time wisely
5. Use Money wisely, etc…