This presentation is based on the course offered by Dr. Kaul and covers the basic things about the financial concepts mainly in Time Value of Money.

1. INTRODUCTION TO FINANCE
By: NIKHIL LOHIYA

2. WHAT IS FINANCE AND ITS
APPLICATIONS??
• Dictionary Definition: the management of large amounts of money,
especially by governments or large companies.
• Simply managing money – Small/large!
• Where is it used??
• Daily Life (Pocket money)
• Reading ET
• Making tough financial decisions (Banking etc.)
• For making decisions of a company
• For running government.

3. TWO-PILLARS OF FINANCE
• Economics
• Definition: It is the branch of knowledge concerned with the production,
consumption, and transfer of wealth.
• Heart of finance.
• Accounting
• Definition: It is the process or work of keeping financial accounts.
• Language of communication.

4. >TIME VALUE OF MONEY
>CAPITAL BUDGETING

5. WHAT TVM?
• Definition of Time Value of Money
• Why time is important ?
• Notations
• Formulas
• Example Calculation
• Benefits of the Knowledge of Time Value of Money

6. INTRODUCTION
DEFINITION
time value of money is the premise that an investor prefers to receive a
payment of a fixed amount of money today, rather than an equal
amount in the future, all else being equal.

7. ESSENCE OF DECISION MAKING
• Which would you rather have -- $1,000 today or $1,000 in 5 years?
• Money received sooner rather than later allows one to use the funds
for investment or consumption purposes.

8. ESSENCE OF DECISION MAKING
• Which would you rather have -- $1,000 today or $1,000 in 5 years?
• Money received sooner rather than later allows one to use the funds
for investment or consumption purposes.
• All other factors being equal, it is better to have $1,000 today.
• Simply put this is the concept of the time value of money.

9. SOME TERMINOLOGY
• PV = Present Value ($)
• FV = Future Value ($)
• n = Number of Periods (#)
• r = Interest Rate (%) > 0 (Assumption)
• Pmt = Payments
• Remember, No uncertainty. (For now)

10. IMPORTANCE OF TIME-LINES
• N
• PV
• FV
• R
• Pmt

11. EXAMPLE
• Question: Suppose a bank pays 10% interest rate per year and you are given
a choice between two plans:
• A: Receive $100 today.
• B: Receive $100 one year from now.

12. FUTURE VALUE
• TIME-LINE
• COMPUTING THE FUTURE VALUE
• FV = P + r*P = (1+r)P
initial payment + accumulated interest
• FV = P(1 + 𝑟) 𝑛
• (Compounding)

13. FUTURE VALUE EXAMPLE-1
• What is future value of $100 two years from now at 10% interest rate?
• Suppose you invest $500 in you bank account at an interest rate of 7%? How
much will you have at the end of 10 years?
• HOW TO DO THIS PROBLEM USING EXCEL??

14. FUTURE VALUE EXAMPLE-2
• Ques: Peter Minuit bought the Manhattan Island from the Native Americans
for $24 in 1626. Suppose that Native Americans could have earned 6% on
their investments all these year. How much would they have today?

15. FUTURE VALUE EXAMPLE-2
• Ques: Peter Minuit bought the Manhattan Island from the Native Americans
for $24 in 1626. Suppose that Native Americans could have earned 6% on
their investments all these year. How much would they have today?
• Ans: ($177,622,793,082.56)

16. PRESENT VALUE
• FV = P(1 + 𝑟) 𝑛
• Payment = Present Value
• It is the value of money that you need to invest today to obtain a fixed
amount in future keeping the time and rate of interest constant.
• Representation on timeline.

17. EXAMPLE
• Question: What is the present value of $110 one year from now if the interest
rate is 10%.
• **Concept of discounting!

18. MULTIPLE PAYMENT: ANNUITIES
• Annuities: It is a special case of payments : C or Pmt
• Why C and Pmt?
• Payments are made back for the obligations.

19. FV - ANNUITIES
• Concept of annuities in future value.
• Doing table analysis of the FV of annuities.
• Generating the formula for the FV of annuities.

20. FV - ANNUITIES
• Concept of annuities in future value.
• Doing table analysis of the FV of annuities.
• Generating the formula for the FV of annuities.
• Ques: What will be the value of the port folio at the retirement if you deposit
$100,000 every year in a pension fund. You plan to retire in 40 years and
expect to earn 8% on your portfolio.

21. FV - ANNUITIES
• Concept of annuities in future value.
• Doing table analysis of the FV of annuities.
• Generating the formula for the FV of annuities.
• Ques: What will be the value of the port folio at the retirement if you deposit
$100,000 every year in a pension fund. You plan to retire in 40 years and
expect to earn 8% on your portfolio.
• Ans: $25,905,651.87

22. FV - ANNUITIES
• Concept of annuities in future value.
• Doing table analysis of the FV of annuities.
• Generating the formula for the FV of annuities.
• Ques: What will be the value of the port folio at the retirement if you deposit
$100,000 every year in a pension fund. You plan to retire in 40 years and
expect to earn 8% on your portfolio. If you have $1m as today how much
total do you have 40 years from now?

23. FV - ANNUITIES
• Concept of annuities in future value.
• Doing table analysis of the FV of annuities.
• Generating the formula for the FV of annuities.
• Ques: What will be the value of the port folio at the retirement if you deposit
$100,000 every year in a pension fund. You plan to retire in 40 years and expect to
earn 8% on your portfolio. If you have $1m as today how much total do you have 40
years from now?
• Ans: ($47,630,173.37)
• What happens if the rate drops to 5% ?

24. EXAMPLE FV - ANNUITY
• Ques: Suppose you want to guarantee yourself $500,000 when you retire 25
years from now. How much should you invest each year:
• Starting at the end of this year at 8% interest rate?
• Starting today at 8% interest rate?

25. EXAMPLE FV - ANNUITY
• Ques: Suppose you want to guarantee yourself $500,000 when you retire 25
years from now. How much should you invest each year:
• Starting at the end of this year at 8% interest rate?
• Starting today at 8% interest rate?
• Ans: ($6,839.39)
($6,253.56)

26. PV - ANNUITY
• Concept of annuities in present value.
• Doing table analysis of the PV of annuities.
• Generating the formula for the PV of annuities.

27. PV - ANNUITY
• Concept of annuities in present value.
• Doing table analysis of the PV of annuities.
• Generating the formula for the PV of annuities.
• Ques: How much money do you need in the bank today so that you can
spend $10,000 every year for the next 25 years, starting at the end of this
year. Suppose r = 5%.

28. PV - ANNUITY
• Concept of annuities in present value.
• Doing table analysis of the PV of annuities.
• Generating the formula for the PV of annuities.
• Ques: How much money do you need in the bank today so that you can
spend $10,000 every year for the next 25 years, starting at the end of this
year. Suppose r = 5%.
• Ans: ($140,939.45)

29. PV - ANNUITY
• Concept of annuities in present value.
• Doing table analysis of the PV of annuities.
• Generating the formula for the PV of annuities.
• Ques: You plan to attend a business school and you will be forced to take
out $100,000 in a loan at 10%. You want to figure out your yearly payments,
given that you will have 5 years to pay back the loan.

30. PV - ANNUITY
• Concept of annuities in present value.
• Doing table analysis of the PV of annuities.
• Generating the formula for the PV of annuities.
• Ques: You plan to attend a business school and you will be forced to take
out $100,000 in a loan at 10%. You want to figure out your yearly payments,
given that you will have 5 years to pay back the loan.
• Ans: ($26,379.75)

31. LOAN - AMORTIZATION
YEAR BEGNING
BALANCE
YEARLY BALANCE INTEREST AMOUNT PRINCIPLE
PAYMENT
1
2
3
4
5

32. AMORTIZATION
YEAR BEGNING
BALANCE
YEARLY BALANCE INTEREST AMOUNT PRINCIPLE
PAYMENT
1 100000 26380
2 26380
3 26380
4 26380
5 26380

33. AMORTIZATION
YEAR BEGNING
BALANCE
YEARLY BALANCE INTEREST AMOUNT
(10%)
PRINCIPLE
PAYMENT
1 100000 26380 10001.05 16378.95
2 83621.05 26380
3 26380
4 26380
5 26380

34. AMORTIZATION
YEAR BEGNING
BALANCE
YEARLY BALANCE INTEREST AMOUNT
(10%)
PRINCIPLE
PAYMENT
1 100000 26380 10001.05 16378.95
2 83621.05 26380 8362.11 18017.89
3 65603.16 26380
4 26380
5 26380

35. AMORTIZATION
YEAR BEGNING
BALANCE
YEARLY BALANCE INTEREST AMOUNT
(10%)
PRINCIPLE
PAYMENT
1 100000 26380 10001.05 16378.95
2 83621.05 26380 8362.11 18017.89
3 65603.16 26380 6560.32 19819.68
4 45783.47
5

36. AMORTIZATION
YEAR BEGNING
BALANCE
YEARLY BALANCE INTEREST AMOUNT
(10%)
PRINCIPLE
PAYMENT
1 100000 26380 10001.05 16378.95
2 83621.05 26380 8362.11 18017.89
3 65603.16 26380 6560.32 19819.68
4 45783.47 26380 4578 21802
5 23982

37. AMORTIZATION
YEAR BEGNING
BALANCE
YEARLY BALANCE INTEREST AMOUNT
(10%)
PRINCIPLE
PAYMENT
1 100000 26380 10001.05 16378.95
2 83621.05 26380 8362.11 18017.89
3 65603.16 26380 6560.32 19819.68
4 45783.47 26380 4578 21802
5 23982 26380 2398 23982

38. POWER OF FINANCE!!
• How much do you owe a bank or a lender after some n years?
• Loan Refinancing!
• Relate to previous example.

39. CHANGING TIMELINE!
• Annual rates!!
• Monthly rates!!
• Quarterly rates!!
• How to change timeline and problems if the interest compounds monthly?
• How much is new annual r?
• EXAMPLE

40. VALUING PERPETUITIES
• A perpetuity is simply a set of equal payments that are paid forever, with or
without growth.
• Examples: Stocks.

41. VALUING PERPETUITIES
• A perpetuity is simply a set of equal payments that are paid forever, with or
without growth.
• Examples: Stocks.
• Formulas but not true always.
• PV = C/R
• PV = C/(R-g)

42. MEGA EXAMPLE -1
• Ques: Suppose you are exactly 30 years old. You believe that you will be
able to save for the next 20 years, until you are 50. For 10 years following
that, and till your retirement at age 60, you will have a spike in your expenses
due to your kids’ college expenses, weddings, etc., and you will not be able
to save. If you want to guarantee yourself $100,000 per year starting on your
61st birthday, how much should you save every year, for the next 20 years,
starting at the end of this year.
Assuming that your investments are expected to yield 8% and you are likely
to live till 80.

43. MEGA EXAMPLE -1
• Ques: Suppose you are exactly 30 years old. You believe that you will be
able to save for the next 20 years, until you are 50. For 10 years following
that, and till your retirement at age 60, you will have a spike in your expenses
due to your kids’ college expenses, weddings, etc., and you will not be able
to save. If you want to guarantee yourself $100,000 per year starting on your
61st birthday, how much should you save every year, for the next 20 years,
starting at the end of this year.
Assuming that your investments are expected to yield 8% and you are likely
to live till 80.
• Answer:

44. MEGA EXAMPLE - 2
• Ques: You plan to retire 33 years from now. You expect that you will live 27
years after retiring. You want to have enough money upon reaching
retirement age to withdraw $180,000 from the account at the beginning of
each year you expect to live, and yet still have $2,500,000 left in the account
at the time of your expected death (60 years from now). You plan to
accumulate the retirement fund by making equal annual deposits at the
end of each year for the next 33 years. You expect that you will be able to
earn 12% per year on your deposits. However, you only expect to earn 6%
per year on your investment after you retire since you will choose to place
the money in less risky investments. What equal annual deposits must you
make each year to reach your retirement goal?

45. MEGA EXAMPLE - 2
• Ques: You plan to retire 33 years from now. You expect that you will live 27
years after retiring. You want to have enough money upon reaching
retirement age to withdraw $180,000 from the account at the beginning of
each year you expect to live, and yet still have $2,500,000 left in the account
at the time of your expected death (60 years from now). You plan to
accumulate the retirement fund by making equal annual deposits at the
end of each year for the next 33 years. You expect that you will be able to
earn 12% per year on your deposits. However, you only expect to earn 6%
per year on your investment after you retire since you will choose to place
the money in less risky investments. What equal annual deposits must you
make each year to reach your retirement goal?
• Ans: ?

46. >CAPITAL BUDGETING
>TIME VALUE OF MONEY

47. INTRODUCTION – ESSENCE OF
DECISION MAKING
Capital budgeting, or investment appraisal, is the planning process used to
determine whether an organization's long term investments.
• PROPERTIES OF GOOD DECISION MAIKING:
• Make sense!
• Unit of measurement.
• Benchmark – analysis? What is good and what is bad?
• Easy to communicate
• Easy to compute
• Easy to compare different projects/ideas.

48. FUNDAMENTAL TECHNIQUES
• NPV
• IRR
• Payback Period
• B-C Ratio