Learning Objectives part 1 of 2

1
Chapter 4
2
Learning Objectives (part 1 of 2)

• Compute the future value of an investment
• Compute the present value of a future cash
  requirement or benefit
• Explain how to select an interest rate for a time
  value of money problem
• Describe an annuity
• Compute the future and present value of an annuity

3
Learning Objectives (part 2 of 2)

• Compute the future and present value of a growing
  annuity
• Explain how to adjust a problem when compounding
  is more than once per year
• Compute an effective annual rate
• Compute an inflation rate
• Compute an after tax rate of return Define the
  six steps of the personal financial planning
  process

4
Future Value Single Period

• V0 x (1 r) V1
• V0 the initial cash you have to invest
• r the interest rate at which you invest the
  cash, and
• V1 the ending value of your investment.

5
Future Value Multiple Periods

• V0 x (1 r)N VN
• N Number of periods
• (1 r)N Future value interest factor

6
Sample Problem (part 1 of 2)

• Stan Hoi has just borrowed 1,000 from his
  parents. He has promised to pay them all
  principal and interest in 6 years. The interest
  rate is set at 5 percent (his parents view the
  low interest rate as a gift). How much will he
  owe in six years?

7
Sample Problem (part 2 of 2)

• V0 1,000
• r .05
• N 6
• VN ?
• Solution 1,000 x (1 .05)6 1,340.10

8
Present Value Single Period

• Single Period

9
Present Value Multiple Periods
10
Sample Problem (part 1 of 2)

• Stan Hoi knows that he would like to have
  1,000,000 on the day he retires. He plans to
  retire in 30 years. He believes he can earn a 10
  percent rate of return on his money. How much
  would he have to set aside today to achieve his
  goal?

11
Sample Problem (part 2 of 2)

• 1,000,000 X 1/(1.10)30 1,000,000 x .5730855
  
• 57,308.55

12
Selecting an Interest Rate

• Opportunity Rate of Return
• Equal riskiness of cash flows
• Importance attached to outcome
• Less importance allows higher discount rate

13
Future Value of an Annuity (part 1 of 2)

• Annual Deposit x FVIFAr,N FVA
• FVIFA r,N future value interest factor of an
  annuity where the interest rate is r and the
  number of time periods is N, and
• FVA future value of an annuity.

14
Future Value of an Annuity (part 2 of 2)
15
Sample Problem (part 1 of 2)

• Stan wants to accumulate 1,000,000 by the time
  he plans to retire in 40 years. He believes he
  can achieve a rate of return of 10 percent on his
  investments. How much money must he set aside at
  the end of each year in order to reach his goal?

16
Sample Problem (part 2 of 2)

• Annual Deposit x FVIFAr,N FVA
• Annual Deposit x 442.59 1,000,000
• 1,000,000 / 442.59 2,259.43

17
Present Value of An Annuity

• Annual Withdrawal x PVIFAr,N Initial
  Investment
• PVIFA r,N present value interest factor of an
  annuity where the interest rate is r and the
  number of time periods is N

18
P.V. of Annuity Interest Factor
19
Sample Problem (part 1 of 2)

• Stan Hoi has achieved his goal of accumulating
  1,000,000 upon retirement. Stan expects to live
  no more than 25 years. He plans to keep this
  money invested at a rate of 6 percent. If he
  wants to withdraw equal dollar amounts from his
  savings at the end of each year for the next 25
  years, how much could he withdraw?

20
Sample Problem (part 2 of 2)

• Annual Withdrawal x PVIFAr,N Initial
  Investment
• Annual Withdrawals x 12.7834 1,000,000.
• 1,000,000/ 12.7834 78,226.45

21
Compounding more than once per year

• Determine the number of times per year
  compounding occurs (m)
• Multiply the number of years (N) by the frequency
  of compounding
• Divide the interest rate by the frequency of
  compounding

22
Sample Problem (part 1 of 2)

• Stan Hoi has put 200 into a two-year certificate
  of deposit at his credit union. The account pays
  interest at the rate of 6 percent per year,
  compounded monthly. How much will Stan's deposit
  be worth at the end of two years?

23
Sample Problem (part 2 of 2)

• Present value x (1 r/m)NT Future value
• 200 x (1.06/12) (2x12) 225.43

24
Nominal vs. Effective Annual Rate (EAR)

• Rear (1rnom/m)m 1
• rear effective annual interest rate,
• rnom stated nominal annual interest rate, and
• m number of times per year compounding occurs

25
Sample Problem (part 1 of 2)

• You look at your credit card statement and note
  that the interest rate is 18 percent. As the
  interest on credit cards is charged each month on
  the unpaid balance, the interest is compounded
  monthly or twelve times per year. What is the
  effective annual rate?

26
Sample Problem (part 2 of 2)

• rear (1 .18/12)(1 x 12) - 1 .1956 or
  19.56.

27
Consumer Price Index

• Current value of the index
• Value of Basket in current month
• ------------------------------------------ x 100
• Value of Basket in base period

28
Rate of Inflation

• How would one compute the rate of inflation from
  August 1999 to August 2000?
• CPI Aug. 00 CPI Aug99
• Inflation rate --------------------------
• CPI Aug99
• (172.8 167.1)/167.1 .034

29
How a planner might use an estimate of the
inflation rate

• Projecting the future price of a purchase
• Projecting the purchasing power of a lump sum of
  cash

30
Computing an after-tax rate of return

• rafter-tax rpre-tax x (1 marg. tax rate)
•  
• rafter-tax after-tax rate of return, and
• rpre-tax pretax rate of return