Time Value of Money

Question 1

Types of cash flows:

Answer 1

– Lump sum
– Annuity
– Uneven cash flow

Question 2

Time Line

Answer 2

Time lines show timing of cash flows (Slide 6)

Question 3

What is the relationship of time and the value of money?

Answer 3

FVN + PV (1+I)N = 0.

 There are 4 variables.
 If 3 are known, you can (or the calculator will) solve for the 4th.
 Financial calculators solve this equation

Question 4

FV- Lump sum

Answer 4

Finding FVs (moving to the right on a time line) is called compounding
(Fomula: Slide 14)

Question 5

Four Ways to find FV

Answer 5

• Step-by-step approach using time line (as shown in previous slides).
• Solve the equation with a regular calculator (formula approach).
• Use a financial calculator.
• Use a spreadsheet.

Question 6

Annuity

Answer 6

Ordinary Annuity vs. Annuity Due

Question 7

Nominal rate

Answer 7

• Stated in contracts, and quoted by banks and brokers.
• Not used in calculations or shown on time lines
• Periods per year (M) must be given.
• Examples:
• > 8%; Quarterly
• > 8%, Daily interest (365 days)

Question 8

Periodic rate

Answer 8

• IPER = INOM/M, where M is number of
  compounding periods per year. M = 4 for quarterly, 12 for monthly, and 360 or 365 for daily compounding.
• Used in calculations, shown on time lines. -
  Examples:
  -> 8% quarterly: IPER = 8%/4 = 2%.
  -> 8% daily (365): IPER = 8%/365 = 0.021918%.

Question 9

The Impact of compounding: Will the FV of a lump sum be larger or smaller if we compound more often, holding the stated I% constant?

Answer 9

LARGER!
If compounding is more frequent than once a year–for example, semiannually, quarterly, or daily–interest is earned on interest more often.

Question 10

Formula

Answer 10

Slide 44-45

Question 11

Effective Annual Rate

Answer 11

• The EAR is the annual rate that causes PV to grow to the same FV as under multi- period compounding.
• The effective annual interest rate is calculated by taking the nominal interest rate and adjusting it for the number of compounding periods the financial product will experience in the given period of time

Question 12

Comparing Rates

Answer 12

• An investment with monthly payments is different from one with quarterly payments. Must put on EFF% basis to compare rates of return. Use EFF% only for comparisons.
• Banks say “interest paid daily.” Same as compounded daily.

Question 13

Can the effective rate ever be qeual to the nominal rate?

Answer 13

Yes, but only if annual compounding is used, i.e., if M = 1.

If M > 1, EFF% will always be greater than the nominal rate.

Question 14

When is each rate used?

Answer 14

• Inom :
  Written into contracts, quoted by banks and brokers.
  Not used in calculations or shown on time lines.
• Iper: Used in calculations, shown on time lines.
• EAR Used to compare returns on investmetns with different payments per year. Used for calculations if and only if dealing with annuities where payments don’t mach interest compounding periods

Question 15

Amortization

Answer 15

Construct an amortization schedule for a $1,000, 10% annual rate loan with 3 equal payments.
Step 1: Find the required payments
Step 2: Find interest charge for Year 1.
Step 3: Find Repayment of principal Year 1.
Step 4: Find ending balance after Year 1.

Question 16

Amortization tables:

Answer 16

Amortization tables are widely used–for home mortgages, auto loans, business loans, retirement plans, and more. They are very important!
Financial calculators and spreadsheets are great for setting up amortization tables.