unit 4 | time value of money

Question 1

Time Value of Money (TVM)

Answer 1

Value of a dollar today is not the same as the value of a dollar 1 year from now

Question 2

Why does the worth of money change over time?

Answer 2

• Buy different things (inflation)
• Buy things at different times (consumer preference)

Question 3

What does TVM describe?

Answer 3

TVM describes the relationship between the value of a current dollar & the value of a future dollar

Question 4

Importance of TVM

Answer 4

• Finance is about the future
• The current value of any asset (stock, bond, company, real estate) is the asset’s future cash flows discounted to today

Question 5

If finance is about the future…

Answer 5

we need to be able to project & calculate future values

Question 6

If the value of assets are future cash flows discounted to today…

Answer 6

we need to be able to discount future values to today (present)
- Net present value (NPV)

Question 7

How is TVM expressed?

Answer 7

Net present value (NPV)

Question 8

What variables are included in discount rates?

Answer 8

• Inflation
• Consumer preferences
• Risk (uncertainly of future cash flow)

Question 9

How are the market’s discount rates for different assets estimated?

Answer 9

*** NEED EXPLANATION

Question 10

Interchangeable Terms

Answer 10

Finance uses different terms to mean the same thing:
- All interest rates are also a discount rate
- All Cost of Equity “rates” are also a discount rate (for equity)
- The differences lies in what asset the discount rate is applied to:
> Ex. you use a government bond yield with government bond cash flows & an equity cost of capital with equity cash flows

Question 11

How is a Discount Rate used?

Answer 11

Discounted rates convert future expected values, often cash flows, into a value today
- Present Value (PV) & Future Value (FV)

Question 12

Time Lines

Answer 12

Graphically represent the cash flows on a time line

Question 13

Why is PV is set at time = 0?

Answer 13

Since we make all decisions today, we really only care about the PV today

Question 14

How does compounding come into play?

Answer 14

When we deal with multiple time periods (years of cash flow) we must compound the discounting

Question 15

Formula for finding PV when given FV

Answer 15

PV = $value / (1 + r)^[# of periods]

Question 16

Compounding (Example)

If you had $10 000 in an investment account & the account was paying 10% interest per year → how much would you have in the account in 7 years? 20 years? 75 years?

Answer 16

7 years: $10 000 x (1.10)⁷ = $19 487.17
20 years: $10 000 x (1.10)²º = $67 275.00
75 years: $10 000 x (1.10)⁷⁵ = $12 718 953.71

Question 17

What kind of information is PV?

Answer 17

PV is a value, not a cash amount
($95 PV is not $95 of cash → it is the value of $100 cash received 1 year from now)

Question 18

Value depends on:

Answer 18

• The assumed cash flow
• Assumed discount rate
• It has no physical reality
  > But it is the input into decision making → we might spend $90 of cash on something that has a value of $95

Question 19

Formula for finding FV when given PV

Answer 19

FV = $value x (1 + r)^[# of periods]