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COMM 221: Financial Markets > Lecture 1 > Flashcards

Lecture 1 Flashcards

1
Q

What is the rate in finance?

A

The rate is the amount of return, often referred to as interest, you get for some investment, often referred to as principal.

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2
Q

What are variable rates and fixed rates?

A

Variable rates can change and depend on factors such as investments, borrowers, and length of time.

Fixed rates stay constant for a set term.

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3
Q

How is simple interest different from compound interest?

A

Simple interest is computed on the original amount borrowed, while compound interest is computed on the most recent outstanding balance.

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4
Q

Provide an example of calculating simple interest.

A

If I borrow $1000 for one year at an effective rate of 10%, in one year, I will owe:

1.10×$1000=$1100

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5
Q

How do you compare simple interest and compound interest over time with a 10% interest rate?

A

Time period | Simple Interest Balance | Compound Interest Balance |
| 0 | 1000 | 1000 |
| 1 | 1100 | 1100 |
| 2 | 1200 | 1210 |
| 3 | 1300 | 1331 |
| 4 | 1400 | 1464.1 |

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6
Q

What is the difference between reinvestment of interest in compound interest vs simple interest?

A

Compound interest grows faster due to reinvestment of interest proceeds, whereas simple interest does not reinvest the interest.

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7
Q

How do you calculate the Return on Equity (ROE) or Return on Investment (ROI)?

A

ROE (ROI) = E1 / E0

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8
Q

Provide an example of calculating ROE with given values.

A

If ending equity (E1) is 17K and original loan value (E0) is 5K:

ROE (ROI) = 17K / 5K = 3.4

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8
Q

What is the significance of the balance rolling over and compounding?

A

It means that the interest earned or owed accumulates on the initial principal plus any interest from previous periods, leading to a growth in balance over time.

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9
Q

How does the frequency of compounding affect the growth of an investment or loan?

A

More frequent compounding results in higher total interest earned or owed.

For example, an investment compounded quarterly will grow faster than one compounded annually at the same nominal rate.

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10
Q

Provide an example comparing annual and quarterly compounding.

A

Investing $1000 at 12% annually results in:
Opening Balance: 1000
Interest: 120
Closing Balance: 1120

Investing $1000 at 3% quarterly (equivalent to 12% annually) results in:
Period (Quarters) | Opening Balance | Interest | Closing Balance
0 | 1000 | 30 | 1030
1 | 1030 | 30.9 | 1060.9
2 | 1060.9 | 31.82 | 1092.72
3 | 1092.72 | 32.78 | 1125.50

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11
Q

What does the table in the example demonstrate about the effective rate?

A

It shows that an apparently equivalent rate (e.g., 12% compounded annually versus 12% compounded quarterly) can result in different amounts due to the effect of compounding frequency.

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12
Q

What is the effective rate?

A

The effective rate is the genuine annual interest rate accounting for compounding within the year, reflecting the actual financial impact of interest.

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13
Q

What are quoted rates?

A

Quoted rates are those that are stated and are usually not equal to the effective interest rate. They often need to be converted to reflect the true cost of borrowing.

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14
Q

How are quoted rates commonly expressed?

A

Quoted rates are often expressed as an Annual Percentage Rate (APR), which might not accurately reflect the true annual cost due to compounding.

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15
Q

What must be done for all-time value calculations regarding quoted rates?

A

Quoted rates must be converted into effective rates to understand the true financial impact of interest over time.

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16
Q

Provide an example of converting a quoted rate to an effective rate.

A

Commander Klang borrows $1000 at an annual quoted rate of 20% compounded monthly. To find the effective annual rate (EAR):

Convert the quoted rate to the effective monthly rate (EMR):
EMR = 20% / 12 = 1.666%

Use the EMR to calculate the EAR:
EAR = (1 + 0.01666)^12 - 1 = 21.93%

Compute the interest for one year:
$1000 * 21.93% = $219.39

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17
Q

How can quoted rates be converted to effective rates?

A

Divide the quoted rate by the compounding frequency and then use a power/root to change the frequency to annual.

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18
Q

Illustrate the conversion from APR to EMR and then to EAR with an example.

A

For a 20% APR compounded monthly:

Convert APR to EMR:
EMR = 20% / 12 = 1.666%

Convert EMR to EAR:
EAR = (1 + 0.01666)^12 - 1 = 21.93%

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19
Q

Explain the concept of Effective Daily Rate (EDR).

A

To convert EAR to EDR for daily compounding:

EDR = (1 + EAR)^(1/365) - 1

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20
Q

What does compounding mean in finance?

A

Compounding in finance refers to the process where the value of an investment grows because the earnings on an investment, both capital gains and interest, earn interest as time passes.

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21
Q

What is the effect of compounding frequency on an investment?

A

The more frequently interest is compounded, the greater the amount of interest accrued.

For example, an investment compounded quarterly will grow faster than one compounded annually at the same nominal rate.

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22
Q

Provide an example to illustrate the difference in growth between annual and quarterly compounding.

A

If $1000 is invested at 12% annually, it grows to $1120 after one year. If $1000 is invested at 3% quarterly, it grows to $1125.50 after four quarters, demonstrating higher growth due to more frequent compounding.

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23
Q

What is the balance growth for annual compounding at 12% for $1000?

A

Opening Balance: $1000, Interest: $120, Closing Balance: $1120.

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24
Q

What is the balance growth for quarterly compounding at 3% for $1000?

A

Period 0: Opening Balance: $1000, Interest: $30, Closing Balance: $1030.

Period 1: Opening Balance: $1030, Interest: $30.9, Closing Balance: $1060.9.

Period 2: Opening Balance: $1060.9, Interest: $31.82, Closing Balance: $1092.72.

Period 3: Opening Balance: $1092.72, Interest: $32.78, Closing Balance: $1125.50.

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25
Q

What are quoted rates?

A

Quoted rates are the interest rates that are stated or advertised, which do not typically reflect the true annual cost of a loan or the true annual yield of an investment.

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25
Q

Why do we need to understand the effective rate?

A

The effective rate tells us the genuine annual interest rate taking into account the frequency of compounding, which helps in making accurate financial decisions.

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26
Q

How can quoted rates be misleading compared to effective rates?

A

Quoted rates often understate the true cost of borrowing because they do not account for the compounding effect. Effective rates, on the other hand, reflect the actual financial impact of interest compounding over time.

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27
Q

What is the formula for converting APR to EMR (Effective Monthly Rate)?

A

A: To convert APR to EMR, divide the APR by the number of compounding periods per year.

For example, 20% APR compounded monthly is:
EMR = 20% / 12 = 1.666%

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28
Q

How do you convert EMR to EAR (Effective Annual Rate)?

A

Use the formula:
EAR = (1 + EMR)^12 - 1

For example, with an EMR of 1.666%:
EAR = (1 + 0.01666)^12 - 1 = 21.93%

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29
Q

How do you calculate the Effective Daily Rate (EDR) from EAR?

A

Convert EAR to EDR using the formula:
EDR = (1 + EAR)^(1/365) - 1

For example, if EAR is 21.93%, then:
EDR = (1 + 0.2193)^(1/365) - 1 = 0.0551% per day

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30
Q

What is the formula for computing the effective rate from the quoted rate?

A

k = (1 + QR/m)^f - 1

Where QR is the quoted rate, m is the number of compounding periods per year, and f is the frequency of compounding.

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31
Q

Why is it important to understand the conversion from quoted rates to effective rates?

A

Understanding the conversion helps avoid relying on formulas without comprehension, which is crucial for accurate financial calculations and deeper understanding.

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32
Q

What are the steps involved in converting a quoted rate to an effective rate?

A
  1. Divide the quoted rate (QR) by the number of compounding periods (m).
  2. Add 1 to get a gross rate.
  3. Raise the result to the power of the ratio of the frequency (f).
  4. Subtract 1 to get the effective rate.
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33
Q

What happens to the compounding process if it is done infinitely?

A

If the compounding process is done infinitely, the formula approaches the exponential function:

lim (N→∞) (1 + APR/N)^N = e^(r*t)

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34
Q

How do you calculate the present value using continuous compounding?

A

Use the formula:
PV = e^(-rt)

For example, the present value of $1 at 5% continuous compounding for 6 months:
PV = $1 * e^(-0.05*0.5) = $0.98

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35
Q

How do you calculate the future value using continuous compounding?

A

Use the formula:
FV = e^(rt)

For example, the future value of $10 at 7% continuous compounding for 8 months:
FV = $10 * e^(0.07*8/12) = $10.47

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36
Q

How does the continuous compounding rate compare to other compounding frequencies?

A

The continuous compounding rate is typically higher than monthly or annual compounding rates because it compounds more frequently.

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37
Q

What is a mortgage?

A

A mortgage is a loan usually backed by real property, such as a house or building, and involves regular payments consisting of both principal and interest.

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38
Q

How are Canadian mortgages typically quoted and computed?

A

Canadian mortgages are usually quoted with a semi-annual compounding rate.

For example, a 5.5% quoted rate would have:

An effective six-month rate of 5.5% / 2 = 2.75%
An effective monthly rate of (1.0275)^(1/6) - 1 = 0.4532%
An effective annual rate (EAR) of (1.004532)^12 - 1 = 5.5756%

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39
Q

Who generally determines rates in the market?

A

Rates are generally determined by the market, not by a government bureau.

40
Q

What is the central bank rate?

A

The central bank rate is the rate set by the central bank that commercial banks use for short-term loans.

This rate is crucial for maintaining the demand of commercial banks for short-term loans.

41
Q

Provide an example of how the central bank rate is used.

A

In Canada, if a bank like CIBC or TD needs to borrow money for a couple of days, they do so at the central bank rate set by the Bank of Canada (BOC).

42
Q

What role does the Federal Reserve play in the United States regarding rates?

A

The Federal Reserve meets a few times a year to set the central bank rate. They raise the rate to slow down the economy and lower it to stimulate borrowing and economic activity.

43
Q

What is the policy of raising central bank rates known as?

A

The policy of raising central bank rates is known as tightening.

44
Q

What is the policy of reducing central bank rates known as?

A

The policy of reducing central bank rates is known as loosening.

45
Q

Why would people shop around for a lower rate if offered a high EAR, such as 75%?

A

People would shop around for a lower rate because such high rates are generally unaffordable and only used by those who desperately need money and have no other options.

46
Q

What determines most market set rates?

A

Most market set rates are determined by supply and demand equilibrium.

47
Q

How does supply and demand affect the cost of capital?

A

If many investors are willing to lend money, borrowers can get good (low) rates.

If investors are nervous or have little capital, borrowers have to accept higher rates due to high demand for capital.

48
Q

How does the risk of an investment affect the returns?

A

Higher risk investments require higher rates of return to compensate for the increased risk.

49
Q

Give an example of how risk affects lending preferences.

A

Investors might prefer lending to a surgeon over a social influencer because the perceived risk of getting their money back is lower with the surgeon, leading to a lower required rate of return.

50
Q

What is the concept of “premia” in finance?

A

Premia is the rate paid to compensate for some kind of risk. The higher the risk, the higher the premia.

51
Q

Why do riskier projects demand higher rates of return?

A

Riskier projects demand higher rates of return to compensate for the increased risk involved.

52
Q

What is the time value of money?

A

The time value of money is the concept that money available now is worth more than the same amount in the future due to its potential earning capacity.

53
Q

Why is there a need for compensation for delaying consumption?

A

Compensation is needed because delaying consumption means giving up potential current benefits, which must be offset by future returns at least equal to the rate of inflation.

54
Q

How do governments typically manage low risk-free rates?

A

Solvent governments can maintain low risk-free rates because they can print money or raise taxes to fulfill their obligations, leading to relatively low risk for their bonds.

55
Q

What does combining risk premia and time value of money achieve?

A

Combining risk premia and time value of money helps determine the total cost of borrowing or the rate of return on an investment.

56
Q

What is present value?

A

Present value is the value of some asset or cash-flow in today’s dollars.

57
Q

What is future value?

A

Future value is the value of some asset or cash-flow as measured in future dollars (as of a particular date).

58
Q

Why is money today worth more than money tomorrow?

A

Money today is worth more than money tomorrow because of the positive interest rates and the erosion of purchasing power over time due to inflation.

59
Q

How do you convert present value to future value?

A

Multiply present values by a factor to get future values. Alternatively, multiply future values by the reciprocal of the factor to get present values.

60
Q

How do you compute the future value of $1000 invested today at 10% per year for 20 years?

A

Use the formula:
Future Value = $1000 × (1 + 0.10)^20 = $6727.50

60
Q

How do you compute the present value of $250,000 needed in 5 years if the investment rate is 5%?

A

Use the formula:
Present Value = $250,000 / (1 + 0.05)^5 = $195,881.50

61
Q

Why should present values be smaller than their associated future values?

A

Present values should be smaller because interest rates are normally positive, causing dollar amounts to grow over time.

62
Q

What is an annuity?

A

An annuity is a fixed cash-flow that repeats for a number of years.

63
Q

What is a perpetuity?

A

A perpetuity is a fixed cash-flow that repeats forever.

64
Q

How do you compute the present value of an annuity?

A

Compute an annuity factor for each period, multiply it by the payment in each period, and add them up.

65
Q

Provide an example of computing the present value of a bond with a $100 coupon paid annually for 5 years and a $1000 principal repayment at the end of the 5th year, with a 10% interest rate.

A

Year | 1 | 2 | 3 | 4 | 5
Coupon | 100 | 100 | 100 | 100 | 100
Principal | - | - | - | - | 1000
PVIF | 0.909 | 0.826 | 0.751 | 0.683 | 0.621
Present Value | 90.90 | 82.64 | 75.13 | 68.30 | 683.01

Adding up the present values, the bond is worth $1000 in present day dollars.

66
Q

What is the present value of an annuity formula?

A

PV(a_{r,n}) = (1 - (1 + r)^{-n}) / r

67
Q

How do you calculate the present value of a bond with $100 annual coupons for 5 years and $1000 principal repayment at a 10% interest rate using the annuity formula?

A

Bond Value = (100 * (1 - (1 + 0.10)^{-5}) / 0.10) + (1000 / (1 + 0.10)^5)

Bond Value = 379.08 + 620.92 = $1000

68
Q

What is the future value of an annuity formula?

A

FV(a_{r,n}) = ((1 + r)^n - 1) / r

69
Q

How do you calculate the future value of $1200 invested annually for 25 years at a 6% interest rate?

A

FV = 1200 * ((1 + 0.06)^{25} - 1) / 0.06
FV = 1200 * (4.29187072 - 1) / 0.06
FV = $65,837.41

70
Q

How is the present value of a perpetuity calculated?

A

Present value of Perpetuity = Perpetuity Cash Flow / Interest Rate

71
Q

Provide an example of a perpetuity with a $10,000 investment at 3% interest and $300 annual withdrawal.

A

The present value of the perpetuity is $10,000, and it will generate $300 each year indefinitely.

72
Q

How do you calculate the present value of the construction cost of $175M/year for 3 years at a 5% interest rate?

A

PV = 175M * (1 - (1 + 0.05)^{-3}) / 0.05

PV = $476.568M

73
Q

How do you calculate the present value of an upgrade costing $25M in 20 years at a 5% interest rate?

A

PV = 25M / (1 + 0.05)^{20}
PV = $9.422M

74
Q

How do you calculate the present value of continuous maintenance costing $1M/year indefinitely at a 5% interest rate?

A

PV = 1M / 0.05
PV = $20M

75
Q

How do you calculate the total financing needed using 4% coupon bonds for combined costs of $505.99M with 50 years duration?

A

FV = (Annual Coupon * Annuity Factor for Coupons) + (PV of Face Value of Bonds)

FV = (0.04 * 18.25593 * 505.99M) + (0.087204 * 505.99M)

FV = $618.992M

76
Q

What is a growing cash-flow?

A

A growing cash-flow is one where the cash inflow increases at a constant rate over time.

77
Q

How is the present value of a growing annuity calculated?

A

PV = D1 / (r - g) = (D0 * (1 + g)) / (r - g)

Where D0 is the current dividend (cash-flow),

D1 is the forecasted cash-flow for one period hence,

r is the cost of capital,

and g is the growth rate.

78
Q

Provide an example calculation for a stock that pays an annual $5 dividend today with dividends growing at 3% per year and the cost of capital is 12%.

A

PV = 5 * (1.03) / (0.12 - 0.03) = 57.22

79
Q

What is a basis point?

A

A basis point is 1/100th of a percent of an interest rate. For example, 250 basis points equal 2.5%.

80
Q

What is a lessee?

A

A lessee is a person or corporation that leases equipment from the owner or lessor.

81
Q

What is a mortgage?

A

A mortgage is a loan used to finance home ownership, usually with a blend of capital and interest payments.

It differs from bonds, where the principal is repaid in one lump sum at maturity.

82
Q

What is amortization?

A

Amortization is a feature of a loan, often a mortgage, where the final balance at maturity is zero, meaning no large principal repayment is necessary.

83
Q

What is an annuity due?

A

An annuity due is an annuity where the payment is made immediately, rather than at the end of the period.

84
Q

How do you calculate the present value of an annuity that pays $100 at the end of each year for 5 years at a 5% interest rate?

A

PV = 100 * (1 - (1 + 0.05)^{-5}) / 0.05
PV = $432.95

85
Q

How do you calculate the present value of an annuity due that pays $100 at the end of each year for 5 years at a 5% interest rate?

A

PV = 100 + 100 * (1 - (1 + 0.05)^{-4}) / 0.05

PV = $454.60

86
Q

How should you value a project when all rates are assumed to be zero?

A

Add together all the cash-flows (CFs).

For example, if promised $100/month for 12 months, the value is $100 * 12 = $1200.

87
Q

How should you value a project when inflation is not zero?

A

Discount the cash-flows before adding them together to account for the fact that a dollar tomorrow is worth less than a dollar today.

88
Q

What is the discounted cash-flow (DCF) method?

A

The DCF method involves determining the discount factor or rate and applying it to each cash-flow to find its present value.

89
Q

How do you calculate the present value of $1000 to be received one year from now at a 15% discount rate?

A

PV = $1000 / (1 + 0.15) = $869.56

90
Q

What is the present value (PV) formula?

A

PV = ∑ (CF_i / (1 + r_i)^t)

91
Q

What does the present value formula tell you?

A

It tells you to take each cash-flow from a project, discount it by some factor, and then add up the discounted values to get the value in present day dollars.

92
Q

How do you value a project using the Net Present Value (NPV) method?

A

Add all parts together to get the Net Present Value of the project.

If NPV is greater than zero, it indicates the project adds value.

93
Q

What is the importance of the discount rate in NPV calculations?

A

The discount rate affects the profitability of a project. As it fluctuates, the benefits of the project can vary widely.

94
Q

How do you calculate the NPV for a project costing $6M today, with an 8M sale after 3 years, and 9.38% EAR?

A

NPV = -6 + (0.0679 + 6.113) = $792K

95
Q

What are depletable projects?

A

Projects that generate cash-flows and can be exhausted, such as oil fields or fisheries.

96
Q

What is the difference between depletable and renewable resources?

A

Depletable resources can be exhausted and cannot be used again in their original form, while renewable resources can be replenished.

97
Q

How do you calculate the value of a depleting oil field with $10M profit shrinking by 4% per year at a 12% discount rate?

A

PV = 10M / (0.12 - (-0.04)) = $62.5M

98
Q

How do you calculate the value of a sustainably harvested fishery with $10M profit growing by 4% per year at a 12% discount rate?

A

PV = 10M / (0.12 - 0.04) = $125M

COMM 221: Financial Markets (8 decks)

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