CFA Level 1 2021 Lotes

CFA Level 1 Notes - 2021
CFA Level 1 Notes - 2021 1




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Real time saver!

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Reading 6 - The Time Value of
Money
Module 6.1 EAY and Compounding Frequency
LOS 6.a Interpret interest rates as required rates of return, discount
rates, or opportunity costs

Explain the concept of compound interest?



💡 Compound interest: The process of the value of money
growing over time due to the effect of interest accumulating
on previously earned interest


Explain what interest rates represent in terms of cash flow modelling?

In terms of cash flow modelling interest rates represent:

The required rate of return, ie the rate at which NPV = 0

Discount rate

Opportunity cost: If i=5%, the unearned interest of 5% is the
opportunity cost, if current consumption is elected over investing

What is the difference between real and nominal GDP?

Real GDP = GDP with the inflation effect stripped out



LOS 6.b Explain an interest rate as the sum of a real risk-free rate and
premiums that compensate investors for bearing distinct types of risk

What is the formula for the nominal risk free rate?

Nominal Rf = Real Rf + Expected inflation rate

What are the risks associated with investing in securities?
Types of risk investing in securities:


Reading 6 - The Time Value of Money 1

, Default risk: The risk that the borrower won’t be able to meet
payments / obligations

Liquidity risk: The risk of selling for less than Fair value if needed to
be sold QUICKLY

Maturity risk: Longer term securities are of higher risk than shorter
term

What is the formula for the required rate of return for a security
involving the above risks?

Required rate of return on a security = NOMINAL RF + Default risk +
Liquidity risk + Maturity risk




LOS 6.c Calculate and interpret the effective annual rate, given the
stated annual interest rate and the frequency of compounding

What is the formula for the effective annual rate?

EAR = Equivalent annual rate for a compounded IR

EAR = (1 + I/m)m –1



LOS 6.d: Solve time value of money problems for different frequencies of
compounding

What are the formulas for quarterly, monthly and daily compounding
frequencies?

Quarterly = (1 + r/4)4 –1

Monthly = (1 + r/12)12 –1

Daily = (1 + r/365)365 –1




Module 6.2 Calculating PV and FV


Reading 6 - The Time Value of Money 2

, LOS 6.e Calculate and interpret the future value FV and present value
PV of a single sum of money, an ordinary annuity, an annuity due, a
perpetuity PV only), and a series of unequal cash flows



LOS 6.f Demonstrate the use of a time line in modeling and solving time
value of money problems

What is the formula for a future value?

F uture V alue = P V (1 + I/m)mn

Calculator example: What is the FV of a £100 investment after 2 years
with a interest rate of 10% compounded annually?

N = 2, I/Y = 10, PV = 100, PMT = 0 ⟶ CPT FV = $121

What is the formula for a present value of a single sum?

Calculator example: What is the PV of a £100 FV with a interest rate of
10% compounded annually?
N = 2, I/Y = 10, PMT = 0, FV = 100 ⟶ CPT PV = $83

P resent V alue = F V /(1 + I/m)m∗n

What is the difference between an ordinary annuity and an annuity due?



💡 Ordinary Annuity: The most typical type of annuity, cash
flows occur at the end of each period for a finite number of
periods




💡 Annuity Due: Annuities where cash flow occurs at the
beginning of each period


What is the future value of an ordinary annuity that pays $1,000 per
year at the end of the next 3 years, with a 10% interest rate?

N = 3, I/Y = 10, PV = 0, PMT = 1,000 —- > FV = $3,310




Reading 6 - The Time Value of Money 3

, What is the present value of an ordinary annuity that pays $1,000 per
year at the end of the next 3 years, with a 10% interest rate?

N = 3, I/Y = 10, PMT = 1,000, FV = 0 —- > PV = $2,487

What is the future value of an annuity due that pays $1,000 per year at
the beginning of the next 3 years, with a 10% interest rate?

Set calculator to BGN mode — > N = 3, I/Y = 10, PV = 0, PMT = 1,000
—- > FV = $3,641

What is the present value of an annuity due that pays $1,000 per year
at the beginning of the next 3 years, with a 10% interest rate?

Set calculator to BGN mode — > N = 3, I/Y = 10, PMT = 1,000, FV = 0
—- > PV = $2,735

How do you calculate the present value of a perpetual cash flow?

Cash flow
P resent value of a perpetuity =
(I/m)

What is the present value of the following uneven set of cash flows over
a three year period at a 10% interest rate: Year 1100, Year 2200, Year
3300?

Using the calculator:

Cash flow 1 N = 2, I/Y = 10, PV = 100, PMT = 0 —- > FV = $121

Cash flow 2 N = 1, I/Y = 10, PV = 200, PMT = 0 —- > FV = $220
Cash flow 3 N = 0, I/Y = 10, PV = 300, PMT = 0 —- > FV = $300
Therefore total future value = $641

What is the future value of the following uneven set of cash flows over
a three year period at a 10% interest rate: Year 1100, Year 2200, Year
3300?

Using the calculator:

Cash flow 1 N = 1, I/Y = 10, PMT = 0, FV = $100 —- > PV = $91
Cash flow 2 N = 2, I/Y = 10, PMT = 0, FV = $200 —- > PV = $165

Cash flow 3 N = 3, I/Y = 10, PMT = 0, FV = $300 —- > PV = $225

Therefore total present value = $481




Reading 6 - The Time Value of Money 4

, What is the cash flow additivity principle?



💡 Cash Flow Additivity Principle: PV of a set of cash flows =
the present value of each cash flow individually... added
together




Reading 6 - The Time Value of Money 5