CFA Level 1 Quantitative Methods
questions with answers.
Three ways interest rates can be thought of ANS -First, they can be considered required rates of return
—that is, the minimum rate of return an investor must receive in order to accept the investment.
Second, interest rates can be considered discount rates. In the example above, 5.26 percent is that rate
at which we discounted the $10,000 future amount to find its value today. Thus, we use the terms
"interest rate" and "discount rate" almost interchangeably.
Third, interest rates can be considered opportunity costs. An opportunity cost is the value that investors
forgo by choosing a particular course of action. In the example, if the party who supplied $9,500 had
instead decided to spend it today, he would have forgone earning 5.26 percent on the money. So we can
view 5.26 percent as the opportunity cost of current consumption.
How are interest rates set in the marketplace? ANS -Supply and demand
Interest rate formula ANS -r=Real risk-free interest rate+Inflation premium +Default risk
premium+Liquidity premium+Maturity premium
real risk-free interest rate ANS -the single-period interest rate for a completely risk-free security if no
inflation were expected. In economic theory, the real risk-free rate reflects the time preferences of
individuals for current versus future real consumption.
Inflation Premium ANS -compensates investors for expected inflation and reflects the average inflation
rate expected over the maturity of the debt
Nominal Risk Free Interest Rate ANS -The sum of the real risk-free interest rate and the inflation
premium. (T-bill).
Liquidity premium ANS -compensates investors for the risk of loss relative to an investment's fair value
if the investment needs to be converted to cash quickly.
Maturity Premium ANS -compensates investors for the increased sensitivity of the market value of debt
to a change in market interest rates as maturity is extended, in general (holding all else equal).
,Simple Interest ANS -Interest rate times the principle.
Is simple or compound interest more important? ANS -Compound.
Important consequence of present value and future value being separated in time? ANS -We can add
amounts of money only if they are indexed at the same point in time.
EAR formula ANS -EAR = (1 + Periodic interest rate)^m - 1
EAR=e^rs−1
EAR = Non EAR ANS -0.0816=(1+Periodic rate)^2−1
1.0816=(1+Periodic rate)^2
(1.0816)^1/2−1=Periodic rate
(1.04)−1=Periodic rate
4%=Periodic rate
calculate the continuously compounded rate corresponding to an effective annual rate of 8.33% ANS -
Find interest rate that solves:
EAR=e^rs−1
0.0833=e^rs−1
1.0833=e^rs
To solve this equation, we take the natural logarithm of both sides. (Recall that the natural log of e^rs is
ln e^rs=rs .) Therefore, ln 1.0833 = rs, resulting in rs = 8 percent. We see that a stated annual rate of 8
percent with continuous compounding is equivalent to an EAR of 8.33 percent.
Difference between ordinary annuity and annuity due? ANS -Annuity due has first cash flow that occurs
immediately while ordinary annuity has first cash flow that occurs one period from now.
,future value annuity factor
Also need to know PV annuity for ordinary annuity and annuity due
perp formula
Solve for interest rate and growth rate
annual compounding periods needed to reach a value
calculate size of payment annuity
calculate amount needed now to fund future annuity
calculate lump sum annuity ANS -FV=A[(1+r)^n - 1 / r]
(1+r)^n = FV/PV
N ln(1+r) =ln(2)
N = ln(2) / ln(1+r)
ln(2)/ln(1.07) = 10.24
Cash flow additivity principle ANS -the idea that amounts of money indexed at the same point in time
are additive
Working capital management ANS -Management of the company's short-term assets and short-term
liabilities.
Steps in computing and applying NPV Rule ANS -1) Identify all cash flows associated with the investment
—all inflows and outflows.1
2) Determine the appropriate discount rate or opportunity cost, r, for the investment project.2
3) Using that discount rate, find the present value of each cash flow. (Inflows have a positive sign and
increase NPV; outflows have a negative sign and decrease NPV.)
, 4) Sum all present values. The sum of the present values of all cash flows (inflows and outflows) is the
investment's net present value.
5) Apply the NPV rule: If the investment's NPV is positive, an investor should undertake it; if the NPV is
negative, the investor should not undertake it. If an investor has two candidates for investment but can
only invest in one (i.e., mutually exclusive projects), the investor should choose the candidate with the
higher positive NPV.
What is the IRR? ANS -The discount rate that makes the NPV = 0.
What is necessary to recognize a compound rate of return that is equal to the IRR over the life of the
investment? ANS -Only if we can reinvest all interim cash flows at exactly the IRR.
IRR Rule ANS -uses the opportunity cost of capital as a hurdle rate, or rate that a project's IRR must
exceed for the project to be accepted. Note that if the opportunity cost of capital is equal to the IRR,
then the NPV is equal to 0. If the project's opportunity cost is less than the IRR, the NPV is greater than
0.
IRR Formula
Investment ANS -CF/Investment
CF/IRR
What do IRR and NPV rule do when projects are independent? ANS -Give same accept or reject
decision.
When does NPV and IRR rank projects differently? ANS -When they don't have enough money to do all
of them and must rank them in terms of profitability.
The IRR and NPV rank differently when:
1) the size or scale of the projects differ.
2) timing of the projects' cash flows differ.
What do you follow when NPV and IRR are different? ANS -NPV
questions with answers.
Three ways interest rates can be thought of ANS -First, they can be considered required rates of return
—that is, the minimum rate of return an investor must receive in order to accept the investment.
Second, interest rates can be considered discount rates. In the example above, 5.26 percent is that rate
at which we discounted the $10,000 future amount to find its value today. Thus, we use the terms
"interest rate" and "discount rate" almost interchangeably.
Third, interest rates can be considered opportunity costs. An opportunity cost is the value that investors
forgo by choosing a particular course of action. In the example, if the party who supplied $9,500 had
instead decided to spend it today, he would have forgone earning 5.26 percent on the money. So we can
view 5.26 percent as the opportunity cost of current consumption.
How are interest rates set in the marketplace? ANS -Supply and demand
Interest rate formula ANS -r=Real risk-free interest rate+Inflation premium +Default risk
premium+Liquidity premium+Maturity premium
real risk-free interest rate ANS -the single-period interest rate for a completely risk-free security if no
inflation were expected. In economic theory, the real risk-free rate reflects the time preferences of
individuals for current versus future real consumption.
Inflation Premium ANS -compensates investors for expected inflation and reflects the average inflation
rate expected over the maturity of the debt
Nominal Risk Free Interest Rate ANS -The sum of the real risk-free interest rate and the inflation
premium. (T-bill).
Liquidity premium ANS -compensates investors for the risk of loss relative to an investment's fair value
if the investment needs to be converted to cash quickly.
Maturity Premium ANS -compensates investors for the increased sensitivity of the market value of debt
to a change in market interest rates as maturity is extended, in general (holding all else equal).
,Simple Interest ANS -Interest rate times the principle.
Is simple or compound interest more important? ANS -Compound.
Important consequence of present value and future value being separated in time? ANS -We can add
amounts of money only if they are indexed at the same point in time.
EAR formula ANS -EAR = (1 + Periodic interest rate)^m - 1
EAR=e^rs−1
EAR = Non EAR ANS -0.0816=(1+Periodic rate)^2−1
1.0816=(1+Periodic rate)^2
(1.0816)^1/2−1=Periodic rate
(1.04)−1=Periodic rate
4%=Periodic rate
calculate the continuously compounded rate corresponding to an effective annual rate of 8.33% ANS -
Find interest rate that solves:
EAR=e^rs−1
0.0833=e^rs−1
1.0833=e^rs
To solve this equation, we take the natural logarithm of both sides. (Recall that the natural log of e^rs is
ln e^rs=rs .) Therefore, ln 1.0833 = rs, resulting in rs = 8 percent. We see that a stated annual rate of 8
percent with continuous compounding is equivalent to an EAR of 8.33 percent.
Difference between ordinary annuity and annuity due? ANS -Annuity due has first cash flow that occurs
immediately while ordinary annuity has first cash flow that occurs one period from now.
,future value annuity factor
Also need to know PV annuity for ordinary annuity and annuity due
perp formula
Solve for interest rate and growth rate
annual compounding periods needed to reach a value
calculate size of payment annuity
calculate amount needed now to fund future annuity
calculate lump sum annuity ANS -FV=A[(1+r)^n - 1 / r]
(1+r)^n = FV/PV
N ln(1+r) =ln(2)
N = ln(2) / ln(1+r)
ln(2)/ln(1.07) = 10.24
Cash flow additivity principle ANS -the idea that amounts of money indexed at the same point in time
are additive
Working capital management ANS -Management of the company's short-term assets and short-term
liabilities.
Steps in computing and applying NPV Rule ANS -1) Identify all cash flows associated with the investment
—all inflows and outflows.1
2) Determine the appropriate discount rate or opportunity cost, r, for the investment project.2
3) Using that discount rate, find the present value of each cash flow. (Inflows have a positive sign and
increase NPV; outflows have a negative sign and decrease NPV.)
, 4) Sum all present values. The sum of the present values of all cash flows (inflows and outflows) is the
investment's net present value.
5) Apply the NPV rule: If the investment's NPV is positive, an investor should undertake it; if the NPV is
negative, the investor should not undertake it. If an investor has two candidates for investment but can
only invest in one (i.e., mutually exclusive projects), the investor should choose the candidate with the
higher positive NPV.
What is the IRR? ANS -The discount rate that makes the NPV = 0.
What is necessary to recognize a compound rate of return that is equal to the IRR over the life of the
investment? ANS -Only if we can reinvest all interim cash flows at exactly the IRR.
IRR Rule ANS -uses the opportunity cost of capital as a hurdle rate, or rate that a project's IRR must
exceed for the project to be accepted. Note that if the opportunity cost of capital is equal to the IRR,
then the NPV is equal to 0. If the project's opportunity cost is less than the IRR, the NPV is greater than
0.
IRR Formula
Investment ANS -CF/Investment
CF/IRR
What do IRR and NPV rule do when projects are independent? ANS -Give same accept or reject
decision.
When does NPV and IRR rank projects differently? ANS -When they don't have enough money to do all
of them and must rank them in terms of profitability.
The IRR and NPV rank differently when:
1) the size or scale of the projects differ.
2) timing of the projects' cash flows differ.
What do you follow when NPV and IRR are different? ANS -NPV
