TVM

Question 1

Interpret interest rates as required rates of return

Answer 1

Minimum acceptable return on investment

Question 2

Interpret Interest Rates as Discount Rates

Answer 2

How much one pays today to receive a CF in the future

Question 3

Interprest Interest Rates as Opportunity costs

Answer 3

Rate on can earn on risk-free security

Question 4

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

Answer 4

r = sum of real-risk free rate + liquidity premium + maturity premium + default premium + inflation premium

Nom. r = Real rate + inflation premium (real rate as part of nominal rate assumes no inflation no risk)

Question 5

Calc, interpret the EAR, given the SAR and the frequency of compounding

Answer 5

The effective annual rate (EAR) is (1 + Periodic interest rate[aka nom rate/periods])^n – 1

*When rates are compounded periodically then EAR>SAR because of interest on principal and prior periods

Question 6

Solve TVM problems for different frequencies of compounding

Answer 6

Annually, semi-annually, quarterly, monthly, daily, continuos

Question 7

Calc, interpret the FV of a single sum (e)

Answer 7

Interpretation: The FV of an investment is a function of the interest rate and the time to maturity

Question 8

Calc, interpret the FV of an ordinary annuity (e)

Answer 8

“How much will you have at the end of 20 years if you deposit 2k at the end of each year and earn 7% / year?”
Mode=END
Fv = 1,990.98

Question 9

Calc, interpret the FV of an annuity due (e)

Answer 9

Annuity Due = BEG

PMT, N, I, Due = BEG, FV

“How much will you have at the end of 20 years if you deposit 2k at the beginning of each year and earn 7% / year?”

*Any TVM PROB: Clean Calc, check proper MODE

Question 10

Calc, interpret the FV of a series of uneven CF’s (e)

Answer 10

blarffg?

Question 11

Calc, interpret the PV of a single sum (e)

Answer 11

TVM: FV, I/Y, N, CPT -> PV

CPT I/Y = FV, PV, N, CPT -> I/Y

If $1,000 in 8 years is worth $582.01 now,
what is the annual compounded interest
rate? (*Pv is -N [as it’s an outlay here])

How long will it take $1,000 to grow to $1,469.33
at 8% interest? (*PV here is an initial cash outflow, -PV)

Question 12

Calc, interpret the PV of an ordinary annuity (e)

Answer 12

PMT, N, I

Calc. the PV of receiving 2k at the end of each year for the next 20 years at 7%

Calculate the implied interest rate if
$21,188.03 now is equal to $2,000 at the
end of each year for 20 years. (PV or PMT is -n when computing implied interest rate)

If you invest $1,000,000 today at 7.75% interest
and take out $100,000 at the end of each year,
how long will your money last?

Question 13

Calc, interpret the PV of a perpetuity (e)

Answer 13

Perpetuity ‘perpetual annuity’:goes on forever
Ex. perpetuity: Preferred stock: PV = A/r

Find the PV of a share of preffered stock that will pay $2.4 div/year, forever and you want to earn 8%

PV = div/year ($2.4)/return as decimal (0.08) =$$

or

Calculate the rate of return if a share of
preferred stock that pays an annual
dividend of $2.40 is selling for $30.00

r=A/PV

OTher:

Calculate the Present Value of an infinite
series of cash flows that will grow at 3%
per year. It will pay $2.40 next year and
you want a 8% return.

PVcg = D1/r-g

$2.4/.08-.03 (vs. $30 if no growth)

Question 14

Calc, interpret the PV of an annuity due (e)

Answer 14

Calc. the PV of receiving 2k at the beg. of each year for the next 20 years at 7%

PMT, N, I, BGN

If you save $10,000 at the beginning of each
year and earn 8% interest, how many years
will it take to reach $1,000,000?

Question 15

Calc, interpret the PV of a series of unequal CF’s (e)

Answer 15

Use CF keys
CF0 is initial outlay

“Find PV of receiving $100 at the end of year
1, $200 at the end of year 2, $400 at the end of
year 3 and $600 at the end of year 4, using
10%,”

CF0,CF1…etc…NPV, I, CPT NPV
NFV, NPV then down arrow is NFV

Question 16

Demonstrate the use of a Timeline in modeling and solving TVM problems

Answer 16

blargfffGgg!

Question 17

Annuity

Answer 17

A series of equal, periodic payments

Question 18

Ordinary Annuity

Answer 18

Annuity at the END of each period

Looks like: How much will you have at the end of 20 years if you deposit $2,000 at the end of each year

Question 19

Annuity Due

Answer 19

Annuity at the BEGINNING of each period

Looks like: California lottery, you get the 1st payment now and at the start of each subsequent year

Question 20

College savings problem

Answer 20

Assume you just had a child and expect her
to start college in 18 years. You want to
have a $100,000 saved when they start
college. If you can earn 5% per year, how
much should you save at the end of each
year for the next 18 years?

Question 21

Practice Problem 1 (to be ok on PV, FV, annuity, etc)

Answer 21

• Assume you have $150,000 saved for retirement.
• You can save $10,000 at the end of each year for the next
10 years. You will earn 7% during that period.
• You plan retiring 25 years from now. You want this fund
to be able to pay $100,000 at the end of each year for 25
years (starting with year 26). You can earn 5% during this
period.
• If you can earn 6% from year 11 to 25, how much do you
have to save each year to fulfill your goal?

Question 22

The difference in yield on otherwise identical US treasury and corporate bonds is attributable to default risk

Answer 22

.

Question 23

TVM Applications

Answer 23

Mortgages and Savings for college tuition or retirment