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My own FM212 > MT (1-2) Time Value of Money > Flashcards

MT (1-2) Time Value of Money Flashcards

1
Q

What is a discount rate?

A

this is a reward to investors demand for accepting delayed rather than immediate gratification. Can also be called interest rate or required rate of return.

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2
Q

What is simple interest
Use this example to help, the original amount invested is £100 at t=0 and the annual simple interest rate is 10% then the year end total the amounts up to year 3 are ?

A

Only pays interest on the original principal

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3
Q

What is compound interest?
If the original amount invested is £100 at t=0 and the annual compounded
interest rate is 10% then the year end total amounts up to year 3 are:?

A

Compound interest pays interest not only on the original principal but also on
accumulated interest.

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4
Q

What earns more simple or compound interest?

A

With compound interest since we also earn interest on interest the terminal
wealth at the end of three years is greater than with simple interest . OVER YEARS THE DIFFERENCE IS HUGE.

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5
Q

Suppose your bank pays interest monthly with an effective compounded
monthly rate of 0.5%.
How can we state this as an annual rate?

A
  1. Stated annual interest rate ( WITH SIMPLE INTEREST ONLY)

2. Effective annual rate (EAR) ( OR WE CAN INCLUDE ON INTEREST ON INTEREST, COMPOUND INTEREST)

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6
Q

What is stated annual interest rare and use this example

If we are told the stated annual interest rate is 6% with monthly compounding 0.5%, the calculation

A

The simplest way to convert an effective monthly rate to an annual figure is to
multiply the effective monthly rate by 12 (12 monthly periods in a year). ( simple interest only)
12(0.005) = 0.06 ( if we are given stated first, we divide this by 12 to find monthly compounding) . ( doesn’t take into account interest on interest as you can see.)

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7
Q

What is the effective annual rate ( EAR)

?

A

The effective annual rate (EAR) indicates the actual amount of interest that will
be earned at the end of the year after taking into consideration compounding
i.e. interest on interest.

Its essentially APR, so lets say you go to a bank and they state 5% of interest and you go to another bank and they again have stated a rate of 5% but bank A and B earn different amounts, this is because of the number of compounding periods.
Formula for EAR =
EAR = ( 1 + interest rate/100)^n -1
As you can see when we were compounding with simple interest the return was 6% but within compounding interest its 6.12% which is greater.

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8
Q

How do you convert stated annual interest to EAR?

A 
k = number of compounding periods in a year \
i = stated annual interest rate

The greater compounding period the greater EAR is.

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9
Q

If the stated annual interest rate is quoted as 5% with the compounding
frequencies, do annual, quarterly monthly and daily.

A
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10
Q

Lets say we want to get to effective rate to effective rate (i.e equivalent n time period of effective discount rate ( 1+r)^n-1 ( e.g. you been given effect rate of one month, to effective rate of 2 months. What os the formula

A

(1 + r)^n - 1

r = effective rate for that time period.

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11
Q

If the effective monthly rate is 1% then the effective rate for 2 months is:

A
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12
Q

How do you get from effective rate to the stated annual interest rate? ( e.g. compound effective rate to simple interest ( APR) ?

A

r(k)
r is the effective rate of that interest period
k = is the number of time periods in a year.

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13
Q

How do you get from Stated annual interest rate to Effective rate

A
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14
Q

If the stated annual interest rate is 12% with monthly compounding the effective 6 month rate is:

A
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15
Q

If stated annual interest rate is 12% with semi-annual compounding what is the
effective monthly rate? ( be careful)

A

So its 2 6 months periods, so its monthly ratio is different from if it was 12% divide by a year.

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16
Q

What can we say here?

A

So investors are indifferent in earning 0.6% over 6 months or 0.0098 every month over 6 months.

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17
Q

If the EAR is 12% what is the effective quarterly rate?
If the effective monthly rate is 1% what is the stated annual interest rate with
monthly compounding ?

A
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18
Q

If the annual interest rate is 8% what is EAR?

A

The EAR is 8%. Note that although it just says annual interest rate, it cannot be
a stated annual interest rate as it does not use the term stated and no level of
compounding is given. Thus, by default it must be the EAR.

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19
Q

If the annual interest rate is 8% what is effective rate for 6 months?

A
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20
Q
A
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21
Q

What else can we use when calculating PV?

A

Discount factors ( A discount factor is just the present value of £1.)

22
Q

Use discount factor to solve this.

A
23
Q

A building company is considering buying a plot of land costing £2,000,000
today. It plans to build 5 houses on the plot. Construction will take 2
years to complete, with each house’s building costs comprising £75,000 in one
year and £40,000 in two years. If the company expects to sell each house for
£600,000 two years from now and the interest rate is 8% per annum, should the project be taken on?

A
24
Q

Whats the difference between nominal and real interest rate?

A

Nominal Interest Rate
The rate at which the balance of a deposit grows in cash terms. Denote it by r .

Real Interest Rate
The rate at which the balance of a deposit grows in purchasing power terms.
Denote it by i.

25
Q

What is the relationship between Inflation, nominal and real interest rate?

A
26
Q

What is the annual real interest rate if the annual nominal interest rate is 2%
and annual inflation is 2%

A
27
Q

We know that stocks pay dividends on a regular basis and bonds make regular interest payments, we can use pv techniques to arrive at a total value today for these cash flow streams. What 4 shortcut formulas do we have?

A

Annuity
Annuity with growth
Perpetuity
Perpetuity with growth

28
Q

What is the Geometric series SUM formula

What is the geometric series formula when if n is infinite?

A

|x| <1 S= a/ 1-x

29
Q

What is annuity with growth and what is the formula?

A

Annuites are a constant cash flow over time

Growing Annuites = are a constant growth cash flow over time.

30
Q

What are 6 key characteristics of annuity with growth?

A
  1. ) cash flow occurs at the end of the first period
  2. ) cash flows must grow at a constanst rate each period
  3. ) timing of cash at constant intervals
  4. ) discount rate is the effective rate and is constant over time
  5. ) n time periods between the cash flows, where n is finite
  6. ) the PV valuation is one period before the first cash flow
31
Q

You work for a pharmaceutical company that has developed a new drug. The
patent on the drug will last 17 years. You expect that the new drug will generate a cash inflow of £4 million in its first year (assume the cash flow occurs at the end of the year, t=1) and that this amount will grow at a rate of 6% every year until the patent expires. Once the patent expires assume cash flows after this point are zero. What is the present value of the new drug if the interest rate is 8% per year?

A
32
Q

What are the 6 characteristics of an annuity?

A
  1. ) cash flow occurs at the end of the first period
  2. ) cash flow must be constant each period
  3. ) timing of cash at constant intervals
  4. ) discount rate is the effective rate and is constant over time
  5. ) n time periods between the cash flows, where n is finite
  6. ) the PV valuation is one period before the first cash flow
33
Q

What is the formula for annuity?

A
34
Q

You have won the lottery! You can chose between £7 million today or you can
receive monthly payments of £40,000 at the end of every month for 30 years
starting today i.e. first payment in one month’s time. The annual stated interest
rate is 6% with semi-annual compounding. What option do you choose?
First of all whats the problem here?

A

We have been given the stated annual interest rate so we need to convert to the monthly effective rate to use the annuity formula
Since the stated annual interest rate is quoted with semi annual compounding k = 2.

Also there are 360 months ( 12 x 30 years)

35
Q

Now answer this question You have won the lottery! You can chose between £7 million today or you can
receive monthly payments of £40,000 at the end of every month for 30 years
starting today i.e. first payment in one month’s time. The annual stated interest
rate is 6% with semi-annual compounding. What option do you choose?

A
36
Q

What is a perpetuity and what is a growing perpetuity?

A

A perpetuity with growth = A stream of periodic payments that grow at a constant rate and continue to grow forever.
A perpetuity = an annuity which its term is inifinte.

37
Q

What are the 7 characteristics of a perpetuity with growth?

A

The first cash flow occurs at the end of the 1st period and is denoted by C.
2. The cash flows must grow at a constant rate each period denoted by g.
3. The timing of the cash flows occur at constant intervals.
4. The discount rate is the effective rate for the period in between cash flows
and is constant over time and is denoted by r.
5. n the number of periods tends to infinity.
6. The PV valuation point is one period before the first cash flow.
7. The discount rate for the period in between cash flows has to be greater
than the growth rate between cash flows i.e. r > g.

38
Q

What is the PV of a perpeutiy with growth?

A
39
Q

A rich relative has bequeathed you a growing perpetuity. The first payment will
occur in one year and will be £2000. Each year after that you will receive a
payment that is 8% larger than the previous payment. This pattern of payments
will go on forever. If the interest rate is 15% per year what is today’s value of the bequest?

A
40
Q

What are the 6 characteristics of a perpeutiy?

A
  1. The first cash flow occurs at the end of the 1st period and is denoted by C.
  2. The cash flow C must be constant each period.
  3. The timing of the cash flows occur at constant intervals.
  4. The discount rate is the effective rate for the period in between cash flows
    and is constant over time and is denoted by r.
  5. n the number of periods tends to infinity.
  6. The PV valuation point is one period before the first cash flow.
41
Q

What is the PV of perputity without growth formula?

A
42
Q

You are going to enter into a contract to receive cash flows of £50 every year
forever with the first cash flow starting at t=3. What is the present value of these cash flows today, t=0 if the stated annual interest rate is 6% with semi-annual compounding?
What do we have to do first?

A

We need to convert the stated annual interest rate to the effective rate ( as n = k this is just the formula for EAR.

43
Q

We said that as an assumption of the perpeutiy formula that The first cash flow occurs at the end of the 1st period and is denoted by C?
What does it mean here?

A

The first cash flow C of £50 occurs at t=3. This makes the 1st period the
3rd year. This makes t=2 the valuation point for the perpetuity formula.

44
Q

You are going to enter into a contract to receive cash flows of £50 every year
forever with the first cash flow starting at t=3. What is the present value of these
cash flows today, t=0 if the stated annual interest rate is 6% with semi-annual
compounding?
SO NOW SOLVE THIS!! BE CAREFUL ABOUT START DATES..

A
45
Q

So in the 4 short cut formulas what have we done which is key?

A

In the four shortcut formulas we have derived the cash flows occur at the end of each period. We could use our 4 shortcut formulas to derive the cash flows occurring at the beginning of each period.

46
Q

Write the Annuity due formula (Cash flow at the beginning of the first period.)

A
47
Q

what is the Future value of an annuity

A

g

48
Q

Assume a world where annual interest rates are expected to be constant at 3%
for the foreseeable future. You wish to buy a flat and a mortgage company
agrees to lend you £950,000 today. The mortgage has a term of 25 years. You
promise the mortgage company a fixed repayment at the end of each of the
next 25 years. What is the fair repayment?

A

Rearrange the PV of annuity formula then solve for C

49
Q

You have just received information about future cash flows you will be receiving from an
investment you made in a friend’s business. You will be receiving £10,000 at the end of this
year, t = 1, £20,000 at the end of the following year, t = 2, and £30,000 at the end of the
year after that, t = 3. The discount rate for the cash flows is 3.5% per year.
(a) What is the present value of the cash flows you will receive?
(b) What is the future value at t = 3 of the cash flows you will receive?

A
50
Q

You are going to enter into a contract to receive cash flows of £10 every year forever with the first cash flows starting at t = 2 What is the present value of these cash flows when the relevant semi annual APR is 12?%?

A
51
Q

What is fishers approximation?

A

Real interest rate approximately equals nominal interest rate + inflation rate.

My own FM212 (13 decks)

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