MT (1-2) Time Value of Money

Question 1

What are the key characteristics of an annuity with growth? (six characteristics)

Answer 1

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

Question 2

What is the Geometric series SUM formula

Answer 2

Sn= a (1-x^n) / (1-x)

Question 3

What is the Geometric series sum formula if n tends towards infinity

Answer 3

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

Question 4

Write the PV Annuity with Growth Formula

Answer 4

PV= C [ 1 - (1+g / 1+r)^n / r-g ]

Question 5

Write the Converting a Stated annual interest rate to an EAR formula

Answer 5

1+EAR = ( 1+stated annual interest rate / k)^k

where k is the number of compounding periods in a year

Question 6

Write the Effective rate –> Stated annual interest rate formula

Answer 6

r(k) where r is the effective rate for the time period, k is the number of time periods in a year

Question 7

Write the Stated annual interest rate to effective rate for n periods formula

Answer 7

[1 + (stated annual interest rate/k)]^n - 1 = Effective rate for n periods

Question 8

What is the Future value formula

Answer 8

FV = C (1+r)^T (T is the number of time periods and r is the effective rate for the time period)

Question 9

What is the Present Value formula

Answer 9

PV = C / (1+r)^T (T is the number of time periods)

Question 10

What is the Discount Factor formula

Answer 10

Dt = 1 / (1+r)^T (T is the number of time periods and r is the effective rate for the time period and over time)

Question 11

What is the NPV Formula Procedure

Answer 11

Take each cash flow and compute its present value.

Sum present values across all cash flows.

Question 12

what is the formula for real interest rate.

Answer 12

(1+r) = (1+i) / (1+pi)

r= real interest rate
I = nominal interest rate 
pi = inflation rate

Question 13

Give the Approximation for real interest rate when rates are low

Answer 13

r approximately –> i - pi
I approximately —> r + pi

nominal interest rate = inflation rate + real interest rate

Real interest rate = nominal rate - inflation rate

Question 14

What is the Continuous compounding formula

Answer 14

1+ EAR = e^p

P IS THE ANNUAL CONTINOUSLY COMPIUNDED RATE (have to use logs to find p)

Question 15

Define the six characteristics of an Annuity

Answer 15

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

Question 16

what is the PV of Annuity without growth formula

Answer 16

PV = C [ 1 - ( 1 / 1+R)^n / r]

Question 17

Define the seven Perputity with growth characteristics

Answer 17

1. ) cash flow occurs at the end of the first period
2. ) cash flow must grow at a constant each period
3. ) timing of cash is 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 tends to infinity
6. ) the PV valuation is one period before the first cash flow
7. ) r > g (the discount rate must be greater than the growth rate.

Question 18

What is the PV of perputity with growth fomula

Answer 18

PV = C/ r - g

Question 19

What is the PV of perputity without growth formula

Answer 19

PV = C/ r

Question 20

Define the Perputity without growth characteristics (6)

Answer 20

1. ) cash flow occurs at the end of the first period
2. ) cash flow must be constant each period
3. ) timing of cash is 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 tends to infinity
6. ) the PV valuation is one period before the first cash flow

Question 21

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

Answer 21

PV = C + C [ 1 + (1/1+r)^n-1 / r] (NOTE N-1)

Question 22

what is the Future value of an annuity with growth formula

Answer 22

FV= (1+r)^n x C[1-(1+g/1+r)^n / r-g)

Question 23

Readjust the PV of an annuity with growth formula to find C

Answer 23

C=PV/ [1- (1+G)/(1+R)^N /R-G]