All Semester 1 Maths Formulas (Weeks 1-10) (Still on Week 6)

Question 1

How do we calculate Future Value? (WEEK 4: Time Value of Money)

Answer 1

FV = PV(1+R)n

Question 2

How do we calculate Present Value? (WEEK 4: Time Value of Money)

Answer 2

PV = FV/(1+R)n
OR
PV = FV X 1/(1+R)n

where n is to the power of

Question 3

What is the calculation for the Future Value when we consider differing time period payments (i.e monthly, quarterly etc.) (WEEK 4: Time Value of Money)

Answer 3

FV = PV (1+R/M)txm

txm is to the power of

Where:
R is annual interest
M number of compound periods per annum
t number of years

Question 4

What is the calculation for FV and PV when we are looking at continuous compounding?(WEEK 4: Time Value of Money)

Answer 4

FV= PV e (txr)

Where t x r is to the power of

PV = FV e (-t x r)

Where - t x r is to the power

Question 5

How do you calculate the effective interest rate(EAR)? (WEEK 4: Time Value of Money)

Answer 5

(1+r/m)(m) - 1

Where m is to the power of

Question 6

How do you calculate Perpetuity? (Present Value of things that may go indefinitely) (WEEK 4: Time Value of Money)

Answer 6

Formula given as:
PV = C/R

Where C is cashflow/coupon

Question 7

How do you calculate the Ordinary Annuity? (Things that pay you for a fixed number of time) (WEEK 4: Time Value of Money)

Answer 7

PV = C/R (1- 1/(1+R)t)

Where t is to the power of

Question 8

How do you find the cashflow in an Ordinary Annuity? (Used to calculate Mortgage repayments) (WEEK 4: Time Value of Money)

Answer 8

C = PV x R/ 1 - (1/1+R) t

Where T is to the power of

Jusr rearranging the Ordinary Annuity

Question 9

How do you calculate the Ordinary Annuity for the future (FV)? (WEEK 4: Time Value of Money)

Answer 9

FV = C/R x ((1+R)t - 1)

Where t is to the power of

Question 10

How do you calculate the Holding Period Return? (WEEK 4: TIME VALUE OF MONEY)

Answer 10

r = (D1 +P1 - P0)/ P0

Where:
P0: Denotes value of investment at beginning of holding period
P1: Denotes value of investment at end of holding period
D1: Denotes dividend or interest payment received during that period

Question 11

How do you calculate the nominal rate of return? (WEEK 4: TIME VALUE OF MONEY)

Answer 11

Real rate of return x Inflation

e.g Real rate of Return = 8%
Inflation 4% (add it on to the existing 100%)

Looking at T0: £1000

1. 08 X 1.04 = 1.1232
2. 1232 X 100 = 1123.20 Nominal Cash flow T1
3. 20 is financially equal to 1000 in the last period

Can see the nominal rate of return is 12.32%

Question 12

what is the Ex-ante nominal interest rate? (WEEK 4: TIME VALUE OF MONEY)

Answer 12

Rt ≈ r + Eπ

Question 13

what is the Ex-POST nominal interest rate? (WEEK 4: TIME VALUE OF MONEY)

Answer 13

R ≈ r + π

Question 14

How do you calculate Perpetual Bonds? (WEEK 5: BONDS)

Answer 14

PV = C/R
Where:
- PV: Present Value of bond
- C: The coupon rate x Nominal (par) value of the bond

Works the same for regular PV where C is just the Cashflow

Question 15

How you calculate conventional bonds? (Bonds that have fixed payback period) (WEEK 5: BONDS)

Answer 15

PV =
PV(P) = C(1/R-1/(1+R)t) + V/(1+R)t

Where V is the par value

Where t is to the power of

Question 16

How do you calculate the (Nominal) interest yield? (WEEK 5: BONDS)

Answer 16

Coupon/ Market Price

Question 17

How do you calculate the Redemption Yield (or YTM) if the time period is 1?(WEEK 5: BONDS)

Answer 17

R = C+V/P - 1

If any other time period then you have to extrapolate (idfk)

Question 18

How do you calculate spot rates?(WEEK 5: BONDS)

Answer 18

Finding R1:
P= C+V/ 1 +R1
Simply just rearrange

Finding R2:
P= C/1+R1 + C+V/ (1+R2)2
Simply just rearrange

Finding R3:
P = C/1+R1 + C/(1+R2)2 + C+V/ (1+R3)3
Simply rearrange

ETC.

Question 19

How do you calculate Zero Coupon Bonds? (WEEK 5: BONDS)

Answer 19

P0 = 100/ (1 + Rt) t
- Where Rt = tth period spot rate

But can also use:
P0 = 100/ (1+ R) t
- Where r = Yield to maturity

Therefore, Spot Rate equals yield to maturity for zero coupon bonds

Question 20

How do we calculate Forward Rates? (WEEK 5: BONDS) SEE NOTES FOR BETTER EXPLANATIONS

Answer 20

Focusing on £100 in 2 years:

Step 1: Find Present Value of £100 one year from now (PV):

• Use Discount Rate f 1,2 where 1,2 indicates that this is a rate from year one to year two. We refer to it as a forward rate:

PV = £100/ (1+ F 1,2)

Step 2: Find present value of PV0 of PV1:

PV0 = PV1/ (1+R1)

F 1,2 = 100 / PV0 (1+R1)

SEE NOTES FOR BETTER EXAMPLES/EXPLANATIONS

Question 21

How do you calculate the Holding Period of Return? (WEEK 4: TIME VALUE OF MONEY)

Answer 21

r = d1+ P1 -P0/ P0

Where:
D1 - Dividend when Share ends
D0 - Dividend when you bought share
P0 - Price when bought

Question 22

How do you calculate the Dividend Growth Model? (Calculating the Price of Share)? (WEEK 6: VALUATION OF SHARES)

Answer 22

P0 = d1/r-g
D1 = d0(1+g)
Where:
p0 = Current Price 
d1 = Future Dividend
r = Required rate of return 
g = Growth rate of dividend

Question 23

What is the required rate of return based on the second dividend growth model?(WEEK 6: VALUATION OF SHARES)

Answer 23

r = d1/po +g

Question 24

How do you calculate G? (WEEK 6: VALUATION OF SHARES)

Answer 24

D1 - D0/D0