All Semester 1 Maths Formulas (Weeks 1-10) (Still on Week 6) Flashcards
How do we calculate Future Value? (WEEK 4: Time Value of Money)
FV = PV(1+R)n
How do we calculate Present Value? (WEEK 4: Time Value of Money)
PV = FV/(1+R)n
OR
PV = FV X 1/(1+R)n
where n is to the power of
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)
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
What is the calculation for FV and PV when we are looking at continuous compounding?(WEEK 4: Time Value of Money)
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
How do you calculate the effective interest rate(EAR)? (WEEK 4: Time Value of Money)
(1+r/m)(m) - 1
Where m is to the power of
How do you calculate Perpetuity? (Present Value of things that may go indefinitely) (WEEK 4: Time Value of Money)
Formula given as:
PV = C/R
Where C is cashflow/coupon
How do you calculate the Ordinary Annuity? (Things that pay you for a fixed number of time) (WEEK 4: Time Value of Money)
PV = C/R (1- 1/(1+R)t)
Where t is to the power of
How do you find the cashflow in an Ordinary Annuity? (Used to calculate Mortgage repayments) (WEEK 4: Time Value of Money)
C = PV x R/ 1 - (1/1+R) t
Where T is to the power of
Jusr rearranging the Ordinary Annuity
How do you calculate the Ordinary Annuity for the future (FV)? (WEEK 4: Time Value of Money)
FV = C/R x ((1+R)t - 1)
Where t is to the power of
How do you calculate the Holding Period Return? (WEEK 4: TIME VALUE OF MONEY)
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
How do you calculate the nominal rate of return? (WEEK 4: TIME VALUE OF MONEY)
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
- 08 X 1.04 = 1.1232
- 1232 X 100 = 1123.20 Nominal Cash flow T1
- 20 is financially equal to 1000 in the last period
Can see the nominal rate of return is 12.32%
what is the Ex-ante nominal interest rate? (WEEK 4: TIME VALUE OF MONEY)
Rt ≈ r + Eπ
what is the Ex-POST nominal interest rate? (WEEK 4: TIME VALUE OF MONEY)
R ≈ r + π
How do you calculate Perpetual Bonds? (WEEK 5: BONDS)
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
How you calculate conventional bonds? (Bonds that have fixed payback period) (WEEK 5: BONDS)
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
How do you calculate the (Nominal) interest yield? (WEEK 5: BONDS)
Coupon/ Market Price
How do you calculate the Redemption Yield (or YTM) if the time period is 1?(WEEK 5: BONDS)
R = C+V/P - 1
If any other time period then you have to extrapolate (idfk)
How do you calculate spot rates?(WEEK 5: BONDS)
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.
How do you calculate Zero Coupon Bonds? (WEEK 5: BONDS)
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
How do we calculate Forward Rates? (WEEK 5: BONDS) SEE NOTES FOR BETTER EXPLANATIONS
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
How do you calculate the Holding Period of Return? (WEEK 4: TIME VALUE OF MONEY)
r = d1+ P1 -P0/ P0
Where:
D1 - Dividend when Share ends
D0 - Dividend when you bought share
P0 - Price when bought
How do you calculate the Dividend Growth Model? (Calculating the Price of Share)? (WEEK 6: VALUATION OF SHARES)
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
What is the required rate of return based on the second dividend growth model?(WEEK 6: VALUATION OF SHARES)
r = d1/po +g
How do you calculate G? (WEEK 6: VALUATION OF SHARES)
D1 - D0/D0
