8/18/2019 Formula Sheet Foundations of Finance

1/1

Created by Jannine Poletti-Hughes

Formula sheet

Present Value of one cash flow

t)1(

FV=PV

r  

Discount factor is the PV of £1(Discount factor from Table 1) 

t)1(

1

r  DF 

 

FV: Future value

Present Value of multiple cash flows

t 

t 

r 

C 

r 

C 

r 

C  PV 

)1(...

)1()1( 22

1

1

 

If C is the same for all the periods use:Annuity formula

 

t r r r 

C 1

11annuityof PV  

OrC annuityof PV  Annuity factor (Atr )

(Annuity factor from Table 3)

C: cash flow

Perpetuity

r 

C  PV  10    

C: cash flow

This row of formulas is used to calculate thepresent value of a future payment.

Useful to calculate net present values (NPV)which is the cost of a investment minus thereturns. 

Zero Coupon bond

t r 

 F  PV 

)1(    

F: face value

Level Coupon bond

t 

t 

r 

 F C 

r 

C 

r 

C  PV 

)1(...

)1()1(2

2

1

1

 

If C is the same for all the periods use:

C  bondof PV  Annuity factor (Atr )+t 

r 

 F 

)1(    

(Annuity factor from Table 3)

C: Coupon in money terms £F: face value

Consol

r 

C  PV   0  

C: Coupon 

This row of formulas is used to calculate thepresent value of different types of  Bonds.

The return of a bond includes the couponpayments plus the face value.

Stock with no dividend

t r 

 P  P 

)1(

10

 

P 0 : Price of stock at time zeroP 1: Price of stock at time one

Dividend discount model

t 

t t 

r 

 P  DIV 

r 

 DIV 

r 

 DIV  P 

)1(...

)1()1( 22

1

10

 

If DIV is constant for all periods use:

 DIV stock of PV  Annuity factor (Atr )+t 

t 

r 

 P 

)1(    

DIV 1: DividendP 0 : Price of stock at time zeroP t : Price of stock at time t

Stock no growth andhold stock indefinitely

r 

 DIV  P  10    

DIV 1: DividendP 0 : Price of stock attime zero

This row of formulas is used to calculate thepresent value of Stock (shares: P0).The return of a stock includes the dividendpayments plus the capital gains

0

01

0

1

 P 

 P  P 

 P 

 DIV r 

   

The valuation formula can be derived from the

above equation by calling

0

01

 P 

 P  P   =growth (g):

Valuation formula: g r 

 DIV  P 

10

 

DIV 1: DividendP 0 : Price of stock at time zeroP 1: Price of stock at time one

Notes: The formula for nominal rate is: 1+real interest rate=( 1+nominal rate) / (1+ inflation rate). Some formulas are given in the exam with the present value tables. They arespecified above in bold. The remainder of the formulas have to be learnt in preparation for the final exam. (r: rate of discount)