Equations

Question 1

What is the basic Future Value equation?

Answer 1

The Future Value, FV, of an amount today, PV, after t time periods with interest rate r per time period is given by the following equation:

𝐹𝑉=𝑃𝑉 ∗(1+𝑟)^𝑡

Question 2

What is the basic present value equation?

Answer 2

The Present Value, PV, of a Future Value, FV, taken after t periods of time with interest rate r per time period, is given by the following equation:

𝑃𝑉= 𝐹𝑉 X 1 / (1+𝑟)^𝑡

Question 3

What is the equation for PV of a perpetutity?

Answer 3

PV = C / R

A cash flow sequence that pays a fixed amount, C, at each point in time, forever. PV = PRESENT VALUE & R = interest / discount rate

Question 4

What is the equation for PV of a growing perpetuity?

Answer 4

A cash flow (C) sequence that increase by g% per time period, for ever. R is the interest rate.

PV = C / r - g

This only works when r > g

Question 5

What is the equation for present value of an annuities?

Answer 5

𝑃𝑉 =

C | C 1 |
— - | — X. ——— |
r | r (1+𝑟)^𝑇 |

A series of fixed cash flows, C, for some fixed (or finite) number of periods, T. R is the return of the market.

Question 6

Whats the equation for the future value of an annuity?

Answer 6

𝐹𝑉=

   | 1               1       | C X| —   -   ————| (1+r)^T
   | r       r X (1+r) ^T|

where c = cash flow
r = return
T = time

Question 7

What is the Effective Annual Rate Of Return (EAR) equation?

Answer 7

If your money is compounded with frequency k, then the EAR is computed as follows:

EAR = ((1 + APR/K)^k) - 1

APR = annual percentage rate

Question 8

What is the equation for real cash flow?

Answer 8

Real cash flow =

nominal cash flow / (1 + i)^t
where i = inflation rate

Question 9

what is the equation for real interest rate?

Answer 9

real interest rate =

(1 + nominal / 1 + inflation ) - 1

Question 10

What is the gordan growth model?

Answer 10

The gordan growth model is

P0= Dividend / r - g

only apples when r > g

Question 11

What is the equation for net present value?

Answer 11

Net Present Value = Present Value of Future Cash Flows – Initial Investment

Question 12

What is the discounted payback period?

Answer 12

Discounted payback period is the minimum number of years, k, such that:

Cf1/ 1+ r + CF2 /(1+r) ^2 > investment

Discounted payback period, in words, is the minimum length of time, k, such that the sum of the discounted cash flows exceeds the initial investment

Question 13

What is the Internal Rate of Return (IRR)?

Answer 13

i=

c / 1 + IRR + ct / (1 + IRR) T

Question 14

What is the profitability index?

Answer 14

profitability index =
Net present value/ Investment

Question 15

What is the retrun for a stock equation?

Answer 15

Return = (𝑃1 − 𝑃0 + 𝐷𝐼𝑉)/𝑃0

Capital Gains: P1 – P0
Dividend: DIV

Question 16

Whats the equation for asset risk premium?

Answer 16

asset risk premium = Asset return – Return of a risk-free asset

Question 17

whats the equation for the average return of a stock?

Answer 17

Average Return:

R̃= 1/ T ∑ rt

Question 18

whats the equation for the variance of a stock?

Answer 18

Varaince
σ² =1/ T ∑ (rt - R̃)²

Question 19

What is the standard deviation/volitlity of a stock equation?

Answer 19

𝜎̂ = √1/ T ∑ (rt - R̃)²

Question 20

What is the equation for beta?

Answer 20

Y = a + b * X

Apply the same framework to compute market risk (beta)

Y is the return of a company’s stock

X is the return of a market index (proxy for market return)

a is the intercept (the expected return of the stock when the market return is zero).

b is the slope of the regression line, which in this context represents the beta.

Question 21

whats the equation for required return?

Answer 21

Required Return = Risk-Free Return + Risk Premium

Question 22

Whats the equation for Capital Asset Pricing Model (CAPM)?

Answer 22

CAPM E(rᵢ) =

rᶠ + 𝛽𝑖 X (E(rᵐ) - rᶠ)

rᶠ = expected return equal to a riskless asset

Assets with β = 1 should provide an expected return equal to the market (𝑟_𝑚)