The Principles of Corporate Finance
THE PRINCIPLES OF CORPORATE FINANCE
CHAPTER 1: The time value of money
We are going to link the present and the future by using the notion of interest rate that could be called discount rate, required rate of return or cost of capital. Finance is all about cash flows but more precisely about the exact date of the realization of the cash flow.
I) PRESENT VALUE
Example 1:
What is the value today of $110 to be received in one year?
- suppose the interest rate , r =10% - if you had the money today you could : o put in the bank at 19% o wait one year o receive PV * (1,10) = $110 - PV = $110/(1,10) = $100
We can’t compare cash flows of different maturities also we bring all the cash flows down to a common period. That is why most of the time we use the Present Value to compare cash flows and to relate future cash flows with the present.
Example2:
What is the value today of $1100 to be received in two years and $100 in one year?
PV = 100/(1,10)+1100/(1,10)²
A) General Formula:
PV = Present Value CFi = cash flow for period i
PV = CF1 / (1+r1) + CF2 / (1+r2) + CF3 / (1+r3) + CFn / (1+rn)
PV = ∑ CFt / (1+rt) t
B) Constant Annuity:
CF is paid at the end of every year for n years. What is the present value?
PV= CF*[(1-(1+r)-n)/ r] C) Perpetual Constant Annuity:
CF is paid at the end of every year forever. What is the present value?
PV= CF / r
D) Other Helpful Formulas
Constant growth of the cash flow for n periods:
PV = CF1 / r-g * [1-((1+g))n/(1+r))]
Constant growth of the cash flow forever:
PV = CF / r-g
II) TERMINAL VALUE (Future value):
A) General Formula
TV = CF1*(1+r1,n)n-1 + CF2*(1+r2,n)n-2 +…+ CFn-1*(1+rn-1,n)+ CFn
[pic] for an ordinary annuity (constant end of period)
Summary of Class 1:
- Determine the date that each cash flow will be received - Estimate the
CHAPTER 1: The time value of money
We are going to link the present and the future by using the notion of interest rate that could be called discount rate, required rate of return or cost of capital. Finance is all about cash flows but more precisely about the exact date of the realization of the cash flow.
I) PRESENT VALUE
Example 1:
What is the value today of $110 to be received in one year?
- suppose the interest rate , r =10% - if you had the money today you could : o put in the bank at 19% o wait one year o receive PV * (1,10) = $110 - PV = $110/(1,10) = $100
We can’t compare cash flows of different maturities also we bring all the cash flows down to a common period. That is why most of the time we use the Present Value to compare cash flows and to relate future cash flows with the present.
Example2:
What is the value today of $1100 to be received in two years and $100 in one year?
PV = 100/(1,10)+1100/(1,10)²
A) General Formula:
PV = Present Value CFi = cash flow for period i
PV = CF1 / (1+r1) + CF2 / (1+r2) + CF3 / (1+r3) + CFn / (1+rn)
PV = ∑ CFt / (1+rt) t
B) Constant Annuity:
CF is paid at the end of every year for n years. What is the present value?
PV= CF*[(1-(1+r)-n)/ r] C) Perpetual Constant Annuity:
CF is paid at the end of every year forever. What is the present value?
PV= CF / r
D) Other Helpful Formulas
Constant growth of the cash flow for n periods:
PV = CF1 / r-g * [1-((1+g))n/(1+r))]
Constant growth of the cash flow forever:
PV = CF / r-g
II) TERMINAL VALUE (Future value):
A) General Formula
TV = CF1*(1+r1,n)n-1 + CF2*(1+r2,n)n-2 +…+ CFn-1*(1+rn-1,n)+ CFn
[pic] for an ordinary annuity (constant end of period)
Summary of Class 1:
- Determine the date that each cash flow will be received - Estimate the