FFinance: principles of Finance (part 1)
Financial markets and management
Valuation of investment
Value of investment = value of investment’s cash flows
* Concept of present value: value of investment = PV(CF°, CF1, CF2…)
Important characteristics of cash flows:
* Time: for the same amount of money, now is preferred to tomorrow
* Uncertainty: risk and return (1 for sure is preferred to half a chance to get 2)
Opportunity cost of capital:
Definition: opportunity cost of capital is the expected rate of return offered by equivalent investments in financial markets
Net present value (investment rule)
Definition: NPV of an investment is the current market value of its cash ...view middle of the document...
The annuity is then said to have a maturity of T periods
The cash flows of a growing annuity with a maturity of T can be replicated with two growing perpetuities
Then PV = Cr-g*(1-(1+g)T(1+r)T)
Compound Interest Rates
Rate of return vs. rates of interest
You care about rates of return: rate of return = value tomorrow-valuetodayvaluetoday = Vt+l-VtVt
The rate of interest is what is quoted in the market
Compound interest vs. simple interest
Simple interest = earn no interest on interest compound interest = earn interest on interest
Discrete compounding
Interest rates are quoted on a per year basis. However, this does not mean that interest is paid only once a year
If you invest $1 in a security for T years, and the compounding frequency is not annual, then:
* The actual rate of return you will earn is not equal to the stated rate of interest
* Future values increase with the compounding frequency
More generally, future value of C in T years from now at a discrete compounding frequency of m times is: FV = C*(1 + rm)m*T
Continuous compounding:
Corresponds to the limiting case where interests are paid every instant (m tend to infinity)
Then, whe have FV = limm→∞1+rmm*T=er*T e = 2.718
So, obviously, PV = e- r*T
Effective annual yield:
When the compounding frequency is not annual: The actual rate of return is not equal to the stated rate of interest (r% per annum)
Actual rate of return = effective annual yields => effective annual yield increases with the compounding frequency
To calculate the effective annual yield, we relate it to the above calculation of the future value of $1:
* Future value of $1 in T years at a compounding frequency of m times: FV = 1+rmm*T
* The effective annual yield, y, is the actual return earned per year, hence it solves: FV = $1(1 + y)T
With compounding frequency of m times per year, the effective annual yield, y, is:
y = 1+rmm– 1
With continuous compounding: y = et – 1
Adjusting for Inflation
Suppose the inflation over the next year is I = 6%, an investment of $1 at r = 10%:
* You’ll have $1.10 at the end of the year
* But it will only buy the same goods as 1.101.06 = $1.038 can buy today
r is named: nominal rate (rnomi)
Real rate of interest, rreal, is such as: 1 + rreal = 1+rnomi1+i, approximately rreal ≈ rnomi – i
To calculate present values: PV = Cnomi1+rnomi
Project appraisal and capital budgeting
Capital budgeting
The addition to the firm market value that results from undertaking the project is:
NPV = C0+C11+r+C2(1+r)²+…+CT1+rT
Payback
The payback period of a project is the period which elapses until the initial outlay has been recouped
Payback criterion: accept projects that “payback” in a desired time frame
Internal Rate of Return
The IRR is the discount rate such that:
C0+C11+IRR+C2(1+IRR)²+…+CT1+IRRT=0
Profitability index
The profitability index of a proposed investment is defined as the ratio of
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