Formulas Chapter 1 + 2 Flashcards
Gordon Growth Model (Dividends)
P__0 = D__1/(r - g);
“P_0” is the present value of the shares today.
“D_1” is the expected dividend one year from now.
“r” is the opportunity cost of capital (required rate of return).
“g” is the expected constant growth rate in dividends
The intuition behind the model is that the value of a stock is the sum of its future dividend payments, discounted back to present value. The rate at which these dividends are expected to grow (g) is a crucial factor. If g is equal to r (the required rate of return), the stock is considered to be fairly valued. If g is greater than r, it suggests the stock is undervalued, and if g is less than r, it suggests overvaluation.
Present Value Zero Coupon Bond
P__0 = maturity value/(cost*opportunity + 1)^n;
“P_0” is the present value of the zero-coupon bond.
“Maturity value” is the face value or future value of the bond.
“opportunity cost” is the required rate of return or discount rate per period.
“n” is the number of periods until the bond matures.
In simple terms, the formula discounts the future value of the bond back to its present value using the discount rate. Zero-coupon bonds do not make periodic interest payments like regular bonds; instead, they are issued at a discount to their face value and mature at face value. The formula reflects the time value of money, as it accounts for the fact that a given amount of money in the future is worth less than the same amount today.
Present Value Bond
The formula for calculating the present value (P_0) of a bond, which makes periodic interest payments, is the present value of future cash flows. For a bond that pays periodic coupons and returns the face value at maturity, the formula is:
PV\_\_bond=(V\_\_ni)/((1+r)^(1))+(V\_\_ni)/((1+r)^(2))+…+(V\_\_n*i)/((1+r)^(n))+V\_\_n/((1+r)^(n));
“V_n” is the nominal value
“i” is the interest rate
“R” is the risk of return
“n” is the years
This formula essentially calculates the present value of each future cash flow (coupon payments and the face value) and sums them up. The discounting factor (1+r)^n reflects the time value of money, reducing the value of future cash flows to their present value.
Series Present Worth
C = A((1 + r)^n - 1)/((1 + r)^nr);
“C” is the annual cash flow or the equivalent value of money brought back to the zero moment (present value). It represents the annual amount that, when discounted over n periods at the rate r, is equivalent in value to the given annual worth (A).
“A” is the annual worth of monthly installments (constant payments)
“r” is the interest rate
“n” is the amount of periods
In simpler terms, the Series Present Worth calculates the present value of the net cash flows over the entire project life by discounting each cash flow back to its present value using the discount rate. This metric helps in evaluating the profitability and feasibility of an investment or project over time. If the Series Present Worth is positive, it indicates that the project is expected to generate a positive return and may be considered for investment.
Capital Recovery
A = C(1 + r)^nr/((1 + r)^n - 1);
“C” is the annual cash flow or the equivalent value of money brought back to the zero moment (present value). It represents the annual amount that, when discounted over n periods at the rate r, is equivalent in value to the given annual worth (A).
“A” is the annual worth of monthly installments (constant payments)
“r” is the interest rate
“n” is the amount of periods
This expression represents the Capital Recovery or the Annual Worth (A), which is the constant annual cash flow required to recover the initial investment (present value) over a given period at a specific interest rate. It’s essentially the annual payment needed to pay back the initial capital over time.
Future Value of Money Formula
FV = C*(1 + r)^n
“FV” is the future value of money from capital
“C” is the constant cash flow per period
“r” is the interest rate or discount rate per period
“n” is the number of periods
Multiplying C by (1+r)^n calculates the future value of the cash flow series. It’s essentially compounding the constant cash flow over n periods at the given interest rate. This formula is useful for determining the total value of a series of cash flows into the future, taking into account the time value of money.
Present Value of Future Cash Flow
PV = C/(1 + r)^n;
“PV” is the present value of future cash flow
“C” is the constant cash flow per period
“r” is the interest rate or discount rate per period
“n” is the number of periods
This formula calculates the present value of a series of future cash flows by discounting each future cash flow back to its present value. This means, that f you have a future cash flow of $100 occurring every year for the next 3 years and you discount each of those future cash flows at a rate of 5%, the present value would be approximately $86.38.
What this means is that the current value of receiving $100 per year for the next 3 years, discounted at a rate of 5%, is equivalent to having $86.38 in hand today. The present value represents the current worth of future cash flows, taking into account the time value of money. In other words, it reflects the idea that a dollar received in the future is worth less than a dollar received today due to the opportunity to earn a return on that money over time.
Present value of perpetuity
PV = P/i;
“PV” is the present value of an infinite series of cash flows
“i” is the discount rate or interest rate per period
The formula calculates the present value of an infinite series of equal cash flows that continue indefinitely. It’s based on the idea that if you receive a constant annual payment forever, the present value is simply the annual payment divided by the discount rate.
Present value of a perpetuity with constant growth
PV = P/(i - g);
“PV” is the present value of an infinite series of cash flows
“i” is the discount rate or interest rate per period
“g” is the constant growth rate of the cash flows
This formula is used when the cash flows are expected to grow at a constant rate indefinitely. It’s derived from the Gordon Growth Model, which incorporates the growth rate of cash flows into perpetuity
Present value of loan with deffered period (Series Present Worth + Capital Recovery)
This formula can be used to determine the payments of a loan when an installment has been deferred
C__0 = A/(1 + r)^n((1 + r)^n - 1)/((1 + r)^nr);
“C” is the annual cash flow or the equivalent value of money brought back to the zero moment (present value). It represents the annual amount that, when discounted over n periods at the rate r, is equivalent in value to the given annual worth (A).
“A” is the annual worth of monthly installments (constant payments)
“r” is the interest rate
“n” is the amount of periods
Accumulated Capital
A = Prt + P;
“A” is accumulated capital
“P” is the original amount (the initial deposit)
“r” is the annual iinterrest rate
“t” is the time
This formula is used to calculate the simple interest earned or paid on a principal amount over a specific time period. The interest is calculated by multiplying the principal amount by the interest rate and the time the money is invested or borrowed.
