# Finance Essentials: A Guide to Key Concepts and Formulas

Classified in Mathematics

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## Finance Essentials

### Key Concepts

#### Time Value of Money

• Future Value: Amount to which an investment will grow after earning interest
• Present Value: Value today of a future cash flow

#### Interest

• Compound Interest: Interest earned on interest
• Simple Interest: Interest earned only on the original investment
• Annual Percentage Rate (APR): Interest rate that is annualized using simple interest
• Effective Annual Rate (EAR): Interest rate that is annualized using compound interest

#### Cash Flow Streams

• Annuity: Equally spaced level stream of cash flows for a limited period of time
• Ordinary Annuity: End of period cash flows
• Annuity Due: Beginning of period cash flows
• Perpetuity: A stream of level cash payments that never ends

### Bonds

• Bond: Security that obligates the issuer to make specified payments (periodic interest payments and returns of principal) to the bondholder
• Coupon: The interest payments made to the bondholder
• Coupon Rate: Annual interest payment, as a percentage of face value
• Face Value: Payment at the maturity of the bond
• Bond Pricing: The price of a bond is the present value of all cash flows generated by the bond discounted at the required rate of return
• Interest Rate Risk: As interest rates increase, present values decrease (Vice Versa)
• Yield to Maturity (YTM): Approximate rate of return assumes that one will hold the bond until maturity, interest rate for present value of bond cash flows equals the bond price. Yield to maturity, required return, and market rate are used interchangeably.
• Bond Ratings:
• AAA: Strongest
• AA: Strong
• A: Strong but some vulnerability
• Baa (BBB): Adequate
• Ba (BB): Considerable uncertainty
• B: Questionable to be repaid
• Caa (CCC) / Ca (CC): May already be in default
• C: Offer little prospect for principal/interest to be paid
• Ba (BB) or lower: Considered junk bonds
• Corporate Bonds/Default Risk: Market yield to maturity on bonds, other than U.S. Treasury bonds, include default or credit risk premium
• Default Risk Premium: The difference between the yield on a risky bond and a U.S. Treasury bond of similar maturity

### Stocks

• Share of Stock: Gets paid via dividends or from selling the share
• Dividend Discount Model (DDM): P0 = D1 - P1 / 1 + r
• DDM with no Growth: P0 = Div / R
• Constant Growth DDM: P0 = D0(1 + G) / r - g = D1 / r - g
• Expected Rate of Return:
• P0 = D0(1 + G) / r - g = D1 / r - g
• OR
• R = (D0(1 + G) / P0) + G = (D1 / P0) + G

### Calculations using Excel

#### Time Value of Money

• Present Value: `=PV(FV, Nper(Number of Yrs), Rate (Interest))`
• Interest Rate: `=RATE(Nper (years), -PV, FV)`
• Number of Periods: `=NPER(Rate, -PV, FV)`
• Future Value: `=FV(Rate (divided by 12 for monthly, 4 for quarterly, 2 for semi-annual), Nper (multiplied by 12, 4, 2), -PV)`

#### Cash Flow Streams

• Present Value (Cash Flow): `=NPV(Rate, value 1(table with values)`
• Present Value for Annuity: `=PV(Rate, NPER, -PMT)`
• Annuity Payments: `=PMT(Rate (Divided by 12 for monthly, 4 quarterly, etc.), NPER (multiplied by 12, 4, 2), PV)`
• Future Value for Annuity: `=FV(Rate / 12, 4, 2), Nper (x 12, 4, 2), -Pmt)`
• Number of Payments: `=NPER(rate, -pmt, PV)`
• PV of Ordinary Annuity: `=PV(Rate, Nper, -pmt)`
• PV of Annuity Due: `=PV(rate, NPER, -pmt)`

#### Other

• EAR: `=EFFECT(Nominal_Rate(APR), Npery(Compounding)`
• APR: `=NOMINAL(Effect Rate(EAR), Npery(compounding)`
• Yield to Maturity: `=YIELD(Settlement, Maturity, Coupon Rate, PR (Bond Price), Redemption (Face Val), Frequency (Coup per year)`
• Annual Coupons: `=PRICE(Settlement, Maturity, Rate, Yield, Redemption (Face Val), Frequency (Coup)`
• Dollar Price of Bond: `=Bond Price x 10`