Exam 2 Review: Finance Concepts and Calculations

Posted on Aug 22, 2024 in Mathematics

Exam 2 Review

Chapter 5: Time Value of Money (Practice quizzes, MindTap, and class examples)

Key Concepts

  • Future Value (FV): Represents the value of an investment at a specific future date, considering interest earned.
  • Simple Interest: Interest earned only on the principal amount. FV = PV + PV(I)(N)
  • Compound Interest: Interest earned on both the principal and accumulated interest. FV = PV x (1+I)^n
  • Compounding: The process of converting present values into future values.
  • Discounting: The process of converting future values into present values.
  • Annuity: A series of equal payments made at fixed intervals over a specified period.
  • Perpetuity: A series of equal payments made at fixed intervals indefinitely.
  • Ordinary Annuity: Payments occur at the end of each period.
  • Annuity Due: Payments occur at the beginning of each period.

Example: Mortgage Payment Calculation

David Luna buys a $500,000 house with a 20% down payment and a 30-year fixed mortgage at a 3.6% annual interest rate. What’s his monthly payment?

  • N (Number of Periods): 30 years * 12 months/year = 360 months
  • I/Y (Interest Rate per Period): 3.6% / 12 months/year = 0.3%
  • PV (Present Value): $500,000 – (20% * $500,000) = $400,000
  • FV (Future Value): $0 (Mortgage will be paid off)
  • PMT (Monthly Payment): $1,818 (Calculate using a financial calculator or spreadsheet)

Comparing Simple and Compound Interest

Compound interest results in faster growth than simple interest because interest is earned on accumulated interest. The balance will be the same after the first year, but higher with compound interest from the second year onwards.

Effects of Changes in Variables

  • As the interest rate (r) increases, the present value (PV) decreases.
  • As the number of periods (N) increases, the present value (PV) decreases.
  • As interest is compounded more frequently, the present value (PV) decreases.

Key Comparisons

  • If the interest rate is positive, the future value (FV) of a series of payments will be higher than the present value (PV).
  • EAR (Effective Annual Rate): Used to compare interest rates with different compounding frequencies. Higher with more frequent compounding.
  • Nominal Rate (INOM): The stated annual interest rate. Equal to EAR when compounded annually.

Chapter 6: Interest Rates

Understanding components of interest rates:

  • Real Risk-Free Rate (r*): The rate in a riskless and inflation-free environment.
  • Inflation Premium (IP): Compensation for expected inflation.
  • Maturity Risk Premium (MRP): Compensation for the risk of interest rate fluctuations in long-term securities.
  • Liquidity Premium (LP): Compensation for the risk of illiquidity.
  • Default Risk Premium (DRP): Compensation for the risk of default.

Formula

r = r* + IP + DRP + LP + MRP

Chapter 7: Bonds

Understanding bond features:

  • Par Value (Face Value): The principal amount repaid at maturity.
  • Coupon Payment: Periodic interest payment. Calculated as Coupon Rate * Par Value.
  • Coupon Interest Rate: Annual interest rate stated on the bond.
  • Yield to Maturity (YTM): The total return anticipated on a bond if held until maturity.
  • Current Yield (CY): Annual Coupon Payment / Current Price
  • Capital Gains Yield (CGY): Change in Price / Beginning Price or YTM – CY

Bond Types

  • Premium Bond: YTM < Coupon Rate (Price > Par Value)
  • Discount Bond: YTM > Coupon Rate (Price < Par Value)
  • Bond Issued at Par: YTM = Coupon Rate (Price = Par Value)

Bond Provisions

  • Call Provision: Allows the issuer to redeem the bond before maturity.
  • Put Provision: Allows the bondholder to sell the bond back to the issuer before maturity.
  • Convertible Bond: Can be converted into common stock.
  • Warrant: Gives the holder the right to purchase stock at a specific price.

Yield to Call (YTC)

Calculated similarly to YTM, but using the call date and call price. Often relevant for premium bonds.

Bond Valuation

Calculate the present value (PV) of future cash flows (coupon payments and principal repayment) to determine the bond’s current value. Adjust N, I/Y, and PMT for semi-annual payments.

Bond Value Changes

Assuming constant YTM, the value of a premium bond decreases and the value of a discount bond increases as they approach maturity.