4. Basic Concepts of Financial Theory

• Time value of money (TVM) is one of the primary principles of finance. It states essentially that a dollar today is worth more than a dollar tomorrow because a dollar today can be invested to begin earning interest immediately. The application of the TVM concept in finance allows for the comparison of monetary amounts which are available at different points in time, which in turn helps investors to make the most appropriate money management decisions.
• Future value is the sum that will be available in the future given an investment today.

  Formula: FVN = PV(1 + i)^N
• Present value is the amount that must be deposited or invested today to arrive at a desired amount in the future.

  Formula: PV = FVN\(1+i)^N
• An ordinary annuity is when payments are made at the end of a period.

  An annuity due is when payments are made at the beginning of a period.
• Determinants of interest rates are premiums that add to the cost of borrowing. Each premium is impacted, and determined, by its own particular and specific set of factors:

  1. The risk-free rate assumes that there is no risk involved for the borrower;
  2. Inflation makes currency less valuable in the future and is used for calculating the nominal or stated interest rate;
  3. Default risk occurs when borrowers are unable to meet the terms of the loan agreement;
  4. Liquidity premium (treasury, money market instruments);
  5. Maturity premium, when the loan term is completed and paid back.
• Formula for interest rate determinants:

  r = Rf + Ip + Dp + Lp + Mp

  
• Short-term interest rates are heavily influenced by a nation’s central bank, monetary policies in place under a given regime, and the influence of interactions with other nations. Long-term rates are generally representative of market forces rather than governmental influences. The interrelationship between long-term and short-term interest rates can be seen as represented by the yield curve.
• The yield curve is a graphic illustration of the relationship between interest rates and length of time to maturity.

  A positive yield curve occurs when long-term interest rates are higher than short-term interest rates.

  A negative yield curve occurs when short-term interest rates are higher than long-term interest rates.

  
• There are three primary risks that occur when one is dealing with fixed-interest or fixed-income debt securities:

  1. Purchasing power risk: previously-issued debt instrument and interest rates in the market rise, it is now less than what is received by buyers of newly issued debt instruments. This means that this individual has lost purchasing power. This risk is also known as inflation rate risk.
  2. Interest rate risk: This risk also occurs when interest rates rise. An increase in rates makes the older, lower rate issue that an individual is already holding less valuable.
  3. Reinvestment rate risk.
• Interest rate futures are a financial derivative contract which serve as a hedge against rate fluctuations.
• WACC is made up of components that are cost centers for a firm. Long-term debt, common equity, and preferred equity are the three methods a firm has available to raise capital to finance its business undertakings. These are the means of financing investments on the asset side of the balance sheet, which are where costs of capital are created.

  WACC = (wd · rd · (1 − Tc)) + (we · re) + (wp · rp)

  
• The cost of debt is the required return on our company’s debt. Publicly held firms can use the yield to maturity (YTM) of outstanding debt for the cost of debt (rd).
• The cost of a firm’s equity can be calculated in two ways, either using the capital asset pricing model (CAPM) or the expected rate of return formula. If beta and market return are given, along with a risk-free rate, then one has sufficient information to use the CAPM, but if stock price, dividend data, and growth rate information are provided, then one should use the expected rate of return formula to provide a figure for the cost of equity (re) for the WACC calculation.
• Single sum refers to a lump-sum payment received at one point in time in the future. The future value of that sum is the future amount of an initial deposit made today that has been compounded for a given number of periods at a given interest rate.
• Present value of an annuity due (PVAD) is the current value of an expected and regularly-timed series of steady, equal payments from an investment at the beginning of each period. Perhaps the best example of PVAD is retirement funding.
• Interest rate futures are based on an underlying security and move in value as interest rates fluctuate up or down.

  When interest rates climb higher, the buyer of the futures contract pays the seller an amount equal to that of the benefit received by investing at a higher rate versus at the rate specified in the futures contract.

  Conversely, when interest rates move lower, the seller of the futures contract will compensate the buyer for the lower interest rate at the time of expiration.
• As the return earned on a firm’s assets depends on the riskiness of those assets; the cost of capital provides an indication of how the market views the risk of a companyʼs assets.