4) Time Value of Money II

The three requirements to discount/compound

Cashflow

timeline

Interest/relevant rate

Effective Annual Rate (EAR)

The actual amount of interest earnt over a period

EAR = (1+r)ⁿ - 1

Annual Percentage Rate (APR)

The quoted rate (excludes compounding)

APR doesn’t equal EAR if compounded more than once per year

Effective Periodic Rate

The interest rate for a given period (n = number of period per year)

r_n = (1 + EAR)^1/n - 1

r_n = APR / n

Interest only loans (perpetuity)

Borrower makes periodic interest payments

Principal repaid at the loans termination

Amortising loans

Payments are equal and made periodically with the loan being fully repaid on last payment

Each payment includes the interest on the loan, plus some of the principal

Loan = PV(Repayments)

Outstanding Loan Balance

Use PV Annuity formula, with n as payments remaining

Nominal vs Real Interest Rates

Nominal Interest Rate: Quoted by financial institutions and used for discounting/compounding

Real Interest Rate: The rate of growth of your purchasing power, adjusted with inflation

Rule for Real and Nominal Rates

You cannot mix real and nominal interest rates

The answer will be the same when used separately

Interest rates and NPV

Interest rates are inverse to NPV

• When interest rates increase, NPV typically decreases and vice versa

  • This is unless the investment adjusts with inflation

Calculating annuities growing with inflation

If the annuity grows with inflation, the inflation rate is subbed as g into the growing annuity formula