CFA – Ethical & Professional Standards & Quantitative Methods – The Time Value of Money

Calculator – Texus Instruments BAII Plus Calculator manual

  • N      No of compounding periods
  • I/Y    Interest rate per compounding period
  • PV    Present Value
  • FV    Future Value
  • PMT  Annuity payments or constant periodic cash flow
  • CPT  Compute




Required rate of return — The rate of return needed to induce investors or companies to invest in something.


Discount rate — is an interest rate a central bank charges depository institutions that borrow reserves from it.


Opportunity cost — or economic opportunity loss is the value of the next best alternative forgone as the result of making a decision.


Types of risk

  • Default risk  — The risk that  a borrower will not make the promised payments in a timely manner.
  • Liquidity riskis the risk of receiving less than a fair value for an investment if it must be sold for $$$ quickly
  • Maturity risk  — Longer maturity bonds have more maturity risk than the shorter term bonds and require  maturity risk premium


Required interest rate on a security = nominal risk-free rate + default risk premium + liquidity premium + maturity premium


Effective annual rate (EAR)  = (1 + periodic rate)m – 1

periodic rate = stated annual rate/m

m = number of compounding periods per year


Annuity is a stream of equal cash flows that occurs at equal intervals over a given period

  • Ordinary annuity – payment received at the end of each compounding period
  • Annuity due – payment received at start – Calc [2nd][BGN][2nd][SET][2nd][QUIT]

Perpetuity  — a financial instrument that pays a fixed amount of money at set intervals over an infinite period of time


Loan Amortization – is the process of paying off a loan with a series of periodic load payments, whereby a portion of the outstanding loan amount is paid off, or amortized, with each payment.



LOS 5a

An interest rate can be interpreted as the return required in equilibrium, the discount rate for calculating the present value of future cash flows, or as the opportunity cost of consuming now, rather than saving and investing.


LOS 5b

The required rate of return on a security = real risk free rate + expected inflation + default risk premium + liquidity premium + maturity risk premium.


LOS 5c

FV = PV(1+I/Y)N

PV = FV (1+I/Y)N


LOS 5d

An annuity is a series of equal cash flows that occurs at evenly spaced intervals over time.

Ordinary annuity cash flows occur at the end of each time period.  Annuity due cash flows occur at the beginning of each time period.


Perpetuities are annuities with infinite lives  (perpetual annuities)


PV perpetuity = PMT



LOS 5e


The present (future) value of any series of cash flows is equal to the sum of the present (future) values of the individual cash flows.


A mortgage is an amortizing load, repaid in a series of equal payments (an annuity), where each payment consists of the interest for the period (which decreases with each payment) and the amount of principle repaid (which increases with each payment)



For semi annual compounding – halve the interest rate and halve N periods (4 if this was quarterly)