Annuity Due vs. Ordinary AnnuityAnnuity Due vs. Ordinary Annuity

Ordinary Annuity is standard for most set-Ordinary Annuity is standard for most set-ups and implies payment at the end of the ups and implies payment at the end of the periodperiod

Annuity Due is payment at the beginning Annuity Due is payment at the beginning of the periodof the period

Both have the following characteristicsBoth have the following characteristics Regular IntervalRegular Interval Same AmountSame Amount

Annuity Due vs. Ordinary AnnuityAnnuity Due vs. Ordinary Annuity

Look at time line for the cash flows…Look at time line for the cash flows… Note the difference between the two streamsNote the difference between the two streams Same number of total paymentsSame number of total payments Annuity Due has a payment at TAnnuity Due has a payment at T00

Ordinary Due has a payment at TOrdinary Due has a payment at TNN All other Payments are the same!All other Payments are the same!

Adjusting the FVIFAs and PVIFAsAdjusting the FVIFAs and PVIFAs Note the tables and formulas are for Ordinary Note the tables and formulas are for Ordinary

Annuity StreamsAnnuity Streams

Annuity Due vs. Ordinary AnnuityAnnuity Due vs. Ordinary Annuity

FVIFA adjustmentFVIFA adjustment The entire annuity stream receives one The entire annuity stream receives one

additional time period of interest earnings:additional time period of interest earnings: Take Ordinary Annuity FVIFA x (1 +r)Take Ordinary Annuity FVIFA x (1 +r) Or ((1+r)Or ((1+r)NN – 1 ) / r) x (1+ r) – 1 ) / r) x (1+ r) For the calculator just set Mode to BGNFor the calculator just set Mode to BGN

Second Function above PMTSecond Function above PMTThen second and enterThen second and enter

Example…$100 for ten years at 10%.Example…$100 for ten years at 10%.

Annuity Due vs. Ordinary AnnuityAnnuity Due vs. Ordinary Annuity

PVIFA AdjustmentPVIFA Adjustment The entire annuity stream receives one less The entire annuity stream receives one less

discount over the time period or you have an discount over the time period or you have an ordinary annuity of n-1 and a lump sum at Tordinary annuity of n-1 and a lump sum at T00

Take Ordinary Annuity PVIFA for n-1 and Take Ordinary Annuity PVIFA for n-1 and add PMT for Tadd PMT for T00

Or PMT (1- /1(1+r)Or PMT (1- /1(1+r)N-1N-1 – 1 ) / r) + PMT – 1 ) / r) + PMT Or PVIFA = (1- /1(1+r)Or PVIFA = (1- /1(1+r)N-1N-1 – 1 ) / r) + 1 – 1 ) / r) + 1 Example…$100 for ten years at 10%.Example…$100 for ten years at 10%.

Interest RatesInterest Rates

Term Structure of Interest Rates (Yield Curve)Term Structure of Interest Rates (Yield Curve) Rates vary with timeRates vary with time Typically long-term rates higher than short-term Typically long-term rates higher than short-term

ratesrates Problem 6.1 – Draw Yield CurveProblem 6.1 – Draw Yield Curve

Theories of Term StructureTheories of Term Structure Expectations HypothesisExpectations Hypothesis Liquidity PreferenceLiquidity Preference Market SegmentationMarket Segmentation

Different instruments different ratesDifferent instruments different rates Risk of Cash FlowsRisk of Cash Flows Higher Risk investor demands Higher ReturnHigher Risk investor demands Higher Return

Interest RatesInterest Rates

Annual Percentage RateAnnual Percentage Rate

Effective Annual RateEffective Annual Rate

Nominal Interest RateNominal Interest Rate

Real Interest RateReal Interest Rate

Risk-Free Interest RateRisk-Free Interest Rate

Risk Premium (s)Risk Premium (s)

Inflation RateInflation Rate

Fisher Effect: 1 + nominal = (1 + real) x (1 + inf.)Fisher Effect: 1 + nominal = (1 + real) x (1 + inf.)