Chapter 6 Time Value of Money and Accounting u In theory, the fair value or market price of assets and liabilities should equal the present value (PV) of future cash inflows or outflows u Examples: –the fair value of long-term Notes (or Bond) Receivables (or Payables) equals the PV of the principal plus the PV of future interests

Single Sum Problem u Future Valuet: PV=$1, n=5,i=10%; Table I I I I I I $1 FV= $ u Present Value: fv=$1, n=5, i=10%; Table I I I I I I PV= $1

Ordinary Annuity u Future Value: R=$1, n=5,i=10%; Table I I I I I I $1 $1 $1 $1 $1 FV-OA=$ $1 $1 $1 $1 $1 FV-OA=$ u Present Value: R=$1, n=5, i=10%; Table I I I I I I I I I I I I PV-OA=$ $1 $1 $1 $1 $1 PV-OA=$ $1 $1 $1 $1 $1

Annuity Due u Future Value:R=$1;n=5;i=10%; No Table I I I I I I I I I I I I $1 $1 $1 $1 $1 FV-AD=$ u Present Value: R=$1;n=5;i=10%; Table I I I I I I I I I I I I PV-AD=$ $1 $1 $1 $1 $1

Deferred Annuity-- first rent occurs (y+1) periods from now Future Value Present Value R x (FVF-OA;n,i) R x [(PVF-OA;n+y,i) - (PVF-OA;y,i)] or R x [(PVF-OA;n,i) x (PVF;y,i)] or R x [(PVF-OA;n,i) x (PVF;y,i)] FV= PV= e.g.., y=3; n=7; i=10%; R=$ I I I I I I I I I I I $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1

Deferred Annuity Due-- first rent occurs y periods from now Future Value Present Value R x (FVF-AD;n,i) R x [(PVF-AD;n+y,i) - (PVF-AD;y,i)] or R x [(PVF-AD;n,i) x (PVF;y,i)] or R x [(PVF-AD;n,i) x (PVF;y,i)] FV = PV= e.g., y=3; n=7; i=10%; R=$ I I I I I I I I I I I $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1

Deferred Annuity Exercise u What amount must be deposited at 10% on Jan to permit annual withdrawals of $500 each beginning on Jan. 1, 1999 and ending on Jan, ? u Time Diagram: P=? $500 $500 $500 $500 P=? $500 $500 $500 $500

Solution to the Deferred Annuity Problem u An ordinary annuity of 4 rents deferred for 3 periods: PV=R x {(PVF-OA;7,10%) - (PVF-OA;3,10%)} =$500 x { } = $1, =$500 x { } = $1, or PV= R x (PVF-OA; 4,10%) x (PVF; 3,10%) =$500 x x = $1, =$500 x x = $1, u An annuity due of 4 rents deferred for 4 periods: PV=R x {(PVF-AD;8,10%) - (PVF-AD;4,10%)} =$500 x { } = $1, =$500 x { } = $1,190.79

Bond Valuation u On 1/1/95, X Co. issued $1,000, 8%, 3-year bonds with semiannual interest (market rate is 10%), what is the sale price of the bond? u Answer: PV of $1,000= $1,000 x (PVF;6,5%)=$747 PV of $1,000= $1,000 x (PVF;6,5%)=$747 PV of interest= $40 x (PVF-OA;6,5%)=$203 PV of interest= $40 x (PVF-OA;6,5%)=$203 PV of bonds= $747 + $203 = $950 PV of bonds= $747 + $203 = $950