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Chapter 6 Time Value of Money and Accounting In theory, the fair value or market price of assets and liabilities should equal the present value (PV) of future cash inflows or outflows 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 Future Valuet: PV=$1, n=5,i=10%; Table 1 0 1 2 3 4 5 I I I I I I $1 FV= $1.61051 Present Value: fv=$1, n=5, i=10%; Table 2 0 1 2 3 4 5 I I I I I I PV=0.62092 $1 Ordinary Annuity Future Value: R=$1, n=5,i=10%; Table 3 0 1 2 3 4 5 I I I I I I $1 $1 $1 $1 $1 FV-OA=$6.1051 Present Value: R=$1, n=5, i=10%; Table 4 0 1 2 3 4 5 I I I I I I PV-OA=$3.79079 $1 $1 $1 $1 $1 Annuity Due Future Value:R=$1;n=5;i=10%; No Table 0 1 2 3 4 5 I I I I I I $1 $1 $1 $1 $1 FV-AD=$6.71569 Present Value: R=$1;n=5;i=10%; Table 5 0 1 2 3 4 5 I I I I I I PV-AD=$4.16986 $1 $1 $1 $1 $1 Deferred Annuity--first rent occurs (y+1) periods from now Future Value R x (FVF-OA;n,i) Present Value R x [(PVF-OA;n+y,i) - (PVF-OA;y,i)] or R x [(PVF-OA;n,i) x (PVF;y,i)] FV= 9.48717 PV=3.6577 e.g.., y=3; n=7; i=10%; R=$1 0 1 2 3 4 5 6 7 8 9 10 I I I I I I I I I I I $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)] FV = 10.4359 PV= 4.0235 e.g., y=3; n=7; i=10%; R=$1 0 1 2 3 4 5 6 7 8 9 10 I I I I I I I I I I I $1 $1 $1 $1 $1 $1 $1 Deferred Annuity Exercise What amount must be deposited at 10% on Jan.1 1995 to permit annual withdrawals of $500 each beginning on Jan. 1, 1999 and ending on Jan, 1 2002? Time Diagram: 95 96 97 98 99 00 01 02 P=? $500 $500 $500 $500 Solution to the Deferred Annuity Problem An ordinary annuity of 4 rents deferred for 3 periods: PV=R x {(PVF-OA;7,10%) - (PVF-OA;3,10%)} =$500 x {4.86842 - 2.48685} = $1,190.79 or PV= R x (PVF-OA; 4,10%) x (PVF; 3,10%) =$500 x 3.16986 x 0.75131 = $1,190.79 An annuity due of 4 rents deferred for 4 periods: PV=R x {(PVF-AD;8,10%) - (PVF-AD;4,10%)} =$500 x {5.86842 -3.48685} = $1,190.79 Bond Valuation 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? Answer: PV of $1,000= $1,000 x (PVF;6,5%)=$747 PV of interest= $40 x (PVF-OA;6,5%)=$203 PV of bonds= $747 + $203 = $950