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Chapter 6 Time Value of Money and Accounting

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:

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Chapter 6 Time Value of Money and Accounting

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  1. 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

  2. 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

  3. 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

  4. 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

  5. Deferred Annuity--first rentoccurs(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)] 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

  6. Deferred Annuity Due--first rentoccursy periods from now Future ValuePresent 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

  7. 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

  8. 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

  9. 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

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