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Unformatted text preview: Chapter 6: Accounting and the Time Value of Money SingleSum Problems
Present Value $15,000 Future Value? 0 1 2 3 4 5 6 BE61 Chris Spear invested $15,000 today in a fund that earns 8% compounded semiannually. To what amount will the investment grow in 3 years? What table do we use? Present Value of a Single Sum
BE62: Tony Bautista needs $25,000 in 4 years. What amount must he invest today if his investment earns 12% compounded quarterly? Present Value? Future Value $25,000 0 1 2 3 4 5 6 What table do we use? Present Value of a Single Sum
i=3% n=16 $25,000 $25,000
Future Value x .62317
Factor = $15,579
Present Value SingleSum Problems SingleSum Problems Solving for Other Unknowns
Example—Computation of the Number of Periods The Village of Somonauk wants to accumulate $70,000 for the construction of a veterans monument in the town square. At the beginning of the current year, the Village deposited $47,811 in a memorial fund that earns 10% interest compounded annually. How many years will it take to accumulate $70,000 in the memorial fund? SingleSum Problems SingleSum Problems
Example—Computation of the Number of Periods
Illustration 614 Using the future value factor of 1.46410, refer to Table 61 and read down the 10% column to find that factor in the 4period row. SingleSum Problems SingleSum Problems
Example—Computation of the Number of Periods
Illustration 614 Using the present value factor of .68301, refer to Table 62 and read down the 10% column to find that factor in the 4period row. SingleSum Problems SingleSum Problems Solving for Other Unknowns
Example—Computation of the Interest Rate SingleSum Problems SingleSum Problems
Example—Computation of the Interest Rate
Illustration 616 Using the future value factor of 1.76234, refer to Table 61 and read across the 5period row to find the factor. SingleSum Problems SingleSum Problems
Example—Computation of the Interest Rate
Illustration 616 Using the present value factor of .56743, refer to Table 62 and read across the 5period row to find the factor. BE63
C a nd ic e Willis will inve s t $ 3 0 ,0 0 0 to d a y . S h e ne e d s $ 1 5 0 ,0 0 0 in 2 1 ye a rs . Wh a t a nnua l inte re s t ra te m us t s h e e a rn? BE63
PV=$30,000 FV=150,000 0 1 2 3 21 150,000=30,000FVp(21,i) 5 =FVp(21,i) (p.308) i=8% BE64
Bo Newman will invest $10,000 today in a fund that earns 5% annual interest. How many years will it take for the fund to grow to $17,100? BE64
PV=$10,000 FV=$17,100 0 1 2 3 n 17,100=10,000FVp(5%, n) 1.71 =FVp(5%,n) (p. 308) n=11 BE67
John Fillmore’s lifelong dream is to own his own fishing boat to use in his retirement. Jack has recently come into an inheritance of $400,000. He estimates that the boat he wants will cost $300,000 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 12% (compounded annually) to buy the boat at retirement? BE67
PV=400,000 FV=$300,000 0 1 2 3 4 5 PV=300,000*PVf(12%,5) PV=300,000*.56743 PV=170,229 (p.310) BE68
Refer to the data in BE67. Assuming quarterly compounding of amounts invested at 12%, how much of Jack Thompson’s inheritance must be invested to have enough at retirement to buy the boat? BE68
FV=300,000 0 1 2 3 20 PV=300,000*PVf(3%,20) PV=300,000*.55368=$166,104 (p. 310) Annuities
Annuity requires the following:
(1) (2) (3) Periodic payments or receipts (called rents) of the same amount, The samelength interval between such rents, and Compounding of interest once each interval. Two Types Ordinary annuity rents occur at the end of each period. Annuity Due rents occur at the beginning of each period. Ordinary v. Annuity Due
Note: The difference between an ordinary annuity and an annuity due is that:
– Each rent or payment compounds (interest added) one more period in a annuity due, future value situation. – Each rent or payment is discounted (interest removed) one less period under the annuity due situation. – Given the same i, n and periodic rent, the annuity due will always yield a greater present value (less interest removed) and a greater future value (more interest added).
14 14 Annuities
Future Value of an Ordinary Annuity
Rents occur at the end of each period. No interest during 1st period. Present Value
$20,000 20,000 20,000 20,000 20,000 20,000 Future Value
20,000 20,000 0 1 2 3 4 5 6 7 8 Future Value of an Ordinary Annuity
Illustration: Assume that $1 is deposited at the end of each of 5 years (an Illustration: ordinary annuity) and earns 12% interest compounded annually. Following is the computation of the future value, using the “future value of 1” table (Table 61) for each of the five $1 rents. Future Value of an Ordinary Annuity
A formula provides a more efficient way of expressing the future value of an ordinary annuity of 1. Where: R = periodic rent FVFOA = future value factor of an ordinary annuity n,i i = rate of interest per period n = number of compounding periods Future Value of an Ordinary Annuity
Illustration: What is the future value of five $5,000 deposits made at the end of each of the next 5 years, earning interest of 12%? Illustration 619 = $31,764.25 Future Value of an Ordinary Alternate Calculation Annuity
Illustration: What is the future value of five $5,000 deposits made at the end of each of the next 5 years, earning interest of 12%? What table do we use? Future Value of an Ordinary Annuity
i=12% n=5 What factor? $5,000 $5,000
Deposits x 6.35285
Factor = $31,764
Present Value Future Value of an Ordinary Annuity
Present Value
$30,000 30,000 30,000 30,000 30,000 30,000 Future Value
30,000 30,000 0 1 2 3 4 5 6 7 8 BE613 Adams Inc. will deposit $30,000 in a 12% fund at the end of each year for 8 years beginning December 31, Year 1. What amount will be in the fund immediately after the last deposit? What table do we use? Future Value of an Ordinary Annuity
i=12% n=8 $30,000
Deposit x 12.29969
Factor = $368,991
Future Value Annuities
Future Value of an Annuity Due
Rents occur at the beginning of each period. Interest will accumulate during 1st period. Annuity Due has one more interest period than Ordinary Annuity. Factor = multiply future value of an ordinary annuity factor by 1 plus the interest rate.
$20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000 Future Value 0 1 2 3 4 5 6 7 8 Comparison of Ordinary Annuity with an Annuity Due Future Value of an Annuity Due Future Value of an Annuity Due
Computation of Rent
Illustration: Assume that you plan to accumulate $14,000 for a down Illustration: payment on a condominium apartment 5 years from now. For the next 5 years, you earn an annual return of 8% compounded semiannually. How much should you deposit at the end of each 6semiannually. month period? R = $1,166.07 Future Value of an Annuity Due
Computation of Rent
$14,000 12.00611 Alternate Calculation = $ $1,166.07 Future Value of an Annuity Due
Computation of Number of Periodic Rents
Illustration: Suppose that a company’s goal is to accumulate $117,332 by making periodic deposits of $20,000 at the end of each year, which will earn 8% compounded annually while accumulating. How many deposits must it make? How 5.86660 Future Value of an Annuity Due
Computation of Future Value
Illustration: Mr. Goodwrench deposits $2,500 today in a savings account that earns 9% interest. He plans to deposit $2,500 every year for a total of 30 years. How much cash will Mr. Goodwrench accumulate in his retirement savings account, when he retires in 30 years? years? Future Value of an Annuity Due
Present Value
30,000 $30,000 30,000 30,000 30,000 30,000 30,000 Future Value
30,000 0 1 2 3 4 5 6 7 8 Adams Inc. will deposit $30,000 in a 12% fund at the beginning of each year for 8 years beginning January 1, Year 1. What amount will be in the fund at the end of Year 8? What table do we use? Future Value of an Annuity Due
i=12% n=8 12.29969 x 1.12 = 13.775652 $30,000
Deposit Deposit x 13.775652
Factor = $413,270
Future Value Present Value of an Ordinary Annuity
Present Value of an Ordinary Annuity
Present value of a series of equal amounts to be withdrawn or received at equal intervals. Periodic rents occur at the end of the period. Present Value
$100,000 100,000 100,000 100,000 ..... 100,000 100,000 0 1 2 3 4 19 20 Present Value of an Ordinary Annuity
Illustration: Assume that $1 is to be received at the end of each of 5 Illustration: periods, as separate amounts, and earns 12% interest compounded annually. Present Value of an Ordinary Annuity
A formula provides a more efficient way of expressing the present value of an ordinary annuity of 1. Where: Present Value of an Ordinary Annuity
Illustration: What is the present value of rental receipts of $6,000 each, to be received at the end of each of the next 5 years when discounted at 12%? Present Value of an Ordinary Annuity
Present Value
$100,000 100,000 100,000 100,000 ..... 100,000 100,000 0 1 2 3 4 19 20 Jaime Yuen wins $2,000,000 in the state lottery. She will be paid $100,000 at the end of each year for the next 20 years. How much has she actually won? Assume an appropriate interest rate of 8%. What table do we use? Present Value of an Ordinary Annuity
i=5% n=20 $100,000
Receipts x 9.81815
Factor = $981,815
Present Value Present Value of an Annuity Due
Present Value of an Annuity Due
Present value of a series of equal amounts to be withdrawn or received at equal intervals. Periodic rents occur at the beginning of the period. Present Value
$100,000 100,000 100,000 100,000 100,000 100,000 ..... 0 1 2 3 4 19 20 Present Value of an Annuity Due
Comparison of Ordinary Annuity with an Annuity Due
Illustration 631 Present Value of an Annuity Due
Illustration: Space Odyssey, Inc., rents a communications satellite for 4 years Illustration with annual rental payments of $4.8 million to be made at the beginning of each year. If the relevant annual interest rate is 11%, what is the present value of the rental obligations? Present Value of an Annuity Due
Present Value
$100,000 100,000 100,000 100,000 100,000 100,000 ..... 0 1 2 3 4 19 20 Jaime Yuen wins $2,000,000 in the state lottery. She will be paid $100,000 at the beginning of each year for the next 20 years. How much has she actually won? Assume an appropriate interest rate of 8%. What table do we use? Present Value of an Annuity Due
i=8% n=20 $100,000 $100,000
Receipts x 10.60360
Factor = $1,060,360
Present Value BE65
Sally Medavoy will invest $8,000 a year for 20 years in a fund that will earn 12% annual interest. If the first payment occurs at year end, what amount will be in the fund in 20 years? If the first payment into the fund occurs today, what amount will be in the fund in 20 years? BE65
$5,000 $5,000 0 1 2 3 20 Ordinary Annuity : FVa=8,000FVaoa(12%,20) =8,000*72.05244=$576,420 (p.312) Annuity Due: FVa=8,000FVa(12%,20) =8,000(72.05244)*1.12=$645,590 BE66
Steve Madison needs $250,000 in 10 years. How much must he invest at the end of each year at 11% interest, to meet his needs. BE66
FV=$250,000 0 1 2 3 10 250,000=PMT*FVaoa(10,11%) 250,000=PMT*16.72201 14,950=PMT (p.312) BE69 Morgan Freeman is investing $16,380 at the end of each year in a fund that earns 10% interest. In how many years will the fund be at $100,000 BE69
16,380 16,380 FV=$100,000 0 1 2 3 n 100,000=16,380FVaoa(n, 10%) 6.105=FVaoa(n, 10%) (p. 312) n=5 BE610
Henry Quincy wants to withdraw $30,000 each year for 10 years from a fund that earns 8% interest. How much must he invest today if the first withdrawal is at year end? How much must he invest today if the first withdrawal takes place immediately? BE610
30,000 30,000 0 1 2 3 10 PV=30,000*PVaoa(8%,10)=30,000*6.71008 (p. 314) $201,302 PV=30,000*PVaad(8%,10)=30,000*7.24689 (p.316) $217,407 ...
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This note was uploaded on 12/29/2009 for the course ACC 5100 taught by Professor Andrews during the Fall '09 term at Wayne State University.
 Fall '09
 Andrews
 Accounting, Financial Accounting

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