Assets Current Assets
Cash $ 5,700
Accounts receivable 9,200
Inventory 17,400
Total current assets $32,300
Property and Equipment
Equipment $12,000
Less: Accumulated depreciation (7,500)
Total property and equipment 4,500
Total Assets $36,800
Liabilities Current Liabilities
Accounts payable $ 8,700
Salaries payable 1,800
Interest payable 140
Total current liabilities $10,640
Long-Term Liabilities
Notes payable 8,000
Total Liabilities $18,640
Owner's Equity
T. Tunxis, capital $18,160a
Total Liabilities and Owner's Equity $36,800
a$19,100 beginning balance + $22,560 net income - $23,500 withdrawals
WARD SPECIALTY FOODS Worksheet to Convert Trial Balance to Accrual Basis
December 31, 2004
Cash Basis Adjustments Accrual Basis
Debit Credit Debit Credit Debit Credit
Cash
Accounts receivable
Allowance for doubtful accounts Inventory
Equipment
Accumulated depreciation Prepaid rent
Prepaid insurance Accounts payable Accrued expenses Payroll taxes withheld Ward, withdrawals Ward, capital
Sales Purchases
Income summary–inventory Salaries
Payroll taxes Rent
Miscellaneous expense Insurance
Utilities Depreciation
Doubtful accounts expense
18,500 4,500 20,000 35,000
24,000
82,700 29,500 2,900 8,400 3,900 2,400 3,500
235,300
9,000
4,800 850 33,650
187,000
235,300
[1] 3,400 [3] 3,000
[4] 6,300 [5] 600
[8] 900
[7] 4,000 [3] 20,000 [8] 135 [8] 150
[8] 175 [6] 5,800 [2] 1,100 45,560
[2] 1,100
[6] 5,800
[7] 4,000 [8] 1,360
[4] 5,625 [5] 540 [1] 3,400 [3] 23,000
[4] 675 [5] 60
45,560
18,500 7,900 23,000 35,000 6,300 600
24,000
86,700 29,635 3,050 7,725 3,900 2,340 3,675 5,800 1,100 259,225
1,100
14,800
8,800 1,360 850 38,915
190,400 3,000
259,225
PC -18 ( AIC PA a d a p te d sol ut ion ) 1.
C-77
PC-18 (continued) 1. (continued)
Explanations of Adjustments:
[1] To convert 2004 sales to accrual basis
Accounts receivable, 12/31/04 $ 7,900
Deduct: Accounts receivable, 12/31/03 (4,500)
Increase in sales $ 3,400
[2] To record provision for doubtful accounts
[3] To record increase in inventory from 12/31/03 to 12/31/04
Inventory, 12/31/04 $23,000
Inventory, 12/31/03 (20,000)
Increase $ 3,000
[4] To adjust rent expense for prepaid rent at 12/31/03 and 12/31/04
Prepaid 12/31/04 ($8,400 x 9/12) $ 6,300
Prepaid 12/31/03 ($7,500 x 9/12) (5,625)
Rent expense decrease $ 675
[5] To adjust insurance expense for prepaid insurance at 12/31/03 and 12/31/04
Prepaid 12/31/04 ($2,400 x 3/12) $ 600
Prepaid 12/31/03 ($2,160 x 3/12) (540)
Insurance expense decrease $ 60
[6] To record depreciation for 2004
[7] To convert 2004 purchases to accrual basis
Accounts payable 12/31/04 $ 8,800
Deduct: Accounts payable 12/31/03 (4,800)
Increase in purchases $ 4,000
[8] To convert expenses to accrual basis
Payroll taxes $ 400 - $250 $150
Salaries $ 510 - $375 $135
Utilities $ 450 - $275 $175
$1,360 $900
PC-18 (continued)
2. WARD SPECIALTY FOODS
Statement of Changes in Mary Ward, Capital
For the Year Ended December 31, 2004
Mary Ward, capital, 12/31/03 $38,915 [1]
Add: Net income for year 49,475 [2]
$88,390
Deduct: Withdrawals for year (24,000)
Mary Ward, capital, 12/31/04 $64,390
Explanations of Amounts:
[1] Mary Ward, capital, 12/31/03 after adjustment to accrual basis (per worksheet)
[2] Computation of net income on accrual basis for the year ended 12/31/04 (per worksheet)
Sales $190,400
Purchases $86,700
Income summary-inventory (3,000)
Salaries 29,635
Payroll taxes 3,050
Rent 7,725
Miscellaneous expenses 3,900
Insurance 2,340
Utilities 3,675
Depreciation 5,800
Bad debts 1,100 (140,925)
Net income $ 49,475
APPENDIX D
COMPOUND INTEREST
CONTENT ANALYSIS OF EXERCISES AND PROBLEMS
Number Content Time Range
(minutes) ED-1 Future Value. Single investment, compound interest. 5-10 ED-2 Future Value. Single investment, compound interest. 5-10 ED-3 Present Value. Single sum, compound discount. 5-10 ED-4 Future Value. Ordinary annuity, interest compounded
annually. 5-10
ED-5 Present Value. Ordinary annuity and annuity due, interest
compounded annually. 5-15
ED-6 Amount of Each Cash Flow. Future value, interest
compounded annually. 5-10
ED-7 Amount of an Annuity. Various annual withdrawal dates,
interest compounded annually. 10-15
ED-8 Amount of Each Cash Flow. Present value, calculate monthly
installments, compound interest. 10-15
ED-9 Amount of Each Cash Flow. Present value and future value,
two sums, interest compounded annually. 10-15
ED-10 Amount of an Annuity. Different future value dates, amount of
deposits, interest compounded annually. 10-15
ED-11 Compound Interest. Future value and present value, ordinary
annuity and annuity due, withdrawal determination. 15-20 ED-12 Amount of an Annuity. Ordinary annuity. Deposits,
withdrawals, interest compounded annually. 10-15
ED-13 Present Value of Leased Asset. Lease payments. Annuity due.
Interest compounded annually. 5-10
ED-14 Number of Cash Flows. Future value, interest compounded
annually. 5-10
Number Content Time Range (minutes) PD-2 Present Value. Various single sums, compound interest. 15-30 PD-3 Future Value. Annuity due, ordinary annuity, compound interest. 15-30 PD-4 Amount of Each Cash Flow. Different present value dates, interest
compounded annually. 15-25
PD-5 Present Value. Ordinary annuity, annuity due, deferred annuity.
Interest compounded annually. 20-30
PD-6 Present Value. Ordinary annuity, annuity due, compound interest. 20-30 PD-7 Compound Interest Issues. Future value, installment determinations. 30-40 PD-8 Amount of an Annuity. Ordinary annuity, present value, withdrawal
determination, interest compounded annually. 20-30
PD-9 Amount of Each Cash Flow. Numerous first withdrawal dates, future
value compound interest. 30-40
PD-10 Number of Cash Flows. Present value, future value, compound interest. 20-30 PD-11 Serial Installments. Future value, amounts applicable to interest and
principal, interest compounded annually. 20-30
PD-12 Determining Loan Repayments. Present value, recalculation of cash
flow amount, interest compounded annually. 20-30
PD-13 Purchase of Asset. Alternative financing plans to acquire asset.
Ordinary annuity, annuity due. 30-40
PD-14 Fund to Retire Bonds. Ordinary annuity, future value, interest
compounded annually. 10-20
PD-15 Asset Purchase Price. Given future cash inflows, compute purchase
price of asset. 10-20
PD-16 Acquisition of Asset. Compute cost of asset, record purchase, and
prepare amortization table for note. 20-30
PD-17 Present Value Issues. Four different payment plans, determine smallest
present value. 25-35
PD-18 (AICPA adapted). Comprehensive: Compound Interest Issues.
Numerous issues solved by using the present value and future value tables.
30-45
PD-19 Comprehensive: Various Compound Interest Issues. Numerous issues
solved by using the present value and future value tables and formulas. 30-45
ANSWERS TO QUESTIONS
QD-1 Interest is the cost of the use of money over time. Interest and the price of any
merchandise item are similar because both are costs associated with items acquired by a company.
QD-2 Simple interest is interest only on the principal amount. There is no compounding of interest on "previously earned" interest when computations are based on simple interest.
Compound interest is interest that accrues on past unpaid accrued interest, as well as on the principal.
The time value of money is interest. This term indicates that a dollar held today is worth more than a dollar to be received a year from now because a dollar today can be invested to earn a return (interest), whereas a dollar received a year from now yields no return during the year. This future dollar must have the interest element removed from it to determine its value today.
Discount. Discounting involves finding out what a sum or sums of money in the future is worth today by removing the time value of money. Dollars in the future are brought back to the present at some interest rate. The higher the interest rate, the lower the present value.
QD-3 The future amount of 1 tells how much one single monetary unit will accrue to in a given number of periods at a given interest rate. The future value of an ordinary annuity of 1 tells how much a series of end-of-the-period deposits of one monetary unit will accrue to at a given periodic interest rate.
QD-4 Interest Rate Frequency of Compounding Per Period Per Year a. 9% 2 times
b. 4% 4 times c. 1ẳ% 12 times
QD-5 The future value of 1 is 1 plus the interest compounded at a given interest rate for a given number of periods. The present value of 1 is the amount that must be invested today in order to grow to 1 in a given number of periods at a given compound interest rate.
The present value of 1 tells how much one monetary unit in the future is worth today, given the interest rate and the number of periods. The present value of an ordinary annuity of 1 tells how much a series of payments of one monetary unit at the end of each period is worth today, given the interest rate.
QD-6 The only difference between the future value of an ordinary annuity and the future value of an annuity due is the number of time periods over which interest accrues. With the future value of an annuity due, interest accrues for one period after the last cash flow in the series. With the future value of an ordinary annuity, interest compounding ends on the date of the last payment.
QD-6 (continued)
Future value of an {ordinary annuity of 4 cash flows is determined
immediately after the last cash flow is made
$ $ $ $ *_________ __*__________*__________*
Dec. 31 Dec. 31 Dec. 31 Dec. 31 Year 1 Year 2 Year 3 Year 4
Future value of an annuity due of 4 cash flows is determined one period after the last { cash flow is made
$ $ $ $ *_______ ____*__________*__________*__________
Dec. 31 Dec. 31 Dec. 31 Dec. 31 Dec. 31 Year 1 Year 2 Year 3 Year 4 Year 5
Arrows indicate date to which computation applies
QD-7 The present value of an annuity due is based on cash payments made at the beginning of each period, and is determined on the date of the first payment. The present value of a deferred annuity refers to an annuity where the first payment in the series is postponed for two or more periods in the future.
Present value of an annuity due of four cash flows
$ $ $ $ *_______*________*_________*
Jan. 1 Jan. 1 Jan. 1 Jan. 1 Year 1 Year 2 Year 3 Year 4
QD-7 (continued)
Present value of an annuity of
four cash flows deferred three periods
$ $ $ $ ___*___ _ _ ___*________*________*
Jan. 1 Jan. 1 Jan. 1 Jan. 1 Year 5 Year 6 Year 7 Year 8
Jan. 1 Jan. 1 Jan. 1 Jan. 1 Year 1 Year 2 Year 3 Year 4
Arrows indicate date to which computation applies
QD-8 a. Step 1: Compute the present value of 1 at 10% for 4 years, as follows:
0.10)4
(1 1
Step 2: Multiply $10,000 by the answer to step 1.
b. Step 1: To convert the factor obtained in step 1 above from four periods to five periods, simply divide by 1.10, as follows:
1.10
0.10) (1
1
4
Step 2: Multiply $5,000 by the answer to step 1.
c. Step 1: Compute the future amount of an ordinary annuity of 1 for five cash flows, at 10%, as follows:
0.10 1 0.10)
(1 5
Step 2: Multiply $3,000 by the answer to step 1.
QD-9 First, the two desired withdrawals are discounted back to the present at 12%
compounded semiannually. The sum of the two present values of the withdrawals equals the required deposit.
Required deposit =[$40,000(pn 8,i 6%)] [$50,000(pn 20,i 6%)]
QD-9 (continued)
Required deposit = ($40,000 x 0.627412) + ($50,000 x 0.311805) = $25,096.48 + $15,590.25
= $40,686.73
QD-10 All of the factors have two things in common: a 14% interest rate, and 16 periods (cash flows). If the factors given have the same number of time periods and/or cash flows for the same interest rate, the table value classification can be determined without using the table. The number given for e. is the only table value given less than 1. It must therefore be the present value of 1. The reciprocal of the present value of 1 is the future value of 1. Therefore, a. is the future value of 1 (1 á 0.122892 = 8.137249). Of the answers remaining, b. c. and d., the largest is the future value of an ordinary annuity of 1 and the smallest is the present value of an ordinary annuity of 1, again assuming the same number of cash flows and same interest rate. The present value of an annuity due is d. because it is equal to the present value of an ordinary annuity of one less period with 1 added to the factor.
Table Value Classification a. 8.137249 Future value of 1
b. 50.980352 Future value of an ordinary annuity of 1 c. 6.265060 Present value of an ordinary annuity of 1 d. 7.142168 Present value of an annuity due of 1 e. 0.122892 Present value of 1
QD-11 There are two approaches to the determination of the converted factor for a deferred annuity:
1. Converted factor for present value of a deferred annuity of 1 = (Factor for present value of an ordinary annuity of n cash flows of 1) x (Factor for present value of 1 for period of deferment). The ultimate present value of the deferred annuity is determined by multiplying the above factor by the value of each cash flow.
2. Converted factor for present value of a deferred annuity of 1 = (Factor for present value of an ordinary annuity of n + k cash flows of 1) - (Factor for present value of an ordinary annuity of k rents of 1). The ultimate present value of the
deferred annuity is determined by multiplying the above factor by the value of each cash flow.
QD-12
$20,000 present value ¯
$ $ $ ____________*_____ _______*___________*
first second third installment installment installment
The correct table to use is the present value of an ordinary annuity of 1 table.
QD-12 (continued)
Table value:Pon 3,i 14% = 2.321632 Equal installments = $20,000 2.321632 QD-13
a. Invert the given value, or
4.411435 1
b. Square the given value, or (4.411435)2 c. Use the following equation:
0.16 1 value Given
or 0.16 1 4.411435
d. Use the following equation:
0.16
1 Given value 1
or
0.16
4.411435 1 1
e. Use the following equation:
0.16
1 value)
(Given 2
or 0.16 1 (4.411435)2
ANSWERS TO CASES
CD-1
Annual cost of the 1-year plan: $4,480.00 Annual cost of the 3-year plan:
) C(P
Pd dn 3,i 12%
$11,200 = C (2.690051)
$4,163.49 2.690051
$11,200 C
Annual cost of the 5-year plan:
) C(P
Pd dn 5,i 12%
CD-1 (continued)
$4,438.56 4.037349
$17,920 C
The 3-year plan is the least expensive plan given the 12% rate. The savings over the other two plans are computed as follows:
Yearly savings over the 1-year plan
$4,480.00 - $4,163.49 = $316.51 Yearly savings over the 5-year plan
$4,438.56 - $4,163.49 = $275.07 CD-2
Plan 1. Purchase the equipment
The present value of the purchase alternative equals the sum of the initial cash payment, less the present value of the resale value to be received in 5 years, computed as follows:
Initial cash payment $36,800.00
Present value of the resale value:
P of $5,500 for 5 years at 12%:
$5,500 x 0.567427 (3,120.85)
Total present value $33,679.15
Plan 2. Lease the equipment
The present value of leasing the equipment equals the present value of $9,100 per year for 5 years, discounted at 12%. Since the payments are made at the beginning of each year, this is an annuity due situation.
i) dn, d C(P P
)
$9,100(P
Pd dn 5,i 12%
= $9,100 (4.037349)
= $36,739.88*
*Note that when the equipment is leased, the resale value does not accrue to Taylor Company, hence it is not included in the present-value computation.
Solution: Taylor Company should purchase the equipment outright, since the purchase option has the lower present value. The cash saving is
$36,739.88 - $33,679.15 = $3,060.73
Note that this solution ignores other factors such as taxes and risk.
CD-3
1. If White takes the discount, it must pay $396,000. By not taking the discount, White can use the $396,000 for 10 days (assuming that White follows its usual policy of paying after 30 days). For waiting the extra 10 days, the company must pay an additional $4,000.
The effective annual interest cost is
$36.36%
0.3636 10days
360days
$396,000x
$4,000
The 36.36% rate is compared with the effective annual interest cost of borrowing the money from a bank to see if the discount should be taken. The effective annual interest cost of borrowing the funds is computed as shown in the following.
Since White has to keep a 15% compensating balance in the bank, $396,000 equals only 85% of the funds that must be borrowed, therefore,
$396,000 = 0.85 (borrowed amount)
0.85
$396,000 = borrowed amount
$465,882.35 = borrowed amount
The yearly interest charge on the borrowed amount is 14%, or $465,882.35 x 14% = $65,223.53
The effective rate, however, is higher than 14%. Of the amount borrowed ($465,882.35), only $396,000 is usable, due to the 15% compensating balance. This means that White is paying $65,223.53 for the use of $396,000. The effective annual interest cost is
$396,000
$65,223.53
= 0.1647 = 16.47%
Since this rate is lower than the rate for paying after 30 days and not taking the discount, the discount should be taken.
2. The effective annual interest cost of not taking the discount is lower in this case, since White could use the $396,000 for 40 days instead of just 10 days. The effective annual interest cost of waiting the entire 60-day period is
9.09%
0.0909 40days
360days
$396,000x
$4,000
Since this rate is lower than the effective rate of borrowing from the bank (16.47%) White should not take the discount, and pay at the end of the 60-day period.
CD-3 (continued)
3. It has become less desirable for White to borrow from the bank. By waiting one day, or 40 days past the discount period, White must pay $4,000 more than if the discount were taken. The longer White waits to pay, the lower the effective interest cost since White pays the same charge ($4,000), but gets a longer use of the $396,000. Increasing the amount of time funds are used, while keeping the interest charge constant, always lowers the effective interest cost.
CD-4
1. The amount of interest earned equals the future value minus the present value, computed as follows:
23.049803 (4.801021)
) (f
)
(fn 80,i 4% n 40,i 4%2 2 f = $1,500,000 (fn 80,i 4%) f = $1,500,000 (23.049803) f = $34,574,705
Future amount $34,574,705
Less: Present value (1,500,000)
Interest earned $33,074,705
2. If she had invested $10,000 a year instead:
i) on, o C(F F
16%) i 20, on
$10,000(F Fo
Fo= $10,000 (115.379747) Fo= $1,153,797.47
She would only have about 3% as much money, but would have avoided 20 years in prison.
CD-5
1. Either argument may be correct depending on the circumstances. If the note was given solely in exchange for cash, then the president is correct. However, the requirements of FASB Statement No. 57, "Related Party Disclosures," must be considered.
If the note was given in exchange for property, services, or cash and other
considerations, then the accountant is correct. The 4% rate charged by the bank is unrealistic, based on the 16% going rate. Discounting the note at 16% approximates the market value of the note.
CD-5 (continued)
2. Since the interest amount at 4% is compounded annually, the future value due in 5 years is:
f = $300,000 x 1.216653 = $364,995.90 Present value of note at January 1, 2004:
p = $364,995.90 pn 5,i 16%
= $364,995.90 x 0.476113 = $173,779.29
CD-6
Whether or not Perry would pay back the loan would depend on her reinvestment rate.
If she could earn more than 12% on some investment, then she would be earning more than the interest charge on the $5,000 she borrowed. In this case, she would be better off not paying back the principal amount.
On the other hand, if Perry could not earn 12% on some investment, she would be better off if she paid back the money, and avoided the interest charges on the $5,000 debt.
(This solution ignores the fact that, should Perry die, the policy proceeds to the beneficiary would be reduced by $5,000. It also ignores income taxes.)
ANSWERS TO MULTIPLE CHOICE
1. d 3. c 5. d 7. d 9. b
2. a 4. c 6. d 8. b 10. b
SOLUTIONS TO EXERCISES ED-1
1. f = $ 40,000 f n 7, i 12%
= $ 40,000 (2.210681) = $ 88,427.24
2. f = $ 10,000 f n 22, i 4%
= $ 10,000 (2.369919) = $ 23,699.19
3. The compound interest equals the total interest for the 5 years, therefore, Future Value - Present Value = Compound Interest
$6,000 f n 5, i 10% - $6,000 = Cl
$6,000 (1.610510) - $6,000 = CI $9,663.06 - $6,000 = CI $3,663.06 = CI ED-2
f = $ 20,000 f n 8, i 6%
= $ 20,000 (1.593848) = $ 31,876.96
ED-3
1. p = $ 30,000 p n 5, i 12%
= $ 30,000 (0.567427) = $ 17,022.81
ED-3 (continued)
2. p = $ 8,000 p n 18, i 4%
= $ 8,000 (0.493628) = $ 3,949.02
3. Compound Discount = Future Value - Present Value = $ 8,000 - [$8,000 p n 5, i 1 0 % ] = $ 8,000 - [$8,000 (0.620921)]
= $ 8,000 - $4,967.37 = $ 3,032.63
ED-4
1. F o $10,000(F o n 7, i 12% ) = $ 10,000 (10.089012) = $100,890.12
2. The future value determined in (1) accumulates interest for 1 more year ( d F )
F = $100,890.12 (1.12) = $112,996.93 d
or $10,000 (12.299693* - 1) = $112,996.93
* F o n 8, i 12%
ED-5
1. P = $ 8,000 ( o P o n 5, i 10% )
= $ 8,000 (3.790787)
= $ 30,326.30
2. P = $ 8,000 ( d P d n 5, i 10% )
= $ 8,000 (4.169865)
= $ 33,358.92 ED-6
10% ) i 6, o n (F o C F
$30,000 = C (7.715610)
7.715610
$30,000 C
= $3,888.22 ED-7
1. Since the $25,000 is invested one year before the first withdrawal, the calculation is based on the Po formula:
i ) o n, (P o C P
$25,000 = C (P o n 5, i 12% )
$25,000 = C (3.604776)
3.604776
$25,000 C
C = $6,935.24
ED-7 (continued)
2. Since the deposit is made on the date of the first withdrawal, the computation is based on the Pd formula:
12%
i 5, d n P d C P
$25,000 = C (4.037349)
4.037349
$25,000 C
C = $6,192.18
3. This is a deferred annuity, since the $25,000 investment accrues interest for 4 years before the withdrawals begin.
12%