Sharp El738 User Guide
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30 Procedure Key operation Display The number of compounding periods per year is automatically set to 12. Press s to exit the P/Y and C/Y settings. Enter the total number of payments.s 24 N 24~N 2400 Enter the future value.2995 x 10 . % TANS~FV 29950 Enter payment. , 145 u(-145)~PMT -14500 Enter the present value. 2995 v2995~PV 299500 Calculate the annual interest rate.@ fI/Y= 708 Answer: If you lease the computer system, the annual interest rate would be 7.08%, which is less than that of the interest rate on a two-year loan, so it would be more cost-effective to lease a computer system than to purchase one. Calculating the present value of a lease with trade-in value Your client wishes to buy a machine currently leased from your company. On a fi ve-year lease with payments of $200 at the beginning of each month, the machine has a trade-in value of $1,500 with 34 monthly payments remaining. If your company sells the machine at the present value of the lease, discounted at an annual interest rate of 18%, compounded monthly, how much should your company charge for the machine? N = 34...... PV = ? FV = –$1,500 I/Y = 18% PMT = –$200 3 JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
31 4 Procedure Key operation Display Set all the variables to default values.. b 000 Set to annuity due (BGN is displayed).. " 000 Set the number of pay- ments per year to 12.. w 12 QP/Y= 1200 The number of compounding periods per year is automatically set to 12. Press s to exit the P/Y and C/Y settings. Enter the total number of payments.s 34 N 34~N 3400 Enter payment. , 200 u(-2——)~PMT -20000 Enter the annual inter- est rate.18 f18~I/Y 1800 Enter the future value. , 1500 T(-15——)~FV -150000 Calculate the present value.@ vPV= 627995 Answer: $6,279.95 should be charged for the machine. Calculating down payment and amount to borrow You wish to buy a house for $180,000. The fi nance company charges a 5.5% APR, compounded monthly, on a 25-year loan. If you can afford a monthly payment of $900, how much can you borrow? How much do you need for a down payment? N = 12 × 25 years = 300...... I/Y = 5.5% PV = ? FV = 0 PMT = –$900 JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
32
Procedure Key operation Display
Set all the variables to
default values..
b
000
Make sure ordinary annuity is set (BGN is not displayed).
Set the number of pay-
ments per year to 12..
w 12
Q
P/Y=
1200
The number of compounding periods per year is automatically set to 12.
Press
s to exit the P/Y and C/Y settings.
Enter the total number
of payments.s 25
.
<
N
ANS~N
30000
Enter payment.
, 900
u(-9——)~PMT
-90000
Enter the annual inter-
est rate.5.5
f5.5~I/Y
550
Set the future value to
zero. 0
T—~FV
000
Calculate the present
value.@
vPV=
14655892
Calculate the down
payment.s 180000
-
f
v
=18————-PV=
3344108
Answer: You can borrow $146,558.92 in total. The price of the
house is $180,000, so:
Down payment = $180,000 – present value
= $180,000 – $146,558.92
You need $33,441.08 for a down payment.
JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
33 AMRT P1= 100 Amortization Calculations Calculate and create amortization schedules using values stored in the TVM solver. Note: Prior to using amortization, you need to enter values into TVM variables. Variables used in amortization Variable Description Default value AMRT P1 Start of payment (nth time) 1 AMRT P2 End of payment (nth time) 1 BALANCE Remaining balance after payment — ΣPRINCIPAL Principal paid — ΣINTEREST Interest paid over the specifi ed periods — • BALANCE, ΣPRINCIPAL and ΣINTEREST are calculated automatically, so no default values are set. • AMRT P1 and AMRT P2 must be between 1 and 9,999. Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. • All the TVM solver variables retain their previously entered values. If you wish to clear all the data, press . b. 2. Select ordinary annuity or annuity due using . ". 3. Enter the appropriate numeric values for the variables used in the TVM solver. • Confi rm the values of N, I/Y, PV, PMT, FV, P/Y and C/Y. 4. Press * to use amortiza- tion calculation. 5. Enter a value for “AMRT P1” and press Q. 6. Press i, enter a value for “AMRT P2” and press Q. 7. Display values for BALANCE, ΣPRINCIPAL and ΣINTEREST by pressing i once for each. Each value is calculated automatically. JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
34 8. Press i to calculate the next period of the amortization schedule. 9. Repeat steps 5 to 7 above. • If you press @ during “AMRT P1” and “AMRT P2” entry, the values for the next period of payment will be automatically calculated and displayed. • To end amortization calculations, press s. Pressing s during entry will clear the value entered. Calculating mortgage payments and generat- ing an amortization schedule 1. Calculate the monthly payment of a 20-year loan with a loan amount of $90,000 and a 5.45% APR. Procedure Key operation Display Set all the variables to default values.. b 000 Make sure ordinary annuity is set (BGN is not displayed). Set TVM solver vari- ables and calculate payment.. w 12 Q s 20 . < N 90000 v 0 T 5.45 f @ u PMT= -61656 Answer: The monthly payment is $616.56. Now generate an amortization schedule for the fi rst 5 years of the loan. If the fi rst payment is in August, the fi rst year has 5 payment periods and the following years have 12 payment periods each. 2. Calculate the amortization schedule for the fi rst year. Procedure Key operation Display Change to amortization calculation and enter 1 (August) for the starting payment.* 1 Q AMRT P1= 100 Enter 5 (December) for the ending payment.i 5 QAMRT P2= 500 Display the remaining balance.iBALANCE= 8895148 1 JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
35 Procedure Key operation Display Display the principal paid.i ÍPRINCIPAL= -104852 Display the interest paid.iÍINTEREST= -203428 3. Calculate the amortization schedule for the second year. Procedure Key operation Display Change amortization schedule to the second year and enter 6 (Janu- ary) for the starting payment.i 6 Q AMRT P1= 600 Enter 17 (December) for the ending payment.i 17 QAMRT P2= 1700 Display the remaining balance.iBALANCE= 8633592 Display the principal paid.iÍPRINCIPAL= -261556 Display the interest paid.iÍINTEREST= -478316 4. Calculate the amortization schedule for the third year. Procedure Key operation Display Change amortization schedule to the third year and enter the next 12 months automati- cally.i @ i AMRT P2= 2900 Display the remaining balance.iBALANCE= 8357421 Display the principal paid.iÍPRINCIPAL= -276171 Display the interest paid.iÍINTEREST= -463701 5. Repeat the above operation for the fourth and fi fth years. JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
36 Calculating payments, interest, and loan bal- ance after a specifi ed payment You have taken out a 30-year loan for $500,000, with an annual interest rate of 8.5%. If, after the 48th period, you want a balloon payment due, what amount of monthly payment must you make with monthly compounding and how much will the balloon pay- ment be? Procedure Key operation Display Set all the variables to default values.s . b 000 Make sure ordinary annuity is set (BGN is not displayed). Set TVM solver vari- ables and calculate payment.. w 12 Q s 30 . < N 500000 v 0 T 8.5 f @ u PMT= -384457 Answer: The monthly payment is $3,844.57. Now generate an amortization schedule from the fi rst to the 48th payments. Procedure Key operation Display Change to amortization calculation and enter 1 for the starting payment.* 1 Q AMRT P1= 100 Enter 48 (December) for the ending payment.i 48 QAMRT P2= 4800 Display the balance af- ter 48 months. (balloon payment)iBALANCE= 48275524 Display the principal paid over 48 months.iÍPRINCIPAL= -1724476 Display the interest paid over 48 months.iÍINTEREST= -16729460 Answer: The balloon payment after the 48th period would be $482,755.24. 2 JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
37 Discounted Cash Flow Analysis Analyze unequal cash fl ows and calculate the net present value (NPV) and the internal rate of return (IRR). Note: Use the TVM solver for equal and regular cash fl ow analysis (see page 22). Entering cash fl ow data To fi nd NPV and IRR using discounted cash fl ow analysis, enter cash fl ow data, one data item at a time, in the following format: Single cash fl ows Cash fl ow value J Repeated cash fl ows Cash fl ow value > frequency value J Notes: • Before entering data, press > . b to clear any previously entered cash fl ow data. • Press , to enter a negative cash fl ow (outfl ow). • Make sure the calculator is in NORMAL mode. It is not pos- sible to enter cash fl ow data when listed fi nancial variables are shown on the display. Press s to exit. • You can enter a total of up to 100 cash fl ow and/or statistical data items. A single cash fl ow value is counted as one data item, while a cash fl ow value with an associated frequency value is counted as two. • Frequency values must be integers between 1 and 999. • If you wish to correct a value before pressing J, press s to delete the entry and enter the correct value. Entering cash fl ow data Enter cash fl ow data according to the following cash fl ow dia- gram. –$25,000$7,000 $9,000 $5,000 $5,000 $8,000 JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
38 Procedure Key operation Display Bring up the initial dis- play in NORMAL mode.s 000 Enter cash fl ow data. , 25000 JDATA SET:CF 000 7000 JDATA SET:CF 100 9000 JDATA SET:CF 200 5000 > 2 JDATA SET:CF 300 8000 JDATA SET:CF 400 If there is cash fl ow data stored, press > . b to clear it. The format of the data set (cash fl ow and frequency values) number, which is initially set to “0.00,” is dependent on calcu- lator display notation settings. Confi rming and editing data Confi rming data Press > to display any previously entered cash fl ow data. The data is displayed in order by data item (identifi er, number, and value). Use z/ i to display a data item from a previously entered data set. CF D—= -2500000 Cash flow identifierData set number Cash flow value CF N—= 100 Frequency identifierData set number Frequency value *1 *1 *2 *2 JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.
39 • Press . z or . i to jump to the fi rst or the last data item, respectively. • Each data item is displayed in the form CF Dn= (cash fl ow value) or CF Nn= (frequency), where n indicates the data set number. Editing data • Display the data item you wish to modify by using z/ i, enter a new value and press J. • If a frequency value is set to zero, then the associated data set is deleted. Deleting data • Display the data item to be deleted by using z/ i, and press . ?. • If a cash fl ow value/frequency is deleted, the corresponding frequency/cash fl ow value is also deleted. • If you wish to delete all data, press . b. Inserting data Using the z and i keys, specify the correct place to insert your new data by displaying the value that is to come directly after, and then press . e. A new data set with a cash fl ow value of zero and a frequency value of one will be inserted. Modify the new data set to include your data. Correcting cash fl ow data Currently the cash fl ow data is that shown in chart A. Change it according to chart B. –$25,000 $7,000 $9,000 $5,000 $5,000$8,000 Chart A –$30,000 $7,000 $9,000 $6,000 $5,000$8,000 Chart B Procedure Key operation Display Display previously entered cash fl ow data. (Example on page 37)s > CF D—= -2500000 JOBODJBMVODUJPOT$VSSFOUJOEEJOBODJBMVODUJPOT$VSSFOUJOEE1.1.