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FINANCE.DOC
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1994-08-17
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15KB
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286 lines
Financial formulas:
Thi≤ men⌡ contain≤ financia∞ formulas¼ sucΦ a≤ Futurσ Value¼ Payments¼ ì
Presen⌠ Value¼ NPV¼ anΣ IRR.
Iε ordinar∙ annuities¼ thσ payment≤ occu≥ a⌠ thσ enΣ oµ eacΦ period« Iε ì
annuitie≤ due¼ thσ paymen⌠ occur≤ a⌠ thσ beginninτ oµ eacΦ period.
Withiε thesσ formulß wheneve≥ annuit∙ calculation≤ arσ made¼ the∙ arσ donσ s∩ ì
a≤ ordinar∙ annuities¼ no⌠ annuitie≤ due.
==============
| OPTION 1: |
==============
1) Future Value
Thi≤ selectioε calculate≤ thσ Futurσ Valuσ oµ aε ordinar∙ annuity« I⌠ ì
require≤ tha⌠ yo⌡ ente≥ thσ Payment¼ Rate¼ anΣ Period«
==============
ⁿ OPTIO╬ 2║ |
==============
2⌐ Payment:
Thi≤ selectioε calculate≤ ß Loaε paymen⌠ amount« Yo⌡ ente≥ Principle¼ Rate¼ ì
anΣ Period«
==============
ⁿ OPTIO╬ 3║ |
==============
3⌐ Presen⌠ Value║
Thi≤ selectioε calculate≤ thσ Presen⌠ Valuσ oµ aε ordinar∙ annuity« I⌠ ì
require≤ tha⌠ yo⌡ ente≥ thσ Payment¼ Rate¼ anΣ Period«
==============
ⁿ OPTIO╬ 4║ |
==============
4⌐ Conver⌠ AP╥ t∩ AER:
èThi≤ selectioε wil∞ conver⌠ aε Annua∞ Percentagσ o≥ Nomina∞ Interes⌠ Ratσ t∩ ì
aε Annua∞ Effectivσ Rate.
==============
ⁿ OPTIO╬ 5║ |
==============
5⌐ NPV║
Thi≤ selectioε assesse≤ Ne⌠ Presen⌠ Value« I⌠ request≤ thσ initia∞ casΦ ì
outflow¼ ß serie≤ oµ equa∞ casΦ inflows¼ ß fina∞ casΦ inflow¼ thσ period≤ iε ì
thσ project¼ anΣ ß hurdlσ rate¼ 'i'« Oncσ selected¼ optioε ╡ displays:
==========================================================================╜
|
Initia∞ casΦ outflow║ 0.0░ |
Valuσ oµ equa∞ casΦ inflows║ 0.0░
Fina∞ casΦ inflow║ 0.0░
Period≤ iε project║ ░
Hurdle rate, as a decimal: 0.0000 |
|
===========================================================================
/--------------------------\
| Note on |
| using Net Present Value |
\--------------------------/
AlthougΦ intendeΣ t∩ havσ ß specifiπ applicatioε iε solvinτ NP╓ questions¼ ì
thi≤ financia∞ mode∞ caε als∩ bσ useΣ fo≥ othe≥ purposes« Iµ yo⌡ leavσ ì
'Initia∞ casΦ outflowº blanδ whilσ filinτ iε thσ othe≥ fou≥ entries¼ theε i⌠ ì
wil∞ producσ aε accuratσ solutioε fo≥ ß Presen⌠ Valuσ Annuit∙ witΦ aε Endinτ ì
Balloon.
Onσ specifiπ examplσ i≤ iµ aε oi∞ compan∙ offer≤ t∩ bu∙ lanΣ froφ you« Let'≤ ì
sa∙ tha⌠ the∙ proposσ t∩ pa∙ 12░ monthl∙ payment≤ oµ $5,00░ witΦ ß ballooε ì
paymen⌠ oµ $150,00░ iε additioε t∩ thσ las⌠ payment¼ a⌠ aε annua∞ ratσ oµ ì
18%« Yo⌡ woulΣ firs⌠ conver⌠ 18Ñ t∩ thσ monthl∙ equivalen⌠ oµ (18/12⌐ o≥ ì
1.5¼ theε ente≥ tha⌠ a≤ ß decima∞ int∩ thi≤ model:
==========================================================================╜
Initial cash outflow: 0.00 <=== Leave blank |
|
Value of equal cash inflows: 5000.00
Final cash inflow: 150000.00 è
Periods in project: 120
Hurdle rate, as a decimal: 0.0150
Present value of Cash inflows [ordinary annuity]: 277,492
Present value of Final cash inflow: 25,128 |
Net Present Value: 302,621 |
===========================================================================
$302,621 is the Present Value for an ordinary annuity with an Ending Balloon.
==============
| OPTION 6: |
==============
6) IRR:
Thi≤ selectioε show≤ Interna∞ Ratσ oµ Return« I⌠ request≤ thσ initia∞ casΦ ì
outflow¼ ß serie≤ oµ equa∞ casΦ inflows¼ ß fina∞ casΦ inflow¼ thσ period≤ iε ì
thσ project¼ anΣ ß hurdlσ rate¼ 'i'« Oncσ selected¼ optioε ╢ requests:
===========================================================================
|
Initial cash outflow: 0.00 |
Value of equal cash inflows: 0.00
Final cash inflow: 0.00
Periods in project: 0
|
|
===========================================================================
==============
| OPTION 7: |
==============
7) Interest
Thi≤ selectioε find≤ thσ tota∞ interes⌠ paiΣ iε ß loan« I⌠ request≤ ì
Principle¼ Rate¼ anΣ Period«
è
==============
| OPTION 8: |
==============
8) Principle
Thi≤ selectioε determine≤ thσ Principlσ stil∞ oweΣ iε ß loan« I⌠ ask≤ fo≥ ì
Curren⌠ payment¼ Rate¼ PerioΣ oµ loan¼ anΣ numbe≥ oµ payment≤ alread∙ made«
==============
ⁿ OPTIO╬ 9║ |
==============
9⌐ Leasσ
Thi≤ optioε compute≤ ß leasσ payment« I⌠ request≤ thσ cos⌠ oµ thσ asse⌠ o≥ ì
valuσ (PV⌐ ¼ interes⌠ rate¼ perioΣ oµ loan¼ anΣ residua∞ value¼ iµ any« ì
Interes⌠ ratσ i≤ expresseΣ a≤ ß decima∞ pe≥ paymen⌠ period«
/--------------------------▄
| Verify output |
| with Net Present Value |
\--------------------------/
T∩ verif∙ thσ outpu⌠ froφ thi≤ option¼ takσ thσ leasσ paymen⌠ i⌠ calculate≤ ì
anΣ placσ i⌠ int∩ optioε 5¼ NPV¼ alonτ witΦ thosσ component≤ froφ optioε ì
ninσ tha⌠ resulteΣ iε i⌠ creatinτ thσ leasσ payment«
Iε selectioε 5¼ thσ leasσ paymen⌠ i≤ thσ missinτ portioε that¼ oncσ entered¼ ì
wil∞ creatσ aε NP╓ oµ zero.
Let'≤ sa∙ tha⌠ yo⌡ wisΦ t∩ leasσ ß machinσ witΦ ß curren⌠ marke⌠ valuσ oµ ì
$130,00░ fo≥ threσ years« A⌠ thσ enΣ oµ thi≤ time¼ thσ machine'≤ marke⌠ ì
valuσ shoulΣ bσ $90,000« T∩ earε aε annua∞ returε ratσ oµ 24Ñ compoundeΣ ì
monthly¼ wha⌠ shoulΣ bσ thσ monthl∙ payment┐
First¼ conver⌠ thσ percentagσ t∩ thσ monthl∙ equivalent¼ o≥ %▓ (2┤ » 12)¼ ì
theε ente≥ thσ followinτ value≤ int∩ optioε 9:
==========================================================================╜
|
Cost of asset: 130000.00 |
Rate, as a decimal: 0.0200
è Period of loan: 36
Residual value, if any: 90000.00
Lease payment [ordinary annuity]: 3,369.31 |
|
===========================================================================
Observσ tha⌠ i⌠ calculate≤ thσ leasσ paymen⌠ oµ 3,369.3▒ afte≥ yo⌡ havσ ì
entereΣ thσ othe≥ values.
Oncσ completed¼ g∩ t∩ optioε ╡ anΣ inser⌠ thesσ values║
==========================================================================╜
|
Initial cash outflow: 130000.00 |
Value of equal cash inflows: 3369.31
Final cash inflow: 90000.00
Periods in project: 36
Hurdle rate, as a decimal: 0.0200
Present value of Cash inflows [ordinary annuity]: 85,880
Present value of Final cash inflow: 44,120
Net Present Value: -0 |
|
===========================================================================
Thσ Ne⌠ Presen⌠ Valuσ oµ '0º verifie≤ thσ accurac∙ oµ it≤ input.
==============
ⁿ OPTIO╬ A║ |
==============
A⌐ Days
This option finds the number of days between any two dates.
è ==============
ⁿ OPTIO╬ B║ |
==============
B⌐ Rate of Return, no dividends or coupon.
This selection assesses Rate of Return with a zero coupon or payment.
It requests the initial purchase price, the selling price, and
the periods in the project.