ألأقتصاد الهندسى[Engineering economics] by osama mohammed elmardi suleiman khayal

1. Engineering Economic Analysis
Author: Assistant Professor Osama Mohammed Elmardi Suleiman
Khayal
Mechanical Engineering Department
Faculty of Engineering and Technology
Nile Valley University
Atbara, Sudan
‫أ‬‫إل‬‫انُٓذصى‬ ‫قتصاد‬Engineering Economy
‫انًقرر‬ ‫أْذاف‬
-‫إٌّٙذط‬ ‫ِّٙح‬ ٚ ‫إٌّٙذط‬ ٚ ٗ‫إٌٙذع‬ ‫ذؼشيف‬
-ٗ‫اإلٔراظي‬ ٚ ‫اإلٔراض‬ ٚ ‫اإللرظاد‬ ٍُ‫ػ‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-ٗ‫أ٘ذاف‬ ‫ذؽذيذ‬ ٚ ٝ‫إٌٙذع‬ ‫اإللرظاد‬ ‫ذؼشيف‬
-‫اٌّشىالخ‬ ً‫ؼ‬ ٗ‫ِٕٙعي‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-‫اٌغٛق‬ ْ‫ذٛاص‬ ٚ ‫اٌؼشع‬ ٚ ‫اٌطٍة‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-ٌ‫ا‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬‫اٌرؼادي‬ ‫ٔمطح‬ ٚ ‫أٔٛاػٙا‬ ٚ ‫رىاٌيف‬
-ٗ‫إٌمذي‬ ‫اٌرذفماخ‬ ‫أٔٛاع‬ ٚ ‫ٌٍٕمٛد‬ ٗ‫اٌضِٕي‬ ّٗ‫اٌمي‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-‫اٌمشٚع‬ ‫ذغذيذ‬ ٚ ‫اٌرىافؤ‬ ‫ِثذأ‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-‫ٚاؼذ‬ ‫ٌّششٚع‬ ُ‫اٌرميي‬ ‫أظشاء‬
-‫اٌخياساخ‬ ‫ِماسٔح‬ ‫ؽشق‬ ‫إظشاء‬
-‫اإل٘الن‬ ٚ ُ‫اٌرؼخ‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-‫اإلؼالي‬ ً‫ذؽٍي‬ ‫إظشاء‬
‫األٔل‬ ‫انثاب‬ ‫أْذاف‬
-‫ذؼشي‬‫إٌّٙذط‬ ‫ِّٙح‬ ٚ ‫إٌّٙذط‬ ٚ ٗ‫إٌٙذع‬ ‫ف‬
-ٗ‫اإلٔراظي‬ ٚ ‫اإلٔراض‬ ٚ ‫اإللرظاد‬ ٍُ‫ػ‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-ٗ‫أ٘ذاف‬ ‫ذؽذيذ‬ ٚ ٝ‫إٌٙذع‬ ‫اإللرظاد‬ ‫ذؼشيف‬
-‫اٌّشىالخ‬ ً‫ؼ‬ ٗ‫ِٕٙعي‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
ّ‫يقذي‬ : ‫األٔل‬ ‫انثاب‬
-ٗ‫إٌٙذع‬-‫إٌّٙذط‬ ‫ِّٙح‬-‫إٌّٙذط‬
-ٓ‫ظأثي‬ ٍٝ‫ػ‬ ‫اٌّششٚع‬ ‫يؼرّذ‬-‫التذ‬ ُ‫اٌرظّي‬ ‫ِغ‬
-‫اإل‬ ٍُ‫ػ‬‫لرظاد‬-ٗ‫اإللرظادي‬ ٍٗ‫اٌّشى‬
-ٖ‫إٌذس‬
-)ٍٗ‫اٌثذي‬ ٗ‫اٌفشط‬ ‫(ذىٍفح‬ ٗ‫اٌرؼؽي‬ ٚ ‫اإلخرياس‬
-ٗ‫اإللرظادي‬ ٍٗ‫اٌّشى‬ ْ‫أسوا‬
-‫اإلٔراض‬-‫اإلٔراض‬ ًِ‫ػٛا‬
-ٗ‫اإللرظادي‬ ّٗ‫األٔظ‬
-ٗ‫اإلٔراظي‬-ٗ‫اإلٔراظي‬ ‫ِماييظ‬
-ٝ‫اٌعضة‬ ‫اإللرظاد‬-ٍٝ‫اٌى‬ ‫اإللرظاد‬
-ٝ‫إٌٙذع‬ ‫اإللرظاد‬-ٌٕٙ‫ا‬ ‫اإللرظاد‬ ِٓ ‫اٌٙذف‬ٝ‫ذع‬

2. -‫اٌّؽرٛياخ‬
-‫اٌّشىالخ‬ ً‫ؼ‬ ‫ِٕٙعيح‬
-ٌٗ‫ؼا‬ ‫دساعح‬‫ٚاظة‬1
ّ‫انُٓذص‬Engineering
‫أستاغ‬ ‫ذؽميك‬ ٚ ٕٗ‫ِّى‬ ٗ‫ذىٍف‬ ً‫تال‬ ٚ ٓ‫يّى‬ ‫ِا‬ ‫تاتغؾ‬ ‫اٌّعرّغ‬ ‫ِشىالخ‬ ً‫ٌؽ‬ ‫اٌّؼاسف‬ ٚ ٍَٛ‫اٌؼ‬ ‫ذطثيك‬
ٚ‫إ‬ٜ‫اٌز‬ ٚ ً‫تذاة‬ ‫ػذج‬ ٓ‫تي‬ ‫اٌمشاس‬ ‫ذخار‬‫يرؤشش‬‫ا‬ ٚ ٕٝ‫اٌف‬ ‫اٌعأة‬ ٗ‫في‬‫إل‬ٜ‫لرظاد‬
‫انًُٓذس‬ ‫يًٓح‬
‫اػّاس‬‫ا‬ٜ‫اٌثشش‬ ‫اٌّعرّغ‬ ‫ٚسفا٘يح‬ ‫ساؼح‬ ٚ ‫ألسع‬
‫انًُٓذس‬
‫ا‬ ٚ ‫اٌرّٕٛيح‬ ‫اٌؼٍّيح‬ ٝ‫ف‬ ‫اٌشِػ‬ ‫سأط‬ ٛ٘‫إل‬ٗ‫لرظادي‬
ّ‫انًذَي‬ ّ‫انُٓذص‬
‫إٌٙذعح‬ ‫ذخظظاخ‬ ً‫و‬ ٓ‫تي‬ ‫اٌّشرشن‬ ُ‫اٌماع‬
ٍ‫خُاحي‬ ‫ػهى‬ ‫تؼتًذ‬ ّ‫انُٓذص‬ ‫انًشاريغ‬
1.ٗ‫اٌفٕي‬ ٜٚ‫اٌعذ‬
2.ٗ‫اإللرظادي‬ ٜٚ‫اٌعذ‬
ٚ ُ‫اٌرظاِي‬ ‫ٚػغ‬ ‫إٌّٙذط‬ ٍٝ‫ػ‬ُ‫اٌرظّي‬ ‫ذٕفيز‬ ‫ذىٍفح‬ ‫ِؼشفح‬ ِٓ ‫فالتذ‬ ‫فمؾ‬ ُ‫اٌرظّي‬ ٍٝ‫ػ‬ ‫يمرظش‬ ‫ال‬
ٝ‫أألذ‬ ٍٝ‫ػ‬ ‫ٔرفك‬ ْ‫أ‬ ‫التذ‬
ً‫ِشاو‬ ‫ؼالي‬ ‫إٌّٙذط‬
ٗ‫ذمٕي‬ ‫خياساخ‬ ِٓ ُ‫اٌرظّي‬ ْٛ‫يرى‬ ْ ‫أ‬ ‫التذ‬
ٗ‫اٌرىٍف‬ ًِ‫ػا‬ ً‫يذخ‬ ً‫األِص‬ ‫اٌخياس‬ ‫الخرياس‬
‫اإلقتصاد‬ ‫ػهى‬ ‫تؼريف‬
)‫أأليى‬ ‫(ثرٔج‬ ‫صًيث‬ ‫آدو‬‫ِغ‬ ٚ ‫ؽثيؼح‬ ٝ‫ف‬ ‫يثؽس‬ ٜ‫اٌز‬ ٍُ‫اٌؼ‬ُِ‫األ‬ ‫ششاء‬ ‫ثثاخ‬
ّ‫انرفاْي‬ ‫(إقتصاد‬ ٕ‫تيد‬‫ٌشفغ‬ ٍٝ‫اٌى‬ ‫األٔراض‬ ‫صيادج‬ ،ٗ‫أأللرظادي‬ ٗ‫اٌشفا٘ي‬ ‫دساعح‬ )ٌ‫ا‬ٜٛ‫ّغر‬
ٌ‫ا‬ْ‫ٌٍغىا‬ ٝ‫ّؼيش‬
‫يارشال‬ ‫انفرد‬ُٙ‫تثٍٛغ‬ ‫ذشذثؾ‬ ٝ‫ٚاٌر‬ ‫اإلظرّاػيح‬ ُٙ‫ٚذظشفاذ‬ ‫األفشاد‬ ‫ٚاخرياس‬ ‫دساعح‬
ٗ‫اٌّادي‬ ُٙ‫إلؼرياظاذ‬ ُ٘‫ٚاؼشاص‬

3. ٌٕ‫صايهض‬‫ت‬ ‫يخراس‬ ٝ‫اٌر‬ ‫اٌىيفيح‬ ‫دساعح‬‫تٙا‬ ِْٛ‫يغرخذ‬ ٝ‫اٌر‬ ٗ‫اٌطشيم‬ ‫اٌّعرّؼاخ‬ ٚ ‫األفشاد‬ ‫ٙا‬
‫اٌغٍغ‬ ٖ‫٘ز‬ ‫ذٛصيغ‬ ‫ٚويفيح‬ ِٓ‫اٌض‬ ٜ‫ِذ‬ ٍٝ‫ػ‬ ‫اٌغٍغ‬ ‫ِخرٍف‬ ‫إلٔراض‬ ٖ‫إٌادس‬ ‫اإلٔراظيح‬ ُ٘‫ِٛاسد‬
ً‫اٌّغرمث‬ ٚ ‫اٌؽاػش‬ ٝ‫ف‬ ‫األعرٙالن‬ ‫تغشع‬ ‫اٌّعرّغ‬ ٝ‫ف‬ ‫اٌعّاػاخ‬ ٚ ‫األفشاد‬ ‫ِخرٍف‬ ٍٝ‫ػ‬
‫اال‬ ٛ٘ٚ‫ٚيؽذد‬ ٗ‫األلرظادي‬ ٍٗ‫اٌّشى‬ ‫ػٕاطش‬ ‫يؽذد‬ ‫ٔغة‬ً‫ٌؽ‬ ‫اٌعّاػاخ‬ ٚ ‫األفشاد‬ ‫عٍٛن‬ ‫دساعح‬ ‫ٔٙط‬
ٍٗ‫اٌّشى‬ ٖ‫٘ز‬
ّ‫اإلقتصادي‬ ّ‫انًشكه‬ ‫طثيؼح‬
‫إؼرياظاخ‬ ‫ذٍثيح‬ ٍٝ‫ػ‬ ‫اٌّعرّغ‬ ‫لذسج‬ َ‫ػذ‬ ٗ‫اإللرظادي‬ ٍٗ‫اٌّشى‬ٚ ٖ‫ِٚرضايذ‬ ٖ‫ِؽذٚد‬ ‫اٌغيش‬ ٖ‫افشاد‬ِٖ‫رعذد‬
‫إٌذس‬ ‫تغة‬ ٍٗ‫ِرذاخ‬ ٚ)‫(ِؽذٚديرٙا‬ ‫اإلٔراظيح‬ ‫ٌٍّٛاسد‬ ٖٚٗ‫اإلٔراظي‬ ‫اٌّٛاسد‬ ‫وفايح‬ َ‫ػذ‬‫ذٛافمٙا‬ َ‫ػذ‬ ٚ‫أ‬
ٗ‫اإلٔغأي‬ ‫اٌؽاظاخ‬ ‫ِغ‬
‫ي‬ ‫ٚرٌه‬
‫اٌؽاظاخ‬ ‫ذؼذد‬
ٌّ‫ا‬ ‫ٔذسج‬ٛ‫اسد‬
‫ان‬ِ‫ُذر‬Scarcity
ٖ‫اٌّٛظٛد‬ ‫اٌّٛاسد‬ ِٓ ‫أوصش‬ ) ‫(اٌشغثاخ‬ ٖ‫ذشيذ‬ ‫ِا‬
‫اإل‬ّ‫انتضحي‬ ٔ ‫ختيار‬Choice and Sacrifice
‫اٌفشطح‬ ‫ذىٍفح‬ ‫ٚذؼرثش‬ ٜ‫أخش‬ ‫تغٍغ‬ ٗ‫اٌرؼؽي‬ ٚ‫أ‬ ‫اٌرٕاصي‬ ‫اٌغٍغ‬ ‫تؼغ‬ ٍٝ‫ػ‬ ‫اٌؽظٛي‬ ‫يرشذة‬ٍٗ‫اٌثذي‬
ّ‫انثذيه‬ ّ‫انفرص‬ ‫تكهفح‬Opportunity Cost
‫األَتاج‬ ‫ايكاَيح‬ ‫يُحُى‬Production Possibility Frontier

4. O
A
B
1
2
M
N
-‫األٔراض‬ ٓ‫يّى‬ ‫ال‬ ٕٝ‫إٌّؽ‬ ‫خاسض‬
-)‫ٌٍّٛاسد‬ ًِ‫وا‬ ٚ ً‫أِص‬ َ‫أعرخذا‬ َ‫(ػذ‬ ‫األٔراض‬ ٓ‫يّى‬ ٕٝ‫إٌّؽ‬ ً‫داخ‬
-‫األٔراض‬ ٓ‫يّى‬ ‫ال‬ ٖ‫إٌذس‬ٕٝ‫إٌّؽ‬ ‫خاسض‬
-ٍٝ‫ِص‬ ‫تطشيمح‬ ‫اٌّٛاسد‬ َ‫تؤعرخذا‬ ٕٝ‫إٌّؽ‬ ٍٝ‫ػ‬ ٗ‫ٔمط‬ ٜ‫أ‬ ‫اإلخرياس‬M, N
-ًٍّ‫و‬ ٚ ً‫أِص‬ ‫إٔراض‬ ٕٝ‫إٌّؽ‬ ٍٝ‫ػ‬M, N
‫ِصاي‬
‫ِثٍغ‬ ‫خظظد‬ ‫ِا‬ ٗ‫ششو‬10ٓ‫ٔٛػي‬ ‫ٕ٘اٌه‬ ٚ ‫غياس‬ ‫لطؼح‬ ‫ٌششاء‬ ٗ‫ظٕي‬x2ٗ‫ظٕي‬ٚy1ٗ‫ظٕي‬
1.‫ِا‬ ( ‫ِٛاسد٘ا‬ ‫أفاق‬ ٝ‫ف‬ ٗ‫اٌششو‬ ً‫ذمات‬ ٝ‫اٌر‬ ‫اٌخياساخ‬ ً‫و‬ ‫ٚػػ‬)‫اٌغياس‬ ‫لطؼح‬ ‫ٌششاء‬ ٗ‫خظظر‬
2.ٚ ‫اٌغياس‬ ‫لطغ‬ ٝ‫ٔٛػ‬ ‫ششاء‬ ٝ‫ف‬ ٗ‫اٌششو‬ ‫ِٛسد‬ ‫أفاق‬ ‫اِىأيح‬ ُ‫اسع‬ ‫اٌٛاػػ‬ ‫اٌؽش‬ ٜٚ‫اٌيذ‬ ُ‫تاٌشع‬
‫ٚػػ‬ ِٕٗ
‫أ‬.ٍٗ‫اٌثذي‬ ٗ‫اٌفشط‬ ‫ذىٍفح‬
‫ب‬.‫األخرياس‬
‫خ‬.ً‫األِص‬ ‫اٌّٛاسد‬ ‫ذخظيض‬
‫ز‬.ٖ‫إٌذس‬
X2ٗ‫ظٕي‬Y1ٗ‫ظٕي‬
010
18
26
34
42
50

5. O
1 2 3 4 5
10
8
6
4
2
Y
X
‫ِصاي‬
‫ِؽذٚدج‬ )‫(ِٛاسد‬ ‫أشثاع‬ ً‫عاة‬ ٚ ‫ذماتٍٙا‬ ٖ‫ِرعذد‬ ٚ ٖ‫ِؽذٚد‬ ‫غيش‬ ‫ؼاظاخ‬ ٝ٘ ٗ‫األلرظادي‬ ٍٗ‫اٌّشى‬ ‫ؽثيؼح‬
‫إعرغالي‬ ِٓ ٗ‫ذؽميم‬ ٓ‫يّى‬ ‫ِا‬ ٝ‫ألظ‬ ‫ٔؽمك‬ ْ‫أ‬ ‫يعة‬ ٓ‫ٌٚى‬ ‫ذّاِا‬ ٍٗ‫اٌّشى‬ ٖ‫٘ز‬ ٍٝ‫ػ‬ ‫اٌرغٍة‬ ٓ‫يّى‬ ‫ال‬ ٚ
ٝ‫اآلذ‬ ‫ٚػػ‬ ‫اإلٔراض‬ ٗ‫اِىأي‬ ٕٝ‫ِٕؽ‬ ‫ِغرخذِا‬ ‫ٌٍّٛاسد‬
1.ٖ‫إٌذس‬
2.‫ذىٍفح‬ٍٗ‫اٌثذي‬ ٗ‫اٌفشط‬
3.‫األخرياس‬
4.‫ٌٍّٛاسد‬ ً‫األِص‬ َ‫األعرخذا‬
‫اإلصتٓالك‬
‫اال‬ٗ‫اٌعّاػي‬ ٚ ٗ‫اٌفشدي‬ ‫اٌشغثاخ‬ ‫الشثاع‬ ٖ‫اٌعذيذ‬ ‫طٛسذٙا‬ ٝ‫ف‬ ‫اٌغٍغ‬ ٚ ‫ٌّٛاسد‬ ‫اٌّثاشش‬ َ‫عرخذا‬
‫انتثادل‬
)‫اعرٙالن‬ ٚ‫أ‬ ‫أراض‬ ‫(ٚؼذاخ‬ ‫اٌمشاساخ‬ ‫الذخار‬ ‫اٌٛؼذاخ‬ ٓ‫تي‬ ‫اٌّٛاسد‬ ‫أرماي‬
ّ‫األقتصادي‬ ‫انًشكهح‬ ٌ‫أركا‬
‫َُتح‬ ‫يارا‬What to produceّٝ‫و‬ ٚ ٝ‫ٔٛػ‬ ‫ذؽذيذ‬ ، ٖ‫ِؽذٚد‬ ‫ِٛاسد‬
‫َُتح‬ ‫كيف‬How to produce‫ِّىٕح‬ ٗ‫ذىٍف‬ ً‫تؤل‬ ‫ٌإلٔراض‬ ٕٝ‫اٌف‬ ‫األعٍٛب‬ ‫اخرياس‬
‫َُتح‬ ًٍ‫ن‬To whom to produce‫اٌؽ‬ ‫ؼغة‬ ٜٚ‫تاٌرغا‬ ‫اإلٔراض‬ ‫ذٛصيغ‬‫ا‬‫تاٌّعٙٛد‬ ٗ‫ظ‬

6. ‫اإلَتاج‬Production
‫ِٕفؼ‬ ‫خٍك‬ ٌٝ‫ا‬ ٜ‫يؤد‬ ‫ٔشاؽ‬ ٜ‫أ‬‫ػثش‬ ‫فيٙا‬ ٖ‫اٌضياد‬ ٚ‫أ‬ ٖ‫ظذيذ‬ ‫ح‬
‫ِالتظ‬ ‫غضي‬ ٓ‫لط‬ ‫ِٕفؼح‬ ‫ٌألوصش‬ ً‫اٌشى‬ ‫ذغييش‬
ٓ‫ذخضي‬ ‫صِأيا‬ ‫اٌغٍؼح‬ ً‫ٔم‬
‫ذعاس‬ ٓ‫ٌٍشاغثي‬ ‫اٌغٍؼح‬ ‫إذاؼح‬
‫اإلَتاج‬ ‫ػٕايم‬Production Factors
‫أألرض‬Landٗ‫اٌطثيؼي‬ ‫اٌّٛاسد‬
‫انؼًم‬Labor‫أظش‬ ً‫ِمات‬ ‫ٌألٔراض‬ ٝٔ‫اإلٔغا‬ ‫اٌّعٙٛد‬
‫انًال‬ ‫رأس‬Capital
‫أ‬‫إل‬‫دار‬ِ‫ٔانُظاو‬Management and Organizing
)‫ٚأػشاف‬ ‫ٚذماٌيذ‬ ٓ‫(لٛأي‬ ٜ‫اإللرظاد‬ َ‫إٌظا‬ ً‫شى‬ ‫األلرظاديح‬ ٍٗ‫اٌّشى‬ ً‫ؼ‬‫اٌّؽذٚدج‬ ‫اٌّٛاسد‬ ُ‫ٌرٕظي‬
‫األ٘ذاف‬ ‫ٌرؽميك‬
ّ‫أإلقتصادي‬ ًّ‫أألَظ‬Economic Systems
‫اٌثاد‬ ‫ِعّٛػح‬ ٜ‫اإللرظاد‬ َ‫إٌظا‬‫أفشا‬ ٓ‫تي‬ ‫اإللرظاديح‬ ‫اٌؼاللاخ‬ ُ‫ذٕظ‬ ٝ‫اٌر‬ ‫ا‬ُ‫ذؽى‬ ٝ‫ٚاٌر‬ ‫اٌّعرّغ‬ ‫د‬
ٜ‫اإللرظاد‬ ‫إٌشاؽ‬ ‫ِّاسعح‬ ٝ‫ف‬ ُٙ‫عٍٛو‬
‫تكُكٓاو‬ ‫األيريكى‬‫اإل‬ َ‫ػا‬ ٜ‫سا‬ ‫ذماٌيذ‬ ‫(ذششيغ‬ ‫اإللرظاديح‬ ‫اٌؼٍّياخ‬ ٍٝ‫ػ‬ ‫اٌغيطشج‬ ً‫ٚعاة‬ ‫ِعّٛػح‬‫لٕاع‬
)‫اٌشػايح‬
‫انرأصًانى‬ ‫انُظاو‬Capitalism
ٝ‫اٌغٍؼ‬ ‫اإلٔراض‬ ‫ٚعيطشج‬ ‫اٌغٛق‬ ‫إلرظاد‬ ‫عيادج‬،ٗ‫خاط‬ ‫ٍِىيح‬-‫اٌغٛق‬ َ‫ٔظا‬-‫اٌشتػ‬ ‫دافغ‬-‫اٌؽشيح‬
ٗ‫اإللرظادي‬ٜ‫ِشوض‬ ‫غيش‬ ، ٜ‫اإللرظاد‬ ‫إٌشاؽ‬ ٝ‫ف‬ ٌٗٚ‫اٌذ‬ ً‫ذذخ‬ َ‫ػذ‬ ٚ
‫اإلشتراكى‬ ‫انُظاو‬Socialism
‫اٌرٛصيغ‬ ‫ٚػذاٌح‬ ‫اٌىفايح‬ ‫ٌرؽميك‬ ٜ‫اإللرظاد‬ ‫إٌشاؽ‬ ٝ‫ف‬ ‫اٌذٌٚح‬ ً‫ذذخ‬-‫يٛذٛتيا‬-‫ا‬ ‫اٌؼذاٌح‬‫إل‬‫ظرّاػيح‬
‫ظّاػيح‬ ‫ٍِىيح‬(‫ذؼاٚٔيح‬ ‫دٌٚح‬)-ٜ‫ِشوض‬ ‫ذخطيؾ‬–‫صيادج‬ ‫ِؼذي‬ ،‫(خطؾ‬ ِٝٛ‫اٌم‬ ‫اإللرظاد‬ ‫ذّٕيح‬
)ٝ‫طٕاػ‬ ٌٝ‫ا‬ ٝ‫(صساػ‬ ٗ‫٘يىٍي‬ ‫ذغييش‬ ، ‫اإلعرصّاس‬ ، ‫اإلٔراض‬ٗ‫اٌؼشٚسي‬ ‫اٌؽاظاخ‬ ‫إشثاع‬‫(عٍغ‬
)ٗ‫وّاٌي‬ ‫ال‬ ٗ‫ػشٚسي‬
‫األصاليى‬ ‫انُظاو‬Islamic
ٕٗ‫اٌغ‬ ٚ ْ‫اٌمشءآ‬ ِٓ ٗ‫ِٚثادة‬ َ‫األعال‬ ‫ألطٛي‬ ‫ٚفما‬

7. ٗ‫ِضدٚظ‬ ‫ٍِىيح‬ ‫ِثذأ‬-‫ف‬ ٗ‫إلرظادي‬ ٗ‫ؼشي‬‫ٔطاق‬ ٝ‫ِؽذٚد‬ٗ‫خٍمي‬ ٚ ٗ‫ِؼٕٛي‬ ُ‫لي‬ ، ‫(اٌؽذٚد‬–ٝ‫راذ‬ ‫ذؽذيذ‬
ٗ‫ذشتي‬–)ِٗ‫ػا‬ ‫ِظاٌػ‬ ٗ‫ؼّاي‬ ٚ ‫إششاف‬ ‫األِش‬ ٌٝٚ ‫إؼرىاس‬ ‫ستا‬ ‫ِٕغ‬ : ‫اٌششع‬ ‫لٛج‬ ٝ‫ِٛػٛػ‬ ‫ذؽذيذ‬-
ٗ‫اإلظرّاػي‬ ‫اٌؼذاٌح‬ٖٚ‫اٌصش‬ ‫(ذٛصيغ‬–ٗ‫اٌٍّىي‬ ‫أعاط‬ ًّ‫اٌؼ‬ : ٝ‫اإلظرّاػ‬ ْ‫اٌرٛاص‬ ‫ِثذأ‬ ، َ‫ػا‬ ًِ‫ذىا‬ ‫ِثذا‬
–‫اٌرثزيش‬ ٚ ‫إعشاف‬ ‫ِٕغ‬–‫صو‬‫طذلاخ‬ ٚ ‫اج‬
‫ا‬‫إل‬ّ‫َتاخي‬Productivity
‫ٌإلٔراض‬ ‫ِمياط‬–‫ت‬ ًّ‫اٌؼ‬ ‫إٔعاص‬‫ئ‬ً‫أِص‬ ِٓ‫ٚص‬ ‫ِٕاعثح‬ ‫ٚذىٍفح‬ ٌٗٛ‫ِمث‬ ‫تعٛدج‬ ‫اٌّٛاسد‬ َ‫عرخذا‬
‫ِماييغٙا‬
ِ‫انكفاء‬Efficiency‫اٌٙذف‬ ‫ذؽميك‬ ‫ِمياط‬
‫انفؼانيح‬Effectiveness‫ٌٍّٛاسد‬ ً‫األِص‬ َ‫اإلعرخذا‬
‫ا‬‫إل‬‫قتص‬‫ا‬‫اندزئى‬ ‫د‬Microeconomic
‫ي‬ٍٗ‫دخ‬ ‫ترٛصيغ‬ ‫اٌّغرٍٙه‬ َ‫ليا‬ ‫ٚأعظ‬ ‫اٌخذِاخ‬ ٚ ‫اٌغٍغ‬ ‫إٔراض‬ ‫ذسط‬
‫انكهى‬ ‫اإلقتصاد‬Macroeconomic
‫األعؼاس‬ ‫ٚإعرمشاس‬ ِٝٛ‫اٌم‬ ً‫اٌذخ‬ ٚ ً‫وى‬ ‫اٌّعرّغ‬ ً‫ِشاو‬ ٚ ٌٗ‫تاٌثطا‬ ُ‫يٙر‬
‫أ‬‫إل‬‫انُٓذصى‬ ‫قتصاد‬Engineering Economy
‫اٌّشاسيغ‬ ٚ ‫إٌّشآخ‬ ُ‫ٌرميي‬ ِٗ‫اٌّغرخذ‬ ‫أألعاٌية‬ ٚ ‫األعظ‬‫ؼيس‬ ِٓ ‫ِٕٙا‬ ‫االٔغة‬ ‫إخرياس‬ ٚ ٍٗ‫اٌثذي‬
‫فٕيا‬ ‫ظذٚذٙا‬ ‫تؼذ‬ ٗ‫اإللرظادي‬ ٜٚ‫اٌعذ‬
‫اٌرذفماخ‬ ٍٝ‫ػ‬ ‫ذؼرّذ‬ ٚ ‫ِماسٔرٙا‬ ٚ ٗ‫إٌٙذعي‬ ُ‫اٌرظّي‬ ‫خياساخ‬ ٍٝ‫ػ‬ ٜ‫اإللرظاد‬ ً‫اٌرؽٍي‬ ‫ذمٕياخ‬ ‫ذطثيك‬
ْٛ‫يى‬ ‫إٌّظشف‬ ٚ ‫اٌّىرغة‬ ‫اٌّاي‬ ‫ٚػٍيح‬ ‫اٌّؤعغاخ‬ ‫ٚص‬ ٜ‫األياد‬ ٓ‫تي‬ ‫اٌّاي‬ ‫ؼشوح‬ ٝ٘ ٚ ٗ‫إٌمذي‬
ٌٕ‫ا‬ ‫اٌرذفماخ‬ٗ‫مذي‬
‫أ‬ ٍ‫ي‬ ‫انٓذف‬‫إل‬‫انُٓذصى‬ ‫قتصاد‬Objectives of the Course
‫ِماسٔح‬ً‫ٚذؽٍي‬ٗ‫اٌرمٕي‬ ٜٚ‫اٌعذ‬ ‫راخ‬ ُ‫اٌرظّي‬ ‫خياساخ‬
ٜٚ‫اٌعذ‬ ‫دساعاخ‬ ‫إظشاء‬
‫انًحتٕياخ‬Contents
‫انطهة‬ ٔ ‫انؼرض‬Demand & Supply
ّ‫انتكهف‬ ‫إَٔاع‬Types of Costs

8. ‫نهُقٕد‬ ّ‫انزيُي‬ ًّ‫انقي‬Time Value of Money
‫ت‬‫ٔاحذ‬ ‫يشرٔع‬ ‫قييى‬Evaluation of one Project
‫انخياراخ‬ ‫يقارَح‬Comparison of Alternatives
‫انتضخى‬ ٔ ‫األْالك‬Depreciation & Inflation
‫اإلحالل‬ ٔ ‫أألصتثذال‬Replacement Analysis
‫انتأكذ‬ ‫ٔػذو‬ ِ‫انًخاطر‬Risk & Uncertainty
‫انًشكالخ‬ ‫حم‬ ‫يُٓديح‬Problem Solving Methodology
1.‫اٌّشىٍح‬ ‫ذؼشيف‬Problem Definition
2.ً‫اٌؽ‬ ‫ِٚرطٍثاخ‬ ٍٗ‫اٌّشى‬ ‫ؼذٚد‬ ‫ذؽذيذ‬Problem Boundaries
3.ً‫ٌٍؽ‬ ‫خياساخ‬ ‫الرشاغ‬Generating Alternatives
4.‫اٌخياساخ‬ ‫ِماسٔح‬Comparison of Alternatives
5.ً‫األفؼ‬ ‫اٌخياس‬ ‫اخرياس‬Choosing Best Alternative
6.‫اٌخياس‬ ‫ذطثيك‬Implementing Best Alternative
7.ٗ‫األعرشظاػي‬ ٗ‫اٌرغزي‬Feedback
ّ‫انغه‬ ‫تُاقص‬ ٌَٕ‫قا‬
:‫ششٚؽ‬
1.ٜ‫األخش‬ ‫شثاخ‬ ٚ ‫اإلٔراض‬ ِٓ ‫ٚاؼذ‬ ‫ػٕظش‬ ًّ‫يش‬ ‫ذغيش‬
2.‫اٌىيف‬ ٚ ُ‫اٌى‬ ِٓ ٍٗ‫ِرّاش‬ ٗ‫اٌّؼاف‬ ‫اٌٛؼذاخ‬ ْٛ‫ذى‬
3.‫شاتد‬ َ‫اٌّغرخذ‬ ٝ‫اإلٔراظ‬ ‫إٌّؾ‬
ٔ‫اإل‬ ‫ػٕاطش‬ ‫أؼذ‬ ِٓ ٗ‫ِرغاٚي‬ ٚ ٗ‫ِرراٌي‬ ‫ٚؼذاخ‬ ‫أػيفد‬ ‫أرا‬ : ‫يٕض‬ ٜٚ‫األخش‬ ‫اإلٔراض‬ ‫ػٕاطش‬ ِٓ ٗ‫شاتر‬ ‫وّيح‬ ٌٝ‫ا‬ ‫راض‬
‫اٌرٕالض‬ ٝ‫ف‬ ٍٗ‫اٌغ‬ ٖ‫٘ز‬ ٖ‫تؼذ‬ ‫ذثذأ‬ ٓ‫ِؼي‬ ‫ؼذ‬ ٌٝ‫ا‬ ‫اٌٛطٛي‬ ٝ‫ؼر‬ ‫ذرضايذ‬ ٍٗ‫اٌغ‬ ْ‫فئ‬
ٗ‫اٌرعشت‬ ُ‫سل‬‫األسع‬ ‫ِغاؼح‬‫اٌؼّاي‬ ‫ػذد‬ٍٝ‫اٌى‬ ‫اإلٔراض‬‫اإلٔراض‬ ‫ِرٛعؾ‬ٗ‫اٌؽذي‬ ٍٗ‫اٌغ‬
111888
212201012
313331113
414481215
51555117
61660105
7176393
818637.90
919606.7-3
10110555.5-5
: ٗ‫اٌؽذي‬8 – 0 = 8, 20 – 8 = 12, 33 – 20 = 13, 48 –

9. ّ‫دراصي‬ ّ‫حان‬Case Study
‫تّثٍغ‬ ٗ‫عىٕي‬ ‫شمك‬ ٗ‫استؼ‬ ٗ‫ت‬ ٕٝ‫ِث‬ ٜ‫اشرش‬ ‫أطذلاةه‬ ‫أؼذ‬100000ِٕٙ ‫دفؼد‬ ‫دٚالس‬‫ا‬10000‫دٚالس‬
‫ٌذفغ‬ ‫تٕه‬ ‫ِغ‬ ‫اذفاق‬ ٝ‫ف‬ ً‫دخ‬ ٚ ‫اٌخاص‬ ٌٗ‫ِا‬ ِٓ90000‫ِثٍغ‬ ‫يذفغ‬ ْ‫أ‬ ٍٝ‫ػ‬ ‫اإلذفاق‬ ‫يٕض‬ .‫دٚالس‬
10500‫ب‬ ‫ذمذس‬ ٗ‫عٕٛي‬ ٗٔ‫طيا‬ ٗ‫ذىٍف‬ ‫ٕ٘اٌه‬ ٚ ‫عٕٛيا‬ ‫دٚالس‬15000‫غيعاس‬ ُ‫ير‬ ْ‫أ‬ ٓ‫يّى‬ .‫دٚالس‬
‫ب‬ ‫اٌشمك‬360.ٖ‫ٚاؼذ‬ ٗ‫شم‬ ً‫ٌى‬ ‫اٌشٙش‬ ٝ‫ف‬ ‫دٚالس‬
ٝ‫اآلذ‬ ٓ‫ػ‬ ‫أظة‬ ُ‫ش‬ ٌٗ‫اٌؽا‬ ٖ‫٘ز‬ ‫ٔالش‬
1.٘‫؟‬ ٝ٘ ‫ِا‬ ٚ ‫؟‬ ٍٗ‫ِشى‬ ِٓ ‫طذيمه‬ ٝٔ‫يؼا‬ ً
2.ٗ‫شالش‬ ‫أروش‬ ‫اٌّشىٍٗ؟‬ ً‫ٌؽ‬ ‫اٌخياساخ‬ ٝ٘ ‫ِا‬
3.ٝ‫ف‬ ‫ٌٍخياساخ‬ ٗ‫األلرظادي‬ ‫إٌراةط‬ ‫لذس‬2
4.‫اٌخياساخ‬ ‫ٌّماسٔح‬ ٗ‫ؽشيم‬ ‫اخرياس‬
5.‫طذيمه‬ ‫ذٕظػ‬ ‫تّارا‬
‫انثاَى‬ ‫انثاب‬ ‫أْذاف‬
-‫تيّٕٙا‬ ٗ‫ٚاٌؼالل‬ ‫اٌؼشع‬ ٚ ‫اٌطٍة‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-‫اٌغ‬ ْ‫ذٛاص‬ ‫ِثذأ‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬‫األعؼاس‬ ‫ذؽذيذ‬ ٚ ‫ٛق‬
-‫اٌظٕاػاخ‬ َٛٙ‫ِف‬ ‫ذؽذيذ‬
-‫ٚاظة‬2
‫انطهة‬ ٔ ‫انؼرض‬ : ‫انثاَى‬ ‫انثاب‬
-‫اٌطٍة‬
-‫اٌؼشع‬
-‫اٌغٛق‬ ْ‫ذٛاص‬
-ٗ‫اٌظٕاػ‬ َٛٙ‫ِف‬
-‫ٚاظة‬2
‫ٔانطهة‬ ‫انؼرض‬Demand & Supply
‫اٌطٍة‬Demand‫ششاةٙا‬ ٝ‫ف‬ ْٛ‫اٌّغرٍٙى‬ ‫يشغة‬ ٝ‫اٌر‬ ‫اٌىّياخ‬ :
QD = f (P1, I, Ps , Ps , ……, Psn, H, M, ID)
P1ٗ‫اٌغٍؼ‬ ّٓ‫ش‬ :Iً‫اٌذخ‬ ‫ِرٛعؾ‬ :Psٍٗ‫اٌثذي‬ ‫اٌغٍغ‬ ‫ػذد‬ :Hْ‫اٌغىا‬ ُ‫ؼع‬ :M‫األرٚاق‬ :
‫ٚاٌرفؼيالخ‬IDً‫اٌذخ‬ ‫ذٛصيغ‬ :
) ٖ‫رس‬ ، ‫(لّػ‬ ، ) ٓ‫ت‬ ، ٜ‫(شا‬ ‫تؼؼٙا‬ ً‫ِؽ‬ ً‫ذؽ‬ ٍٗ‫تذي‬ ‫عٍغ‬
)ٓ‫تٕضي‬ ، ‫(ػشتاخ‬ ٜ‫أخش‬ ٗ‫عٍؼ‬ ٍٝ‫ػ‬ ٖ‫صياد‬ ‫اؼذا٘ا‬ ّٓ‫ش‬ ‫أخفاع‬ ‫ِؼا‬ َ‫ذغرخذ‬ ‫عٍغ‬ ٍّٗ‫ِى‬ ‫عٍغ‬

10. ‫ػاللح‬Q & Pّٓ‫اٌص‬ ‫إٔخفاع‬ ‫ِغ‬ ‫اٌّطٍٛتح‬ ‫اٌىّيح‬ ‫ذضيذ‬ ٜ‫األخش‬ ًِ‫اٌؼٛا‬ ‫شثاخ‬ ‫ِغ‬
Demanded Quantity
UnitPrice
‫اٌؼشع‬Supply‫إٔراظٙا‬ ٚ‫أ‬ ‫تيؼٙا‬ ٝ‫ف‬ ‫إٌّشآخ‬ ‫ذشغة‬ ٝ‫اٌر‬ ‫اٌىّياخ‬ :
Qs = f (O, T, P1, P2, ......, Pn, Pp , ….., Ppn)
O‫اٌٙذف‬ :T‫ذىٌٕٛٛظيا‬ :P1ٗ‫اٌغٍؼ‬ ّٓ‫ش‬ :P2, ......, Pnٜ‫أخش‬ ‫عٍغ‬ ْ‫أشّا‬ :Pp , ….., Ppn:
‫إٔراض‬ ًِ‫ػٛا‬ ‫خذِاخ‬ ْ‫اشّا‬
‫ػاللح‬Q & P‫ذ‬ ٜ‫األخش‬ ًِ‫اٌؼٛا‬ ‫شثاخ‬ ‫ِغ‬‫ٕمض‬ٌّ‫ا‬ ‫اٌىّيح‬ٗ‫ؼشٚػ‬ّٓ‫اٌص‬ ‫إٔخفاع‬ ‫ِغ‬
Supply Quantity
UnitPrice

11. UnitPrice
Demand & Supply Quantity
Surplus
Shortage
Equilibrium
D S
ٗ‫اٌّخرٍف‬ ‫اٌظٕاػاخ‬ َٛٙ‫ِف‬
1.‫ِاٌه‬Client (Owner)(Investor)
2.ّّْٛ‫ِظ‬Consultant (Advisors) ( Designers)
3.ٌِّْٛٛLenders ( Financiers)
4.ْٚ‫ِٕفز‬Executors (Contractors)
5.ْٚ‫ِٛسد‬Suppliers
6.ِْٛ‫ِغرخذ‬Users
‫ٔاخة‬‫ذخظظه‬ ‫ِعاي‬ ٝ‫ف‬ ‫اٌؼشع‬ ٚ ‫اٌطٍة‬ ٚ ‫إٌّرط‬ ‫أششغ‬ :
ٗ‫اٌّذٔي‬ ٗ‫إٌٙذع‬
ٗ‫اٌغٍؼ‬ٜ‫وثاس‬ ٚ ‫ؽشق‬ ، ‫عذٚد‬ ، ٝٔ‫ِثا‬ ، ‫ِٕشآخ‬ :
ٗ‫اعرشاسي‬ ‫ششواخ‬ : ‫اٌطٍة‬
‫ششواخ‬ َ‫ليا‬ : ‫اٌؼشع‬‫ِماٚالخ‬ ‫ِٕفزج‬
ٗ‫اٌىٙشتاةي‬ ٗ‫إٌٙذع‬
)ٗ‫اٌىرشٚٔي‬ ٚ ‫اذظاالخ‬ ٚ ٗ‫وٙشتاةي‬ ٖ‫(اظٙض‬ ٗ‫عٍؼ‬ٗ‫ؽال‬
ٗ‫ِغرخٍظ‬ ٗ‫ؽال‬ ، ‫اٌغٛق‬ ‫ؼغة‬ ٗ‫عٍؼ‬ : ‫ؽٍة‬
ٗ‫اٌّيىأيىي‬ ٗ‫إٌٙذع‬
)‫(اعثيشاخ‬ ٗ‫عٍؼ‬
‫أراض‬ ‫خؾ‬

12. ٗ‫ؽال‬
ٍ‫ِغرخ‬ ‫أرط‬ ‫خؾ‬ ‫اٌغٛق‬ ‫ؼغة‬ ٗ‫عٍؼ‬ : ‫اٌطٍة‬‫ِغرخٍض‬ ٗ‫ؽال‬ ‫ض‬
ٗ‫اٌىّياةي‬ ٗ‫إٌٙذع‬
ٗ‫اٌىّياةي‬ ‫اٌظٕاػاخ‬ ٗ‫عٍؼ‬
‫أراض‬ ‫خؾ‬ ‫ذظٕيغ‬ ‫ػٍّياخ‬
ٗ‫عٍؼ‬ ‫اٌطٍة‬
‫انثانث‬ ‫انثاب‬ ‫أْذاف‬
-‫اٌرىاٌيف‬ ‫أٔٛاع‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-‫اٌرؼادي‬ ‫ٔمطح‬ ‫ذؽذيذ‬
-ٓ‫آٌيري‬ ٓ‫تي‬ ٗٔ‫اٌّماس‬
: ‫انثانث‬ ‫انثاب‬‫انتكهفح‬Cost
-ٗ‫اٌرىٍف‬ ‫أٔٛاع‬
-‫اٌر‬ ‫ٔمطح‬‫ؼادي‬
-‫ٚاظة‬3
‫انتكهفح‬ ‫إَٔاع‬
ٖ‫اٌّثاشش‬ ‫اٌّٛاد‬Direct Material

13. ‫اٌثاششج‬ ‫اٌؼّاٌح‬Direct Labor)‫ِٕرعاخ‬ ٌٝ‫ا‬ َ‫اٌخا‬ ‫اٌّٛاد‬ ً‫(ذؽٛي‬ ‫اإلظٛس‬ :
ٖ‫ِثاشش‬ ‫اٌغيش‬ ‫اٌرىاٌيف‬Indirect Cost:Over Head Costٓ‫ذؤِي‬ :–‫ػشاةة‬-
‫ايعاس‬
‫اٌرىاٌيف‬ ‫ذظٕيف‬
‫ِث‬ ‫غيش‬ ٚ ٖ‫ِثاشش‬ ‫ذىاٌيف‬ٖ‫اشش‬Direct a& Indirect (Overhead) Costs
ٖ‫ِرغييش‬ ٚ ٗ‫شاتر‬ ‫ذىاٌيف‬Fixed & Variable Costsٖ‫ِرغييش‬ :Variable‫ِغ‬ ‫ذرغييش‬
ٗ‫شاتر‬ ‫األٔراض‬ ُ‫ؼع‬ ‫ذغييش‬Fixed‫األٔراض‬ ٍٝ‫ػ‬ ‫ذؼرّذ‬ ‫ال‬–‫إيعاس‬–‫إ٘الن‬
:‫أيؼا‬
‫ذاسيخيح‬ ‫ذىٍيف‬Historical Cost‫اٌمذيّح‬ ‫اٌذفاذش‬ ٝ‫ف‬ ‫ِغعٍح‬
‫اٌر‬ٗ‫اٌمياعي‬ ‫ىاٌيف‬Standard Cost‫ٌإلٔراض‬ ‫ذمذيشيح‬
‫اإلؼالي‬ ‫ذىاٌيف‬Replacement Cost
ٗ‫ؼذي‬ ‫ذىاٌيف‬Marginal Cost‫إػافيح‬ ٖ‫تٛؼذ‬ ‫اإلٔراض‬ ‫صيادج‬ ِٓ ٗ‫ٔاذع‬ ‫ذىاٌيف‬
‫اٌثذيٍح‬ ‫اٌفشص‬ ‫ذىاٌيف‬Opportunity Cost‫اٌّرخز‬ ‫تاٌمشاس‬ ‫اٌثذيٍح‬ ‫اٌفشطح‬ ْ‫فمذا‬ ‫ذىٍفح‬
‫غاسلح‬ ‫ذىاٌيف‬Sunk Costٗ‫دػاي‬-‫ذذسية‬–ٗ‫طؽي‬
‫ِؤظٍح‬ ‫ذىاٌيف‬Deferred Cost‫ِؼذاخ‬ ٚ‫أ‬ ‫إ٘الن‬
ٗ‫ت‬ ٗ‫اٌخاط‬ ‫اٌرىاٌيف‬ ‫أٔٛاع‬ ‫ؼذد‬ ُ‫ش‬ ‫ذخظظه‬ ‫ِعاي‬ ٝ‫ف‬ ‫ِششٚع‬ ‫أخراس‬ : ‫ٚاظة‬
‫انتؼادل‬ ‫َقطح‬Break Even Point
‫ٌّما‬‫س‬. ‫اٌرىاٌيف‬ ‫ٔاؼيح‬ ِٓ ً‫اٌثذاة‬ ‫ٔح‬
ٗ‫اٌىٍي‬ ‫اٌرىاٌيف‬ ٜٚ‫ذرغا‬ ‫ػٕذِا‬ ‫اٌرؼادي‬ ‫ٔمطح‬ ‫ذؽذز‬Total Cost TC‫اٌىٍيح‬ ‫اٌؼاةذاخ‬ ‫ِغ‬
Total Revenue TR
ٖ‫ٚاٌخغاس‬ ‫اٌشتػ‬ ٓ‫تي‬ ‫ِرؼادٌح‬ ٚ‫أ‬
TC = FC + VC (x) TR = R (x)
‫اٌرؼادي‬ ‫ٔمطح‬ ‫ػٕذ‬
TC (x) = TR (x)
R x = FC + VC (x)
(R - VC) x = FC
Q = x =( FC / (R - VC))
FC : Fixed Cost
VC : Variable Cost
R : Price / Unit
Q : x : Quantity

14. Revenue/Cost
TC
TR
TC
VC
FC
Profit
Loss
QB
Quantity
Q
Break Even Point
A cost structure for manufacturing
‫ِصاي‬(1)
‫اٌرى‬‫ا‬‫ٌيف‬ٝ٘ ٓ‫ِؼي‬ ‫ِٕرط‬ ‫الٔراض‬ ٕٗ‫ِاوي‬ ‫ٌرعٙيض‬ ٗ‫اٌّطٍٛت‬300‫اٌٛؼذج‬ ‫الٔراض‬ ‫اٌرىاٌيف‬ .ٗ‫ظٕي‬2.5ٗ‫ظٕي‬
ٚ ‫ٌٍّٛاد‬1‫ب‬ ٗ‫تيؼ‬ ُ‫ير‬ ‫إٌّرط‬ ْ‫وا‬ ‫ارا‬ .‫اٌّاويٕح‬ ً‫ٌرشغي‬ ٌٗ‫ٌٍؼّا‬ ٗ‫ظٕي‬5ُ‫ش‬ .‫اٌرؼادي‬ ‫ٔمطح‬ ‫أؼغة‬ .ٗ‫ظٕي‬
‫أراض‬ ُ‫ذ‬ ‫ارا‬ ‫اٌخغاسج‬ ٚ‫أ‬ ‫اٌشتػ‬ ‫أؼغة‬1000.‫ٚؼذج‬

15. Revenue/Cost
TC
TR
Profit
Loss
Quantity
Q
X
TR = TC
Rx = FC + VC(X) , 5 x . x , x = 300 / (5 – 2.5) = 200 Units
At x = 1000 Units: Profit or Loss = TR – TC
= 5 X 1000 – (300 + (3.5 X 1000) = 5000 –
+Ve: Profit , -Ve: Loss
‫اٌرؼادي‬ ‫ٔمطح‬ ً‫ٌرمٍي‬
‫داٌح‬ ً‫ِي‬ ‫صيادج‬TR‫صي‬ ٜ‫أ‬)ٖ‫فميش‬ ٗ‫(عياع‬ ‫اٌثيغ‬ ‫عؼش‬ ‫ادج‬
ٗ‫اٌصاتر‬ ‫اٌرىاٌيف‬ ‫ليّح‬ ً‫ذمٍي‬FC)ٗ‫(طؼٛت‬
ٖ‫ِرغيش‬ ‫ذىاٌيف‬ ‫داٌح‬ ً‫ِي‬ ً‫ذمٍي‬VC)ٌٗ‫ػّا‬ ٚ ‫ِٛاد‬ ‫(ذىاٌيف‬
‫ِصاي‬(2)
ٖ‫ِرغيش‬ ‫ذىٍفح‬$ 62 / hr‫اٌثيغ‬ ‫عؼش‬$ 85.56 / hrٕٗ‫اٌغ‬ ٝ‫ف‬160000 hr / yearٗ‫اٌصاتر‬ ‫اٌرىاٌيف‬
$ 2024000 /year‫اؼغة‬
1.‫اٌرؼا‬ ٗ‫ٔمط‬‫ٔغثرٙا‬ ٚ ‫دي‬
2.ٗ‫اٌصاتر‬ ‫اٌرىاٌيف‬ ‫خفؼد‬ ‫ارا‬ ‫اٌرؼادي‬ ‫ٔمطح‬ ٝ‫ف‬ ‫اٌرخفيغ‬ ٛ٘ ‫ِا‬ٖ‫اٌّرغيالس‬ ‫اٌرىاٌيف‬ ٚ‫أ‬
‫اٌثيغ‬ ‫عؼش‬ ‫صاد‬ ٚ‫أ‬
At Breakeven: TR = TC
Rx = FC + VC(x), x = FC / (R – VC) = 2024000/ (85.56 –
= 85908 hour / Year
x = 85908 / 160000 = 0.5 .

16. 10 % reduction in FC:
x = (0.9 (2024000)) / (85.56 – 62) = 77.318 hour / year
(85908 – 77318) / 85908 = 0.10 = 10 % reduction in x
10 % reduction in VC:
x = 2024000 / [85.56 – 0.9(62)] = 68011 hours / year
(85908 – . = 20.8 % reduction in x
10 % increase in R:
x = 2024000/ [1.1(85.56 – 62)] = 63021 hours / year
(85908 – 63021) / 85908 = 0.266 = 26.6 % reduction x
Breakeven point is more sensitive to reduction in variable cost than to
the same percentage reduction in fixed cost and highly sensitive to the
sensitive price.
‫ِصاي‬(3)
ْ‫ِاويٕرا‬ ‫ٌذيٕا‬A, B‫األٔراض‬ ْ‫وا‬ ‫ارا‬ ً‫ذفؼ‬ ‫ايّٙا‬1000‫ٚؼذج‬
ٕٗ‫ِاوي‬Aٕٗ‫ِاوي‬B
‫ذعٙيض‬ + ‫ِؼذاخ‬ + ٗ‫فٛلي‬ ‫ذىاٌيف‬..
ٖ‫اٌٛؼذ‬ ‫أراض‬ ‫ذىاٌيف‬..

17. Quantity
Q
A
B
1000380200
Geometrically
A: 4.15 + 0.11 (x) = TCA,
B: 29.2 +0.044 (x) = TCB
Analytically
Breakeven Point:
TCA = TCB
4.15 + 0.11 (x) = 29.2 +0.044 (x)
0.066(x) = 25.05, x = 379.5 say 380 Units
A: . . .
B: . . .
If x = 100 Units
A: . . .
B: . . .
Choose B which has LESS COST

18. If x = 200 Units
A: 4.15 + 0.11 (200) = 26.15
B: 29.2 +0.044 (200) = 38
Choose A which has LESS COST
‫ِصاي‬(4)
‫األٔراض‬ ‫ػٍّيح‬ ٝ‫ف‬ ‫الرظادا‬ ‫األوصش‬ ٕٗ‫اٌّاوي‬ ‫اخراس‬
AB
‫األٔراض‬ ‫ِؼذي‬100 Parts / hr
‫ٌإلٔراض‬ ٖ‫اٌّرٛلش‬ ‫اٌغاػاخ‬7 hr / day6 hr / day
‫اٌراٌف‬ ‫ٔغثح‬
‫اٌّٛاد‬ ‫ذىٍفح‬‫ذثاع‬ ّٗ‫اٌغٍي‬ ‫اٌمطغ‬ ، ‫اٌٛاؼذج‬ ٗ‫ٌٍمطؼ‬ٌّ‫ا‬ ِٓ ٜ‫أل‬ ً‫اٌرشغي‬ ‫ذىٍفح‬ ،ٓ‫اوٕري‬
$ٝ‫ف‬‫اٌرىاٌيف‬ ،ٗ‫اٌغاػ‬ٗ‫اٌفٛلي‬$ٝ‫ف‬ٗ‫اٌغاػ‬.
1.َٛ‫اٌي‬ ٝ‫ف‬ ‫ستػ‬ ٝ‫ألظ‬ ‫ٌرؽمك‬ ‫ذخراس‬ ٓ‫اٌّاوٕري‬ ٜ‫أ‬
2.ْٛ‫ٌرى‬ ‫اٌراٌف‬ ٗ‫ٔغث‬ ٝ٘ ‫ِا‬B‫وشتػ‬ ٗ‫ِشتؽ‬A(Breakeven).
Profit / day = = R / day – C / day
= (Production rate) (Production hours)(12 / parts) X [1 – (% rejected / 100)]
- (Production rate) (Production hours) (6 / Parts)
- (Production in hours) [(15 / hour) + (5 / hours)]
A = (100) (7) (12) (1 – 0.03) – (100) (7) (6) – (7) (15 – 5) = 3808 / day
B = (130) (6) (12) (1 – 0.10) – (130) (6) (6) – = 3624 / day
To maximize profit choose A
3808 = (130) (6) (12) (1 – X) – (130) (6) (6) –
X = 0.08
The % of parts rejected for machine B can be no higher than 8 % for it to be
as profitable as A

19. Ex : Which of the following is fixed or variable cost?
 Raw material
 Direct labor
 Depreciation
 Suppliers
 Utilities
 Properly taxes
 Interest on borrowed money
 Administrative salaries
 Payroll taxes
 Insurances
 Clerical salaries
 Rent

20. ‫انراتغ‬ ‫انثاب‬ ‫أْذاف‬
-‫ا‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬ٖ‫اٌفاةذ‬ ‫ِؼذي‬ ٚ ‫ٌٍٕمٛد‬ ٗ‫اٌضِٕي‬ ّٗ‫ٌمي‬
-ٗ‫إٌمذي‬ ‫اٌرذفماخ‬ ‫أٔٛاع‬ ‫ذؽذيذ‬
-‫اٌمشٚع‬ ‫ذغذيذ‬ ‫خطؾ‬ ٚ ‫اٌرىافؤ‬ ‫ِثذأ‬ ‫ِؼشفح‬
‫نهُقٕد‬ ّ‫انزيُي‬ ًّ‫انقي‬ : ‫انراتغ‬ ‫انثاب‬
-ٖ‫اٌفاةذ‬ ‫ِؼذي‬
-ٗ‫إٌمذي‬ ‫اٌرذفماخ‬ ‫أٔٛاع‬
-‫اٌرىافؤ‬‫خطؾ‬ :‫اٌمشٚع‬ ‫ذغذيذ‬
-‫ٚاظة‬4
1000َ‫ػا‬ ‫تؼذ‬ ٗ‫ظٕي‬
1.2.11003.20004.10000
LandsComputersEOY
A - BBAN
--
-
-
‫اخرشخ‬ ‫ارا‬Bٗ‫صِٕي‬ ّٗ‫لي‬ ‫ٌٍٕمٛد‬ ْ‫أ‬ ‫اػرثاس‬ ٜ‫ا‬ ٝ‫ذؼط‬ ٌُ
0 54321
300030003000
6000
C
6 7
0 54321
30003000
D
6 7
6000
3000
‫خياس‬Cْ‫ال‬3000َ‫ػا‬ ‫تؼذ‬ ‫ليّرٙا‬ ِٓ ً‫افؼ‬ ْ‫اآل‬

21. ِ‫انفائذ‬ ‫يؼذل‬:
ٚ ٓ‫تاٌغٕي‬ ِٓ‫اٌض‬ ْ‫وا‬ ‫ارا‬ّ‫اٌم‬‫ي‬ٗ‫اٌؽاٌي‬ ٗPresent ValuePٗ‫اٌّغرمثٍي‬ ّٗ‫اٌمي‬ ٚFuture ValueF
F = P + In
Inٝ‫ف‬ ٖ‫اٌضياد‬Pٖ‫فرش‬ ٝ‫ف‬nٝ‫ف‬ ٌٗ‫دا‬ ّٗ‫ِرشاو‬ ٖ‫فاةذ‬ ،P‫فرشاخ‬ ‫ػذد‬ ٚnٚiٜٕٛ‫ع‬
i‫يرغيش‬ ٗ‫في‬ ٜٕٛ‫ع‬ ٖ‫فاةذ‬ ‫ِؼذي‬ٕٗ‫ع‬ ‫خالي‬
1.‫تغيؾ‬ ‫ستػ‬Simple Interest:Inِٓ‫اٌض‬ ٝ‫ف‬ ٗ‫خطي‬ ٌٗ‫دا‬
In = P i n , Fn = P + P i n , Fn = P (1 + i n)
2.‫اٌّشوة‬ ‫اٌشتػ‬Compound Interest‫ذرغيش‬ :Inٝ‫ف‬ ‫ذغيش‬ ‫وّؼذي‬F
I = P i , Fn - = P , F = P , In = i Fn -
In، ٖ‫اخيش‬ ٕٗ‫ع‬ ٝ‫ف‬ ‫ستػ‬Fn -‫ِثٍغ‬Pٖ‫أخيش‬ ٕٗ‫اٌغ‬ ٝ‫ف‬
, , , ……………………., n – 2, n – 1, n
P, , Fn –
, P , Fn
Fn = P + In , Fn = P + i Fn - , Fn – = P
n = 1, Fn – = F = P
n = 2, F = P + i P = P (1 +i)
n = 3, F = P (1 +i) + P (1 +i) i = P (1 +i)
n = 4, F = P (1 +i) + P (1 +i) i = P (1 +i) (1 +i) = P (1 +i)
.
.
.
Fn = P (1 +i)n

22. ّ‫انُقذي‬ ‫انتذفقاخ‬ ‫إَٔاع‬Types of Cash Flows
1.ٜ‫ٔمذ‬ ‫ِعّٛع‬Single Sum of Money
0 nn -121
P
Single Sum
F = ?
……………….. Years (Period)
F = P (1 +i)n
, F = P (F / P i, n)
(1 +i)n
, (F / P i, n): Single Sum Future Worth Factor
ٜ‫ٔمذ‬ ‫ٌّعّٛع‬ ٗ‫اٌّغرمثٍي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬
( ‫ِصاي‬1)
0 54321
P = 1000
F
i= 12 %
F = P (F / P i, n) = 1000 (F/P 12%, 5) = 1000 (1.7623) = 1762.4
0 nn -121
P = ?
Single Sum
F
……………….. Years (Period)
P = F (1 + i)n –
, F = P (F/P i, n)
(1 + i)n –
, (F/P i, n): Single Sum Present Worth Factor

23. ٜ‫ٔمذ‬ ‫ٌّعّٛع‬ ٗ‫اٌؽاٌي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬
( ‫ِصاي‬2)
0 54321
P
F = 10000
i= 9 %
P = F (F/P i, n) = 10000 (P/F 9%, 4) = 10000 (0.7084) = 7084
2.ٍ‫عٍغ‬‫ح‬ٗ‫إٌمذي‬ ‫اٌرذفماخ‬ ِٓSeries of Cash Flow
0 n
An -1
3
2
1
A1
………………….
n -1
An
A2
A3
P = ?
P = A (1 +i) – A (1 – i)-
+ A (1 + i) ± …….- An - (1 + i)n –
+ An (1 + i)n
P = ∑n
t = 1 At (1 + i)- t
, P ∑n
t = 1 At (P/F i, n)
0
n
An -1
3
21
A1
………………….
n -1
AnA2
A3
A0

24. F = Ao (1 +i)n –
+ A (1 +i)n -
+ A (1 +i)n –
– A (1 +i)n –
± ……
+ An – (1 +i)(n – (n –
+ An (1 + i)n -n
F = Ao (1 +i)n
+ A (1 +i)n -
+ A (1 +i)n –
– A +i)n –
± ……
+ An – (1 +i) + An
F ∑n
t = 1 At (1 + i)n – t
, F ∑n
t = 1 At (F/P i, n)
P ∑n
t = 1 At (1 + i)- t
– , F = P (1 +i)n
---
Substitute P from (1) in (2)
F = (1 +i)n
∑n
t = 1 At (1 + i)- t
∑n
t = 1 At (1 + i)- t
(1 +i)n
∑n
t At (1 + i)n – t
( ‫ِصاي‬3)
0 8
3
21
300
200
300
200
P = ?
4 6
400
5 7
F = ?
i= 6%
P = 300 (P/F 6%, 1) – 300 (P/F 6%, 3) + 200 (P/F 6%, 4) + 400 (P/F 6%, 6)
+ 200 (P/F 6%, 8)
P = 300 (0.9434) – . .
. .
F = 300 (F/P 6%, 7) – 300 (F/P 6%, 5) + 200 (F/P 6%, 4) + 400 (F/P 6%, 2)
+ 200 (F/P 6%, 0)
F = 300 (1.5036) – . .
. .

25. F = P (F/P i%, n) = 597.04 (F/P 6%, 8) = 597.04 (1.5036) = 897.71
P = F (P/F i%, n) = 996052 (P/F 6%, 8) = 996.52 (0.5919) = 589.80
3.ّٗ‫(إٌّرظ‬ ٗ‫اٌّرغاٚي‬ ٗ‫إٌمذي‬ ‫اٌرفماخ‬ ‫عٍغٍح‬)Uniform Series of Cash Flow
0 n
A
321
A
…………………. n -1
AA A
P = ?
P ∑n
t = 1 A (1 + i)- t
, P = A [((1 +i)n
– 1) / i(1 +i)n
] , P = A (P/A i%, n)
[((1 +i)n
– 1) / i(1 +i)n
] , (P/A i%, n) : Uniform Series Present Value Factor
ّٗ‫ِٕرظ‬ ‫ٌغٍغٍح‬ ٗ‫اٌؽاٌي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬
( ‫ِصاي‬4)
0
A
321
A AA A
P = ?
A = 2000/ year
i= 12%
4 5
P = A (P/A 12%, 5) = 2000 (P/A 12%, 5) = 2000 (3.6048) = 7209.6
F = A (F/A 12%, 5) = 2000 (F/A 12%, 5) = 2000 (6.3528) = 12705.6

26. ( ‫ِصاي‬5)
0
A
321
A AA
P = ?
A
4 5 6 7
A = 2000/year
i=12%
F
P = A (P/A 12%, 5) (P/F 12%, 2) = 2000 (3.6048) (0.7972) = 5747.49
F = P (F/P 12%, 5) = 5747.49 (1.7623 .
F = A (F/A 12%, 4) = 2000 (4.7793) 9558.6
‫أيؼا‬
A = P [(i(1 +i)n
) / ((1 +i)n
– 1)] , A = P (A/P i% n)
[(i(1 +i)n
+i)n
– 1)], (A/P i% n): Capital Recovery Factor
‫اٌّاي‬ ‫سأط‬ ‫اعرؼادج‬ ًِ‫ِؼا‬
( ‫ِصاي‬6‫اٌؽغاب‬ ٝ‫ف‬ ‫شب‬ ‫يرشن‬ ‫ال‬ ٝ‫ؼر‬ ‫عؽة‬ )
0
A
1
A AA
P = 10000
A
A = ?
i=15%
AA A A A
10
A = P (A/P i%, n) = 10000 (A/p 15%, 10) = 10000 (0.1993) = 1993/ year

27. ( ‫ِصاي‬7ٓ‫عٕري‬ ‫اٌغؽة‬ ‫ذؤخيش‬ )
0
A
1
A AA
P = 10000
A
A = ?
i=15%
A A A
12
P2 = ?
A A
2
P = P (F/P i%, n) = 10000 (F/P 15%, 2) = 10000 (1.3225) = 13225
A = P (A/P i%, n) = 13225 (A/P 15%, 10) = 13225 (0.1993) 2635.74 / year
‫أيؼا‬
F = A [((1 +i)n
– / i] , F = A (F/A i%, n)
[((1 +i)n
– 1) / i] , (F/A i%, n): Uniform Series Future Worth Factor
ّٗ‫ِٕرظ‬ ‫ٌغٍغٍح‬ ٗ‫اٌّغرمثٍي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬
( ‫ِصاي‬8)
0 1
A = ?
i=8%
A F = 150000
35
A = F (A/F i%, n) = 150000 (A/F 8%, 35) = 150000 (0.0058) = 870 / year
( ‫ِصاي‬9)
0
1
i=8%
F = 150000
30
1000 1000
F = A (F/A 8%, 30) = 100 . .

28. P = A (P/A 8%, 30) = 1000 (11.2578) = 11257.8
P = F (P/F 8%, 30) = 113283.2 (10.0627) = 113283.86
‫أيؼا‬
A = F [i / ((1 +i)n
-1)] , A = F (A/F i%, n)
[i / ((1 +i)n
-1)] , (A/F i%, n): Reduced Capital Factor ٌ‫ا‬ ‫اٌّاي‬ ‫سأط‬ ًِ‫ِؼا‬‫ّرٕالض‬
4.ٗ‫اٌّرذسظ‬ ٗ‫إٌمذي‬ ‫اٌرذفماخ‬ ‫عٍغٍح‬Gradient Series Cash Flows
0
1 nn-12 3
A1
A1+G
A1+2G
A1+(n-1)G
A1+nG
P = P1 + P2
P = G [(1 – (1 +ni) (1 +i)-n
) / i] = P (P/G i%, n)
[(1 – (1 +ni) (1 +i)-n
) / i] = (P/G i%, n): Gradient Series Present Worth
Factor ٗ‫اٌؽاٌي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬ٗ‫ِرذسظ‬ ‫ذذفماخ‬ ‫ٌغٍغٍح‬
A = G [(1/i) – (n/i) (A/F i%, n)] = G (A/G i%, n)
[(1/i) – (n/i) (A/F i%, n)] = (A/G i%, n): Gradient to Uniform Series
Conversion Factor ُ‫ِٕرظ‬ ‫ذذفك‬ ٌٝ‫ا‬ ‫اٌّرذسض‬ ‫اٌرذفك‬ ً‫ذؽٛي‬ ًِ‫ِؼا‬
F = G (P/G i%, n) (F/P i%, n) ,
P = Uniform Series = A (P/A i%, n)
P = Gradient Series = G (P/G i%, n)
P = P + P = A (P/A i%, n) + G (P/G i%, n)
A = A + G (A/G i%, n)

29. ( ‫ِصاي‬10)
300
400
500
600
700 P1
P2
300
100
200
300
400
= +
0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5
i= 8%
P = A (P/A i%, n) = 3000 (P/A 8%, 5) = 3000 (3.9927) = 11978.1
P = G (P/G i%, n) = 1000 (P/G 8%, 5) = 1000 (7.3724) = 7372.4
P = P + P . . .
A = A + G (A/G i%, n) = 3000 + 1000 (A/G 8%, 5)
= 3000 + 1000 (1.846.5) = 4846.5 / year
F = P (F/P 8%, 5) = 19350 (1.4693) = 28431.69
F = A (F/A 8%, 5) = 4846.5 ( . .
( ‫ِصاي‬11)
800
0 1 2 3 4 5
800
700
600
500
400
100
200
300
400
= -
0 1 2 3 4 5 0 1 2 3 4 5
i= 8%
A = A – G (A/G i%, n) = 800 – 100 (A/G 8%, 5)
= 800 – 100 (1.8465) = 615.35 / year
F = A (F/A 8%, 5) = 615.35 (5.8666) = 3610.01
P = A (P/A 8%, 5) = 615.35 (3.9927) = 2456.91
P = F (P/F 8%, 5) = 3610.01 (0.680 .

30. Summary
 (1 +i)n
, (F / P i, n): Single Sum Future Worth Factor
ٜ‫ٔمذ‬ ‫ٌّعّٛع‬ ٗ‫اٌّغرمثٍي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬
 (1 + i)n –
, (F/P i, n): Single Sum Present Worth Factor
ٜ‫ٔمذ‬ ‫ٌّعّٛع‬ ٗ‫اٌؽاٌي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬
 [((1 +i)n
– 1) / i(1 +i)n
] , (P/A i%, n) : Uniform Series Present Value
Factor ّٗ‫ِٕرظ‬ ‫ٌغٍغٍح‬ ٗ‫اٌؽاٌي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬
 [(i(1 +i)n
) / ((1 +i)n
– 1)], (A/P i% n): Capital Recovery Factor
‫اٌّاي‬ ‫سأط‬ ‫اعرؼادج‬ ًِ‫ِؼا‬
 [((1 +i)n
– 1) / i] , (F/A i%, n): Uniform Series Future Worth Factor
ّٗ‫ِٕرظ‬ ‫ٌغٍغٍح‬ ٗ‫اٌّغرمثٍي‬ ّٗ‫اٌمي‬ ًِ‫ِؼا‬
 [i / ((1 +i)n
-1)] , (A/F i%, n): Reduced Capital Factor
‫اٌّرٕالض‬ ‫اٌّاي‬ ‫سأط‬ ًِ‫ِؼا‬
 [(1 – (1 +ni) (1 +i)-n
) / i] = (P/G i%, n): Gradient Series Present Worth
Factor
ّٗ‫اٌمي‬ ًِ‫ِؼا‬ٗ‫ِرذسظ‬ ‫ذذفماخ‬ ‫ٌغٍغٍح‬ ٗ‫اٌؽاٌي‬
 [(1/i) – (n/i) (A/F i%, n)] = (A/G i%, n): Gradient to Uniform Series
Conversion Factor
ُ‫ِٕرظ‬ ‫ذذفك‬ ٌٝ‫ا‬ ‫اٌّرذسض‬ ‫اٌرذفك‬ ً‫ذؽٛي‬ ًِ‫ِؼا‬

31. Summary of Cash Flows
0 nn -121
P
Single Sum
F = ?
……………….. Years (Period)
0 nn -121
P = ?
Single Sum
F
……………….. Years (Period)
0 n
An -1
3
2
1
A1
………………….
n -1
An
A2
A3
P = ?
0 n
A
321
A
…………………. n -1
AA A
P = ?
0
1 nn-12 3
A1
A1+G
A1+2G
A1+(n-1)G
A1+nG
P = P1 + P2

32. ّٝ‫األع‬ ‫اٌشتػ‬ ‫ِؼذي‬Nominalَٛ‫(ي‬ ٕٗ‫اٌغ‬ ‫خالي‬ ‫فرشاخ‬ :–‫اعثٛع‬–‫شٙش‬–‫ٔظف‬ ٜٕٛ‫ع‬ ‫ستغ‬
)ٜٕٛ‫ع‬
ٍٝ‫اٌفؼ‬ ‫اٌشتػ‬ ‫ِؼذي‬Effectiveٕٗ‫اٌغ‬ ‫ٔٙايح‬ ٝ‫ف‬ ‫ستػ‬ :
ieff = (1 + (r/m))m
– 1 , i = r / m , ieff = (1 +i)m
– 1 , ieff = (F/P r/m, m) –
r: ّٝ‫اإلع‬ ‫اٌشتػ‬ ‫ِؼذي‬ , m: ٕٗ‫اٌغ‬ ٝ‫ف‬ ٖ‫اٌّذ‬ ‫ِشوثاخ‬ i: ٕٗ‫اٌغ‬ ٝ‫ف‬ ٖ‫اٌّذ‬ ‫ِشوثاخ‬ ٝ‫ف‬ ‫اٌشتػ‬ ‫ِؼذي‬
ieff : ٕٗ‫اٌغ‬ ٝ‫ف‬ ٍٝ‫اٌفؼ‬ ‫اٌشتػ‬ ‫ِؼذي‬
Ex 1000 borrowed 8% compounded quarterly
2% / 3 months
F = P (F/P 2%, 4) = P (1 +i)n
.
. .
F = P (F/P 8.24%, 1) = 1000 (1.0824) = 1084.4 , nominal, 8.24 effective
annual
8% compounded semiannually
ieff . -1 = (F/P 4%, 2) – .
18% compounded monthly
ieff . – 1 = (F/P 1.5%, 12) – .

33. ‫انتكافؤ‬Equivalence
‫انقرٔض‬ ‫تضذيذ‬ ‫خطظ‬
ٖ‫ِمذاس‬ ‫لشع‬ ‫ذغذيذ‬ ‫خطؾ‬10000ٖ‫تفاةذ‬ ٗ‫ظٕي‬9ٕٗ‫اٌغ‬ ٝ‫ف‬ %
I.: ٌٝٚ‫األ‬1، ‫عٕٛيا‬ ٖ‫اٌفاةذ‬ ‫ذذفغ‬ .2‫اٌّاي‬ ‫ٌشأط‬ ٝ‫ظضة‬ ‫دفغ‬ ٝ‫ذمرؼ‬ ‫ال‬ .3‫سأط‬ ‫يذفغ‬ .
ٖ‫اٌفرش‬ ‫ٔٙايح‬ ٝ‫ف‬ ٖ‫ٚاؼذ‬ ٗ‫وذفؼ‬ ٍٗ‫و‬ ٝ‫األعاع‬ ‫اٌّاي‬
0
A
1
A AA
P = 10000
A
A = ?
i=9%
AA A A A
10
F = ?
A = I = Pi = 10000 (0.09) = 900
A = A + I =
II.:ٗ‫اٌصأي‬1ٗ‫ٔظاِي‬ ٗ‫تطشيم‬ ٝ‫األعاع‬ ‫اٌّاي‬ ‫سأط‬ ً‫ذمٍي‬ .2ٖ‫اٌفاةذ‬ ‫ذخفيغ‬ .
1450
1360
1270
1090
1180
0 1 2 3 4 5 6 7 8 9 10
1540
1630
1720
1810
1900
i=9%A = 1000
F (1.0900) = 10900, A ,
P = 10900 –
F . , A
P = 9810 –
F = 8000 (1.0900) = 8720, A
.
.
.

34. F = 1000 (1.0900) = 1090 , A
P = 1090 –
III.:ٗ‫اٌصاٌص‬1ّٗ‫ِٕرظ‬ ٗ‫تطشيم‬ ‫اٌّاي‬ ‫سأط‬ ً‫ذمٍي‬ .2‫ِذفٛػا‬ ‫ِعّٛع‬ َ‫أرظا‬ .‫سأط‬ ٚ ٖ‫اٌفاةذ‬ ‫خ‬
‫اٌّاي‬
0
A
1
A AA
P = 10000
A
A = ?
i=9%
AA A A A
10
A = P (A/P i%, n) = 10000 (A/P 9%, 10) = 10000 (0.1558) = 1558
IV.:ٗ‫اٌشاتؼ‬1‫اٌّاي‬ ‫ٌشأط‬ ٝ‫ظضة‬ ‫دفغ‬ ٝ‫ذمرؼ‬ ‫ال‬ .2ٖ‫اٌفاةذ‬ ‫دفغ‬ ٝ‫ذمرؼ‬ ‫ال‬ .3‫سأط‬ ‫دفغ‬ ُ‫ير‬ .
ٖ‫األخيش‬ ٕٗ‫اٌغ‬ ‫ٔٙايح‬ ٝ‫ف‬ ٖ‫اٌفاةذ‬ ٚ ٝ‫األعاع‬ ‫اٌّاي‬
0 1
P = 10000
i=9%
F
10
F = P (F/P i%, n) = 10000 ( F/P 9%, 10) = 10000 (2.3674) = 23674
IVIIIIIICapitalYear
Total
‫ذرىافؤ‬ ٖ‫أػال‬ ‫اٌّذفٛػاخ‬ ‫ِرٛاٌياخ‬ ً‫و‬ : ‫اٌرىافؤ‬

35. ٗ‫اٌخط‬‫اٌّّرٍه‬ ‫اٌّاي‬
ٗ‫اٌذفؼ‬ ‫تؼذ‬
ٝ‫ف‬ ٗ‫اٌذفؼ‬
ٕٗ‫اٌغ‬ ‫ٔٙايح‬
‫اٌّاي‬ ٌٝ‫اظّا‬
ً‫لث‬ ‫اٌّّرٍه‬
ٗ‫اٌذفؼ‬
ٖ‫اٌفاةذ‬
‫اٌّغ‬ٗ‫رؽم‬
ٕٗ‫اٌغ‬ ‫ٔٙايح‬
ٗ‫اٌخط‬I
ٗ‫اٌخط‬II

36. ٗ‫اٌخط‬‫اٌّّرٍه‬ ‫اٌّاي‬
ٗ‫اٌذفؼ‬ ‫تؼذ‬
ٝ‫ف‬ ٗ‫اٌذفؼ‬
ٕٗ‫اٌغ‬ ‫ٔٙايح‬
‫اٌّاي‬ ٌٝ‫اظّا‬
ً‫لث‬ ‫اٌّّرٍه‬
ٗ‫اٌذفؼ‬
ٖ‫اٌفاةذ‬
ٗ‫اٌّغرؽم‬
ٕٗ‫اٌغ‬ ‫ٔٙايح‬
ٗ‫اٌخط‬III
.
....
....
....
....
....
....
....
. ....
....
....
ٗ‫اٌخط‬IV
.
....
....
....
....
....
....
....
. ....
....
....

37. ‫انخايش‬ ‫انثاب‬ ‫أْذاف‬
-‫ٚاؼذ‬ ‫ٌّششٚع‬ ُ‫اٌرميي‬ ‫أظشاء‬
: ‫انخايش‬ ‫انثاب‬‫ٔاحذ‬ ‫يشرٔع‬ ‫تقييى‬Evaluating Single Project
-‫اٌخطٛاخ‬
-ُ‫اٌرميي‬ ‫ؽشق‬
-‫ٚاظة‬5
‫انخطٕاخ‬
- Prepare Cash Flow
- Determine MARR (i%) : Minimum Attractive Rate of return
‫اٌّعضا‬ ٚ‫أ‬ ٜ‫اٌّغش‬ ‫اٌؼاةذ‬ ‫ِؼذي‬
- Determine Time Horizon ِٕٝ‫اٌض‬ ‫األفك‬
‫انتقييى‬ ‫طرق‬
. Present Worth PW: if PW i MARR ≥ the project is economically
justified
. Future Worth FW: if FW (i = MARR ≥ the project is economically
justified
. Annual Worth AW: if AW i MARR ≥ the project is
economically justified
. Internal Rate of Return IRR: if IRR ≥ MARR the project is
economically justified
i at PW = 0, i = [(PWi min / (PWi min + PWi max)) (imax – imin)] + imin
. Benefit Cost Ratio BCR/ Saving Investment Ratio SIR:
[(PW (i = MARR)(+CF)) / (PW (i = MARR)(-CF)
The project is economically justified
. Payback Period PBP: R ≥ C, at i MARR , Number of years
. Capitalized Worth CW: CW A i , maximum CW at t ∞
Ex
Year
-

38. i = 15 %
0 321
50000
i= 15%
4
A = 20000 / year
5
PW (15%) = -50000 + 20000 (P/A 15%, 5)
= -50000 + 20000 (3.3522) = 17044 > 0 OK
FW (15%) = - 50000 (F/P 15%, 5) + 20000 (F/A 15%, 5)
= 34278 > 0 OK
AW (15%) = - 50000 (A/P 15%, 5) + 20000 = 5085 / year > 0 OK
BCR/ SIR = [(20000 (P/A 15%, 5)) / 50000]
= 67044 / 50000 = 1.3 > 1 OK
PBP Rt ≥ Ct , 20000 + 20000 + 20000 = 60000 > 50000 , t = 3 years
CW = A / i = [- 00 (A/P 15%, 5) + 20000] / 0.15 = 5085 / 0.15
= 33900 > 0 OK
0
PW
i
PWmax
PW min
i
imin
imax
PW = 0
IRR: PW(15%0 = 17044
PW(20%) = -50000 +20000(P/A 20%, 5)
- . -
i = [17044 / (17044 + 9812)] (0.20 – . .
. 7% > 15% MARR OK

39. ‫انضادس‬ ‫انثاب‬ ‫أْذاف‬
-‫اٌخياساخ‬ ٓ‫تي‬ ٗٔ‫اٌّماس‬ ‫ؽشق‬ ‫إظشاء‬
-
: ‫انضادس‬ ‫انثاب‬‫انخياراخ‬ ‫يقارَح‬Evaluation of Alternatives
-‫اٌخطٛاخ‬
-‫اٌخياساخ‬ ‫ِماسٔح‬ ‫ؽشق‬
-ٗ‫اإلػافي‬ ً‫اٌرؽاٌي‬
-‫ٚاظة‬6
‫اٌخطٛاخ‬
1.‫اٌخياساخ‬ ‫ذؽذيذ‬ ٚ ‫ذؼشيف‬Definition of Alternatives
2.‫ذؼ‬ِٕٝ‫اٌض‬ ‫األفك‬ ‫ذؽذيذ‬ ٚ ‫شيف‬Definition of Planning Horizons
3.‫خياس‬ ً‫ٌى‬ ٗ‫إٌمذي‬ ‫اٌرذفماخ‬ ‫أػذاد‬Prepare Cash Flow for all Alternatives
4.ٜ‫اٌّعض‬ ٜ‫اٌغش‬ ٖ‫اٌفاةذ‬ ‫ِؼذي‬ ‫ذؽذيذ‬
Determine of Minimum Attractive Rate of Return (MARR)
5.‫اٌّؼاييش‬ َ‫تئعرخذا‬ ‫اٌخياساخ‬ ‫ِماسٔح‬
Comparison of Alternatives using Analysis Methods
6.ٗ‫اإلػافي‬ ‫اٌرؽٍيالخ‬Additional Analysis – Sensitivity & Risk Analysis
7.ً‫األِص‬ ً‫اٌثذي‬ ‫إخرياس‬Select Optimum Alternative
ٗ‫اٌؽغاعي‬ ً‫ذؽٍي‬Sensitivity Analysisِٕ‫اٌض‬ ‫األفك‬ ‫ترغييش‬ ً‫األِص‬ ‫اٌخياس‬ ٍٝ‫ػ‬ ‫اٌرغيشاخ‬ ‫أشش‬ :ٝ
Planning Horizonٜ‫اٌّعض‬ ٜ‫اٌّغش‬ ‫اٌؼاةذ‬ ‫ِؼذي‬ ٚ‫أ‬MARR
ٖ‫اٌّخاؽش‬ ً‫ذؽٍي‬Risk Analysis‫اإلؼرّاالخ‬ ٚ ‫اإلؼظاء‬ ً‫ذذخ‬ :Probability & Statistics
‫اٌّؽاواج‬ ٚ‫أ‬Simulation
-ٗٔ‫اٌّماس‬ ‫ِؼاييش‬ ٚ ‫ٌٍٕمٛد‬ ٗ‫اٌضِٕي‬ ّٗ‫اٌمي‬ َ‫أعرخذا‬
-‫ِؽمك‬ ٕٝ‫اٌف‬ ‫اٌعأة‬Technically Feasible
-‫ذؽ‬‫اٌخياساخ‬ ‫ذيذ‬Alternatives:
‫اٌخياس‬Alternative‫اٌمشاس‬ ‫الذخار‬ ً‫تذاة‬ :
‫اٌّمرشغ‬Proposal‫اٌّمرشؼاخ‬ ِٓ ْٛ‫ذرى‬ ‫اٌخياساخ‬ ، ‫خياس‬ ْٛ‫يى‬ ْ‫أ‬ ًّ‫يؽر‬ ‫ِٕٙا‬ ‫اٌٛاؼذ‬ :
mِٓٝ‫ذؼط‬ ‫اٌّمرشؼاخ‬m
)ً‫(اٌثذاة‬ ‫اٌخياساخ‬ ِٓ
Do nothing‫خياس‬ ‫يؼرثش‬
ٗ‫ِرٕافي‬ ‫خياساخ‬Mutually Exclusiveٗ‫ِشذثط‬ ‫خياساخ‬ ٚContingent
m = 3 so Alternatives are 2

40. ‫اٌخياس‬‫اٌّمرشؼاخ‬‫اٌرٛػيػ‬
CBA
‫خياس‬ ٜ‫أ‬ ‫اخرياس‬ ُ‫ير‬ ‫ال‬Do nothing
‫اإللرشاغ‬ ‫لثٛي‬C‫فمؾ‬
‫اإللرشاغ‬ ‫لثٛي‬B‫فمؾ‬
‫اإللرشاغ‬ ‫لثٛي‬A‫فمؾ‬
‫اإللرش‬ ‫لثٛي‬‫اغ‬C, B‫فمؾ‬
‫اإللرشاغ‬ ‫لثٛي‬A, C‫فمؾ‬
‫اإللرشاغ‬ ‫لثٛي‬A, B‫فمؾ‬
‫ِمرشؼاخ‬ ‫اٌصالز‬ ‫لثٛي‬
( ‫ِصاي‬1)
ٖ‫ِؽذٚد‬ ٗ‫ِيضأي‬‫خياس‬B‫ب‬ ‫ِشذثؾ‬A،A & Cْ‫ِرٕافيا‬
CBAEOY
---
-4000-
60002
3
4
5
‫اٌخياس‬‫اٌّمرشؼاخ‬ٗ‫اٌرىٍف‬
‫ِالؼظاخ‬ CBA


X
X

X

X
‫اٌخياس‬‫اٌّمرشؼاخ‬ٗ‫اٌرىٍف‬
‫ِالؼظاخ‬ CBA


2
3

41. ٝ‫واآلذ‬ ٗ‫إٌمذي‬ ‫اٌرذفماخ‬ ً‫ذفاطي‬ ‫أِا‬
AAAAEOY
---
--
-ِٕٝ‫اٌض‬ ‫األفك‬Time Horizon‫ٌّماسٔح‬ ٜ‫اإللرظاد‬ ‫ٌألداء‬ ٗ‫اٌّطٍٛت‬ ٗ‫اٌضِٕي‬ ٖ‫اٌفرش‬ ‫ؽٛي‬ :
ً‫اٌرشغي‬ ‫ػّش‬ ‫ٌيغد‬ ، ‫اٌخياساخ‬Working Lifeٝ‫اإل٘الو‬ ‫اٌؼّش‬ ٚ‫أ‬
Depreciation Life
ٝ‫تاآلذ‬ ‫يؽذد‬ ِٕٝ‫اٌض‬ ‫األفك‬
4.‫اٌثغيؾ‬ ‫اٌّشرشن‬ ‫اٌّؼاػف‬T3, 5, 6 is 30
5.ِٕٝ‫ص‬ ‫أفك‬ ً‫أل‬TsSalvage or Book value for 5 & 6 , 3
6.ِٕٝ‫ص‬ ‫أفك‬ ‫أؽٛي‬TL
Salvage ValueNCFCostRevenuesEOY
Rt - CtCtRtt
Alternative (1)
1 –
Alternative (2)
-
Alternative (3)
-

42. -ٗ‫ذىٍف‬ : ٗ‫إٌمذي‬ ‫اٌرذفماخ‬Cost‫ٚػاةذاخ‬Revenueٗ‫ِرثمي‬ ُ‫لي‬ ٚSalvage Value
Net Cash FlowEOY
A3tA2tA1tt
T = 30 years
--
-
-
::::
T = Ts = 3 years
--
T = TL = 6 years
--

43. -ٜ‫ِغش‬ ‫ػاةذ‬ ‫ِؼذي‬MARR‫اٌثٕٛن‬ ٚ‫أ‬ ِٗٛ‫اٌؽى‬ ‫تٛاعطح‬
( ‫ِصاي‬2)
0 321
4000
i= 15%
4
3500 3500 3500
4500
0
1 2 3 4 5 6
5000
1000
2000
3000
4000
5000
6000
i= 15%
ِٕٝ‫اٌض‬ ‫األفك‬ ‫ٔفرشع‬6‫عٕٛاخ‬
FW1 (15%) = 3500 (P/A 15%, 3) (F/P 15%, 6) + 4500 (F/P 15%, 2)
- 4000 (F/P 15%, 6) = 3500 (2.2832) (2.3131) + 4500 (1.3225)
- . .
FW2 (15%) = 1000 (F/A 15%, 6) + 1000 (A/G 15%, 6) (F/A 15%, 6)
-5000 (F/P , . . .
- . .
FW2 (15%) > FW1 (15%) select Alternative 2
‫ؼغثٕا‬ ٚ ِٕٝ‫اٌض‬ ‫ٌألفك‬ ‫اإلػرثاس‬ ٝ‫ف‬ ‫ٔؼغ‬ ٌُ ‫ارا‬AWٓ‫اٌخياسي‬ ‫ٌىال‬
AW1 (15%, 4) = 3000.15 / year
AW2 (15%, 6) = 1776.2 / year
‫ا‬ ‫يٕرط‬ ٗ‫ػٍي‬ ٚ‫اٌخياس‬ ْ1ً‫األفؼ‬ ٛ٘
‫اٌخياساخ‬ ‫ِماسٔح‬ ‫ؽشق‬
1.ٗ‫اٌؽاٌي‬ ّٗ‫اٌمي‬ ٝ‫طاف‬Net Present Worth PW:PW (MARR)‫أوثش‬ ً‫يفؼ‬PW،
‫أطغش‬ ً‫يفؼ‬ ‫فمؾ‬ ٗ‫ذىٍف‬ ‫أِا‬PW
-‫اٌشذة‬Ranking:PW (MARR)‫أوثش‬ ً‫يفؼ‬PW‫أطغش‬ ً‫يفؼ‬ ‫فمؾ‬ ٗ‫ذىٍف‬ ‫أِا‬ ،
PW
-‫اٌفشق‬Incremental:
Challenger ٜ‫ِرؽذ‬ , 0 Defender ‫ِذافغ‬ ,
PW1 – (MARR) > 0 1 is winner
2.ٗ‫اٌغٕٛي‬ ّٗ‫إٌّرظ‬ ‫اإليشاداخ‬ ٝ‫طاف‬AWNet Annual Worth:AW (MARR)
‫أوثش‬ ً‫يفؼ‬AW‫أطغش‬ ً‫يفؼ‬ ‫فمؾ‬ ٗ‫ذىٍف‬ ‫أِا‬ ،AW
-: ‫اٌشذة‬AW (MARR)‫أوثش‬ ً‫يفؼ‬AW‫أطغش‬ ً‫يفؼ‬ ‫فمؾ‬ ٗ‫ذىٍف‬ ‫أِا‬ ،AW

44. -:‫اٌفشق‬
AW1 – (MARR) > 0 1 is winner
3.ٗ‫اٌّغرمثٍي‬ ّٗ‫اٌمي‬ ٝ‫طاف‬Net Future Worth FW:FW (MARR)‫أوثش‬ ً‫يفؼ‬FW
‫أطغش‬ ً‫يفؼ‬ ‫فمؾ‬ ٗ‫ذىٍف‬ ‫أِا‬ ،FW
-:‫اٌشذة‬AW (MARR)‫أوثش‬ ً‫يفؼ‬AW‫أطغش‬ ً‫يفؼ‬ ‫فمؾ‬ ٗ‫ذىٍف‬ ‫أِا‬ ،AW
-‫اٌفشق‬
FW1 – (MARR) > 0 1 is winner
4.ٍٝ‫اٌذاخ‬ ‫اٌؼاةذ‬ ‫ِؼذي‬Internal Rate of Return IRRٖ‫اٌفاةذ‬ ‫ِؼذي‬ :iً‫يعؼ‬ ٜ‫اٌز‬
FW = 0, AW = 0 , PW = 0‫اٌفشق‬ ‫سيمح‬ َ‫ذغرخذ‬ ٚ
0
PW
PWmax
PW min
i
imin
imax
PW = 0
PW1 – (i%) = 0 , Find i if i > MARR , then 1 is winner
i = [(PW / (PW + PW )) (i – i )] + i OR
i = [(PWi min / (PWi min + PWi max)) (imax – imin) ]+ imin
5.‫اٌرىاٌيف‬ ٍٝ‫ػ‬ ‫اٌؼاةذ‬ ‫ِؼذي‬
Benefit Cost Ratio BCR/ Saving investment Ratio SIR‫ِشاسيغ‬ ٝ‫ف‬ َ‫ذغرخذ‬ :
‫اٌفشق‬ ‫فيٙا‬ َ‫ٚيغرخذ‬ َ‫اٌؼا‬ ‫اٌمطاع‬
[(PW - (i = MARR)(+CF)) / (PW - (i = MARR)(-CF)
6.‫اإلعرشداد‬ ‫فرشج‬Payback Period PBPٖ‫اٌفرش‬ ‫ذؽذد‬ :ٌ‫ا‬ ‫اٌّاي‬ ‫العرشداد‬ ِٗ‫اآلص‬‫ّغرصّش‬
‫تئػرثاس‬i = 0‫اعرشداد‬ ‫فرشج‬ ً‫تئل‬ ‫اٌخياس‬ ً‫يفؼ‬ .‫ِغاػذ‬ ‫ِمياط‬ ،
Rt ≥ Ct, at (i = MARR) = 0, Number of years
7.ّٗ‫اٌذاة‬ ‫اإليشاداخ‬ ٚ‫أ‬ ‫اٌّاي‬ ‫سأط‬ ٍٝ‫ػ‬ ‫اٌؼاةذ‬ ‫ؽشيمح‬
Perpetuities and Capitalized Worth CW
‫أوثش‬ ‫طاؼة‬ ً‫يفؼ‬ ٚCW
CW = A / i , maximum CW at t ∞
P = A[(1 - i)n
– 1) / i (1 + i)n
] = (A / i) [(1 - i)n
– 1) / (1 + i)n
]
When n ∞ , P A i i.e : CW A year MARR i
ٍٝ‫أػ‬ ‫طاؼة‬ ‫اٌخياس‬ ً‫يفؼ‬CW

45. ( ‫ِصاي‬1)
‫ٌخياساخ‬ ٗ‫إٌمذي‬ ‫اٌرذفماخ‬ ‫ِغاس‬ ‫يٛػػ‬ ٌٝ‫اٌرا‬ ‫اٌعذٚي‬
AAAAEOY
--0
4500
4500
4500
4500
A : Do Nothing, NCF = Revenue – Cost, MARR = i = 15 %, n = 5 years
. NPW:
- Ranking: PW ,
PW (15%) = 4500 (P/A 15%, n) = 4500 (3.3522) = 15085
PW (15%) = - 50000 + 20000 (P/A 15%, 5)
= - . ) =
PW (15%) = - 75000 + 20000 (P/A 15%, 5) + 5000 (P/G 15%, n)
- . .
Best is A Greater PW
- Incremental: PW1 – (15%) = 4500 (P/A 15%, n) –
= 4500 (3.3522) –
A is better than A
PW2 – (15%) = - 50000 + 20000 (P/A 15%, 5) - 4500 (P/A 15%, n)
= - . - . )
= 17044 – 15085 = 1959 > 0, A is better than A
PW3 – (15%) = [- 75000 + 20000 (P/A 15%, 5) + 5000 (P/G 15%, n)]
– [- 50000 + 20000 (P/A 15%, 5)] = [- 75000 + 20000 (3.3522) +
5000 (5.7751)] – - .
= 20920 –
A is better than A
If PW2 - ≤ Compare A with A
. NAW:
- Ranking: AW
AW (15%) = 4500 / year,
AW (15%) = -50000 (A/P 15%, 5) + 20000
- . = 5085 / year
AW (15%) = -75000 (A/P 15%, 5) + 20000 + 5000 (A/G 15%, 5)
= -75000 (0.2983) + 20000 + 5000 (1.7228) = 6242 / year
The beast is A
- Incremental: AW - (15%) = 4500 – 0 = 4500 / year > 0
A is better

46. AW - (15%) = [-50000 (A/P 15%, 5) + 20000] –
= [-50000 (0.2983) + 20000] – 5085 –
= 585 / year > 0 A is better
AW3 – (15%) = [ -75000 (A/P 15%, 5) + 20000 + 5000 (A/G 15%,
5)] – [-50000 (A/P 15%, 5) + 20000]
=[ -75000 (0.2983) + 20000 + 5000 (1.7228)] – - .
6242 – 5085 = 1157 / year
A is better
. NFW:
- Ranking : FW0 (15%) = 0
FW (15%) = 4500 (F/A 15%, 5) = 4500 (6.7424
FW (15%) = -50000 (F/P 15%, 5) + 20000 (F/A 15%, 5)
- . .
FW (15%) = - 75000 (F/P 15%, 5) + 20000 (F/A 15%, 5)
P/G 15%, 5) (F/P 15%, 5) = - .
. . . = 42073 A is better
- Incremental: FW1 – (15%) = 4500 (F/A 15%, 5) –
= 4500 (6.7424) –
A is better
FW2 – (15%) = [-50000 (F/P 15%, 5) + 20000 (F/A 15%, 5)] – [4500
(F/A 15%, 5)] = [-50000 (2.0114) + 20000 (6.7424)] –
. = 34278 – 30341= 3937 > 0 A is better
FW - (15%) = [- 75000 (F/P 15%, 5) + 20000 (F/A 15%, 5)
+ 5000 (P/G 15%, 5) (F/P 15%, 5)] – [-50000 (F/P 15%, 5) + 20000
(F/A 15%, 5)] = [- . . .
. – - . .
= 42073 – 34278 = 7795 A is better
. IRR: Incremental PW = 0
i1 – : PW1 -0 (i) = 0 = 4500 (P/A i%, 5) , (P/A i%, 5) = 0 ;
0 = A [((1 +i)n
– 1) / i (1 +i)n
, A i , i ∞ PW
i1 – ∞ MARR A is better
PW – (i%) = - 50000 + 20000 (P/A 15%, 5) - 4500 (P/A 15%, n) =
At i = 15%, PW2 – - 50000 + 20000 (P/A 15%, 5) - 4500
(P/A 15%, n) = - . - . ) =
At i = 20%, PW2 – (20%) = - 50000 + 20000 (P/A 20%, 5) -
(P/A 20%, n) = - . - . -
By Interpolation ‫تاإلعرىّاي‬
i = [(PW / (PW + PW )) (i – i )] + i

47. = [(1959 / (1959 + 3648)) (0.20 – 0.15)] + 0.15 = 0.168 = 16.8% >
MARR (15%) A is better
PW3 – (i%) = [- 20000 (P/A 15%, 5) + 5000 (P/G 15%, n)] –
[- 50000 + 20000 (P/A 15%, 5)] = 0
At i = 15%, PW3 –
At i , PW3 – (20%) = [- 75000 + 20000 (P/A 20%, 5) + 5000
(P/G 20%, n)] – [- 50000 + 20000 (P/A 20%, 5)] = [-
. 000 (4.9061)] – - . -
By Interpolation ‫تاإلعرىّاي‬
i = [(3876 / (3876 + 470)) (0.20 – . .
= 0.1945 = 19.5% > MARR (15%)
A is better
. BCR/ SIR : [(PW - (i = MARR)(+CF)) / (PW - (i = MARR)(-CF)
Or BCR/ SIRB – A
= [((+PWB) – (+PWA) at MARR) / ((-PWB) – (-PWA) at MARR)] > 1
BCR/ SIR1 – P A , ∞ A is better
BCR/ SIR2 – = [(20000 (PA 15%, 5) – (4500 (P/A 15%, 5)] / 50000
= [(20000 (3.3522) – . . say 1.4 > 1
A is better
BCR/ SIR3 – = [(20000 (P/A 15%, 5) + 5000 (P/G 15%, 5) – 20000
(PA 15%, 5)] / [75000 – 50000] = [(20000 (3.3522) + 5000 (5.7751) –
20000 (3.3522)] / [75000 – 50000] = 1.155 say 1.16 > 1
A is better
. PBP: at i = Zero when Rt > Ct
‫اٌخياس‬A‫ٌؽظيا‬ ٖ‫إعرشداد‬ ‫ففرشج‬ ٌٝٚ‫أ‬ ‫ِاي‬ ‫سأط‬ ٗ‫ٌذي‬ ‫ٌيظ‬
A : ∑R C
n = 2.5, PBP = 2.5 or n = 3, PBP = 3
A : ∑R C
n = 3, PBP = 3
‫اٌرشذية‬ ْٛ‫يى‬ ٚA , A , A‫اإلعرش‬ ‫فرشج‬ ‫ؼغة‬‫ٌزٌه‬ . ٜ‫األخش‬ ‫اٌّماسٔاخ‬ ‫ػىظ‬ ٝ٘ ٚ ‫داد‬
‫ٚؼذ٘ا‬ َ‫ذغرخذ‬ ‫ال‬
. CW: CW = AW . . ,
CW = AW . . ,
CW = [-50000 (A/P 15%, 5) + 20000] / 0.15
- . . .
CW = AW .
= [-75000 (A/P 15%, 5) + 20000 + 5000 (A/G 15%, 5)] / 0.15
- . . .
.
A is the better

48. ّ‫اإلضافي‬ ‫انتحانيم‬Supplementary Analysis
‫ا‬ ٚ ‫اٌرىاٌيف‬ ‫ذمذيشاخ‬ ٝ‫ف‬ ٗ‫اٌصم‬ َ‫ػذ‬‫لشاس‬ ِٓ ‫اٌّشدٚد‬ ُ‫ٌرمٛي‬ ٗ‫آٌي‬ ‫ذريػ‬ ٗ‫اإلػافي‬ ً‫اٌرؽاٌي‬ ، ‫ٌؼاةذاخ‬
ٝ٘ ‫اٌطشق‬ .‫اإلخرياس‬
1.‫اٌرؼادي‬ ٗ‫ٔمط‬ ً‫ذؽٍي‬Breakeven Analysisِٓ ‫أوصش‬ ٚ‫أ‬ ‫ٌٛاؼذ‬ ٗ‫شم‬ ‫ٕ٘اٌه‬ ْٛ‫ذى‬ ‫ػٕذِا‬ :
‫اٌرؼادي‬ ‫ليّح‬ ِٓ ‫أوثش‬ َ‫أ‬ ً‫أل‬ ٝ٘ ٗ‫ليّر‬ ٍٝ‫ػ‬ ُ‫تاٌؽى‬ ٗ‫ِؼشٚف‬ ‫غيش‬ ٗ‫ليّر‬ ْ‫أ‬ ًِ‫اٌؼٛا‬
2.ٗ‫اٌؽغاعي‬ ً‫ذؽٍي‬Sensitivity Analysisًِ‫اٌؼٛا‬ ‫ٌميّح‬ ‫أوصش‬ ٚ‫أ‬ ‫ٚاؼذ‬ ٝ‫ف‬ ‫اٌرغيشاخ‬ ‫أشش‬ :
‫لشاس‬ ‫اعرعاتح‬ ‫ذؽذيذ‬ ِٕٗ ‫اٌٙذف‬ ٚ .ٜ‫اإللرظاد‬ )‫(اٌّشدٚد‬ ‫اٌؼاةذ‬ ٍٝ‫ػ‬ ٗ‫اٌذساع‬ ٝ‫ف‬ ِٗ‫اٌّغرخذ‬
‫ليّرٙا‬ ‫ذؽذد‬ ‫ال‬ ٜ‫(أ‬ ‫ٌٍٕغيشاخ‬ ‫ذخؼغ‬ ٝ‫اٌر‬ ٚ ‫اعرخذاِٙا‬ ُ‫ذ‬ ٝ‫اٌر‬ ًِ‫اٌؼٛا‬ ُ‫ٌمي‬ ً‫اٌثذي‬ ‫اخرياس‬
،ِٕٝ‫اٌض‬ ‫األفك‬ ًّ‫ذش‬ )ٗ‫تصم‬ٜ‫اٌّعض‬ ٜ‫اٌّغش‬ ‫اٌؼاةذ‬ ‫ِؼذي‬MARRٚ .ٜ‫ٔمذ‬ ‫ذذفك‬ ّٗ‫لي‬ ٜ‫أ‬ ٚ
.‫ذمذيشاذٙا‬ ٝ‫ف‬ ‫خطؤ‬ ‫ٔغثح‬ ‫تفشع‬ ‫رٌه‬
3.ٖ‫اٌّخاؽش‬ ً‫ذؽٍي‬Risk Analysis‫ورٛصيغ‬ ‫تٛػٛغ‬ ٕٗ‫اٌّّى‬ ًِ‫اٌؼٛا‬ ُ‫لي‬ ً‫ّٔصي‬ ُٕ‫ي‬ :
‫ِؽاواج‬ ‫ّٔارض‬ ٚ‫أ‬ ٗ‫ذؽٍيٍي‬ ‫ّٔارض‬ ًّ‫ػ‬ ٛٙ‫ػشٛاةي‬ ‫وّرغيشاخ‬ ‫تّؼاٍِرٙا‬ ،ٌٝ‫اؼرّا‬
(Simulation Models)‫ِصال‬.ٗ‫اٌؽاٌي‬ ّٗ‫ٌٍمي‬ ٌٝ‫اإلؼرّا‬ ‫اٌرٛصيغ‬

49. ‫انضاتغ‬ ‫انثاب‬ ‫أْذاف‬
-ُ‫اٌرؼخ‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
-ٗ‫ؼغات‬ ‫ويفيح‬ ٚ ‫اإل٘الن‬ ٍٝ‫ػ‬ ‫اٌرؼشف‬
‫اإلْالك‬ ٔ ‫انتضخى‬ : ‫انضاتغ‬ ‫انثاب‬
-ُ‫اٌرؼخ‬
-‫اإل٘الن‬
-‫ٚاظة‬7
‫انتضخى‬Inflation
‫خذِاخ‬ ٚ ‫عٍغ‬ ‫اٌّاي‬ ِٓ ‫ِؽذد‬ ‫تّثٍغ‬ ٜ‫ذشرش‬ ‫تؽيس‬ ‫اٌخذِاخ‬ ٚ ‫اٌغٍغ‬ ‫اعؼاس‬ ٗ‫في‬ ‫ذشذفغ‬ ٜ‫اٌز‬ ‫اٌٛػغ‬
.ِٓ‫اٌض‬ ‫ِش‬ ‫وٍّا‬ ً‫أل‬
‫ب‬ ِٕٗ ‫أوثش‬ ْٛ‫يى‬ ٖ‫اٌفاةذ‬ ‫ِؼذي‬-‫ػاٌيا‬ ْٛ‫يى‬ ٜ‫أ‬
1.ً‫أل‬ ‫خذِاخ‬ ٚ‫أ‬ ‫عٍغ‬ ٜ‫يشٕش‬ ٗ‫اٌعٕي‬
2.ٌٝ‫ػا‬ ْٛ‫يى‬ ٖ‫فاةذ‬ ‫ِؼذي‬
ُ‫اٌرؼخ‬ ‫أٔٛاع‬
1.:ٝ‫اٌؽميم‬‫إ‬ ٖ‫صياد‬ ٜ‫ذؤد‬ ‫ال‬‫إٌاذط‬ ٝ‫ف‬ ٜ‫أخش‬ ٖ‫صياد‬ ٌٝ‫ا‬ )‫(األعؼاس‬ ‫اٌطٍة‬ ٝ‫ف‬ ٗ‫ػافي‬
2.‫عشػح‬ ٓ‫ػ‬ ‫إٌظش‬ ‫تغغ‬ ‫ِغرّش‬ ٚ ‫تطب‬ ‫أسذفاع‬ ،‫اٌذٚي‬ ُ‫ِؼظ‬ ُ٘ :‫اٌضاؼف‬ ٚ‫أ‬ ٝ‫اٌرذسيع‬
‫اٌطٍة‬ ‫اصدياد‬
3.‫أسذفاع‬ ‫يغثة‬ ْ‫أ‬ ٓ‫يّى‬ ٜٛ‫ل‬ ُ‫ذشاو‬ ‫يٕرط‬ ‫األعؼاس‬ ‫ذصثد‬ ،‫األعؼاس‬ ‫ذشذفغ‬ ‫ال‬ :‫اٌّىثٛخ‬ ٚ‫أ‬ ‫اٌّميذ‬
‫األعؼاس‬ ٝ‫ف‬ ٜ‫أفعاس‬-‫اٌؽشٚب‬
4.‫اٌعاِػ‬ٚ ‫اٌّؼاسن‬ ٝ‫ف‬ َ‫األٔٙضا‬ ، ٗ‫فٍىي‬ َ‫أسلا‬ ٌٝ‫ا‬ ‫األعؼاس‬ ً‫ذظ‬ ٗ‫إٌمذي‬ ٖ‫اٚؼذ‬ ‫ليّح‬ ‫إٔٙياس‬ :
‫ٌؼٍّيح‬ ‫اٌّميذ‬ ‫غيش‬ َ‫ٌإلعرخذا‬ ِٗٛ‫اٌؽى‬ ٗ‫ذرع‬ ٚ ٗ‫اإلٔراظي‬ ‫اٌؼٍّياخ‬ ‫ايماف‬ ٚ ٜ‫اٌصٛس‬ ‫اٌرذِيش‬
.‫اؼرياظاذٙا‬ ً‫ٌرّٛي‬ ‫اٌطثغ‬
‫إٔرا‬ ‫ٌرىٍفح‬ ‫ِغاٚيا‬ ٍٝ‫اٌى‬ ‫اٌطٍة‬ ْٛ‫يى‬ ْ‫أ‬ ‫تذ‬ ‫ال‬‫اٌؼشاةة‬ ‫رٌه‬ ٝ‫ف‬ ‫تّا‬ ٗ‫ظ‬‫ؼاٌٚد‬ ‫فارا‬ .‫األستاغ‬ ٚ
ُ‫اٌرؼخ‬ ‫إؽاس‬ ‫يٕشؤ‬ ‫أوثش‬ ‫ٔظية‬ ٍٝ‫ػ‬ ‫اإلعرؽٛار‬ ِٗٛ‫اٌؽى‬
:‫األعؼاس‬ ٚ ‫األظٛس‬ ٓ‫تي‬ ‫اٌرغاتك‬
ٖ‫تضياد‬ ْٛ‫يطاٌث‬ ‫األظٛس‬ ٝ‫ٌىاعث‬ ٝ‫اٌؽميم‬ ‫األعرٙالن‬ ‫يٕخفغ‬ ٚ ‫األعؼاس‬ ‫ذشذفغ‬ ‫اٌؼشع‬ ‫يفٛق‬ ‫اٌطٍة‬
‫عرؽاٚي‬ ٛ‫اإلٔراظ‬ ‫ذىاٌيف‬ ‫ذشذفغ‬ ‫األظٛس‬ ‫صيادج‬ ، ٗ‫اٌّؼيش‬ ‫ذىاٌيف‬ ‫ٌّعاتٙح‬ٚ ‫األعؼاس‬ ‫سفغ‬ ِٗٛ‫اٌؽى‬
‫ذٛػغ‬ ٌُ ‫ارا‬ ٚ ٗ‫دافؼ‬ ٖٛ‫ل‬ ُ‫اٌرؼخ‬ ‫يىرغة‬ ٚ ‫األظٛس‬ ‫األعؼاس‬ ‫ذطاسد‬ ٚ ‫األظٛس‬ ‫تضيادج‬ ٗ‫اٌّطاٌث‬ ‫ذرىشس‬
.‫ظاِػ‬ ُ‫ذؼخ‬ ٌٝ‫ا‬ ‫يمٛد‬ ٗٔ‫فئ‬ ‫ػالظاخ‬
.‫اإللرظاد‬ ٚ ٗ‫اٌّاٌي‬ ‫ٚصاسج‬ ‫عياعاخ‬ ٚ ٍٝ‫اٌى‬ ٜ‫إٌمذ‬ ‫اإلٔفاق‬ ‫تخفغ‬ ٗ‫ِىافؽر‬ ً‫ٚعاة‬

50. ‫اإلْالك‬Depreciation
‫أعث‬ٗ‫ات‬
1.‫اٌرّضق‬ ٚ ً‫اٌرآو‬Wear & Tearًٍ‫اٌرؽ‬ ٚ
2.َ‫اٌرماد‬Obsolescenceًِ‫اٌؼٛا‬ ُ٘‫أ‬ ِٓ ِٗ‫اٌّرمذ‬ ‫اٌرىٌٕٛٛظيا‬ ‫ِغ‬ َ‫اٌرظاد‬ :
‫اإل٘الن‬ ‫ؼغاب‬ ‫ؽشق‬
1.ُ‫اٌّغرمي‬ ‫اٌخؾ‬ ‫ؽشيمح‬Straight Line
‫اٌؽظٛي‬ ‫(ذىاٌيف‬ = ٕٗ‫اٌغ‬ / ‫اإل٘الن‬–ٝ‫اإلفرشاػ‬ ‫اٌؼّش‬ / )‫األٔماع‬ ‫لّح‬
Dep. / year = (Initial Cost – Salvage Value) / Time Horizon
( ‫ِصاي‬1)
‫اٌؽظٛي‬ ‫ذىٍفح‬ ٕٗ‫ِاوي‬125000)ٖ‫(اٌخشد‬ ‫األٔماع‬ ‫ليّح‬ ٚ ٗ‫ظٕي‬15000ٝ‫اإلفرشاػ‬ ‫اٌؼّش‬ ٚ10
‫عٕٛاخ‬
Dep. / year = (125000 – 15000) / 10 = 11000 / year
ٕٗ‫ع‬ ً‫و‬ ‫شاتد‬ ‫ِثٍغ‬
2.ٗ‫إٌّرع‬ ‫اٌٛؼذاخ‬ ‫تؼذد‬ ‫األ٘الن‬Units of Output Depreciation
‫اٌؽظٛي‬ ‫(ذىاٌيف‬ = ٖ‫ٚؼذ‬ ً‫ٌى‬ ‫اإل٘الن‬–)ّٝ‫اٌرظّي‬ ‫(اٌؼّش‬ ٗ‫إٌّرع‬ ‫اٌٛؼذاخ‬ ‫ػذد‬ / )‫األٔماع‬ ‫ليّح‬
Dep. / Unit = (Initial Cost – Salvage Value) / (No. of Output units per
Design life)
( ‫ِصاي‬2)
ٌٝٚ‫األ‬ ٕٗ‫اٌغ‬ ٝ‫ف‬ ٗ‫إٌّرع‬ ‫اٌٛؼذاخ‬10000‫اٌص‬ ٕٗ‫اٌغ‬ ٝ‫ف‬ ٖ‫ٚؼذ‬ٗ‫أي‬24000ٝ‫ف‬ ‫اٌٛؼذاخ‬ ‫ػذد‬ ٚ ٖ‫ٚؼذ‬
ّٝ‫اٌرظّي‬ ‫اٌؼّش‬220000ٖ‫ٚؼذ‬
Dep. / Unit = (125000 – 15000) / 220000 = 0.5 / Unit
Dep. At year 1 = 0.5 X 10000 = 5000
Dep. At year 2 = 0.5 X 24000 = 12000
3.‫اٌغٕٛاخ‬ َ‫أسلا‬ ‫تّعّٛع‬ ‫اإل٘الن‬Sum of Year Digits
( ‫ِصاي‬3)
ٕٗ‫ِاوي‬‫اٌؽظٛي‬ ‫ذىٍفح‬125000)ٖ‫(اٌخشد‬ ‫األٔماع‬ ‫ليّح‬ ٚ ٗ‫ظٕي‬15000ٝ‫اإلفرشاػ‬ ‫اٌؼّش‬ ٚ10
‫عٕٛاخ‬
∑year digits
n: No of years, or n [(n+1) / 2] = 10 [(10 +1) / 2] = 10 X 5.5 = 55
Difference = Initial Cost – Salvage Value = 125000 –

51. ‫اٌؼّش‬ ٗ‫ِرثمي‬ ‫عٕٛاخ‬ ‫عٕٛاخ‬ َ‫أسلا‬ ‫ِط‬ / ٗ‫ِرثمي‬ ‫عٕٛاخ‬ ٗ‫اٌٍّٙى‬ ٗ‫اٌىّي‬ ‫اإل٘الن‬
‫اٌغٕٛاخ‬ َ‫أسلا‬ ‫ِعّٛع‬
4.ٗ‫اٌّؼاػف‬ ٗ‫اٌّرٕالظ‬ ٗٔ‫اٌّٛاص‬ ‫ؽشيمح‬
Double Declining – Balance Depreciation
( ‫ِصاي‬4)
‫اٌؽظٛي‬ ‫ذىٍفح‬ ٕٗ‫ِاوي‬125000)ٖ‫(اٌخشد‬ ‫األٔماع‬ ‫ليّح‬ ٚ ٗ‫ظٕي‬15000‫اٌؼ‬ ٚٝ‫اإلفرشاػ‬ ‫ّش‬
10‫عٕٛاخ‬
ّٝ‫اٌرظّي‬ ‫اٌؼّش‬ ‫ِمٍٛب‬ = ‫اإل٘الن‬ ‫ٔغثح‬ :‫أٚال‬% Dep. = 1 / n = 1 / 10 = 10 % / year
ٗ‫إٌغث‬ ٖ‫٘ز‬ ‫ػاػف‬ :‫شأيا‬Double this % = 2 X 10 % = 20 %
Dep. Year 1 = 0.2 X 125000 = 25000
ٕٗ‫اٌغ‬ ‫اٌٍّّٛن‬ ‫ذىٍفح‬ ‫اإل٘الن‬ ٗ‫إٌمذي‬ ّٗ‫اٌمي‬ ‫اإل٘الن‬ ‫ٔغثح‬ ‫اإل‬‫٘الن‬

52. ‫انث‬ ‫انثاب‬ ‫أْذاف‬ٍ‫اي‬
-‫اإلؼالي‬ ً‫ذؽٍي‬ ‫إظشاء‬ ‫ويفيح‬ ‫ِؼشفح‬
: ٍ‫انثاي‬ ‫انثاب‬‫اإلحالل‬Replacement
-‫اإلعرثذاي‬ ٚ ‫اإلؼالي‬ ً‫ذؽٍي‬
-‫ٚاظة‬8
-
Machine Initial Cost P = 1000, Salvage Value = Zero, Cost/ year A = 150 /
year, Increase in Cost / year G = 75/ year, i= 20 %
A(n = 0 (A/P 20%, 1) + 150 + 75 (A/G 20%, 1)
= 1000 (1.2000) + 150 + 75 (0.0000) = 1350 / year
A(n = = 1000 (A/P 20%, 2) + 150 + 75 (A/G 20%, 2)
= 1000 (0.8545) + 150 + 75 (0.4545) = 838.59 / year
A(n = = 1000 (A/P 20%, 3) + 150 + 75 (A/G 20%, 3)
0 (0.4747) + 150 + 75 (0.8721) = 690.63 / year
A(n = = 1000 (A/P 20%, 4) + 150 + 75 (A/G 20%, 4)
= 1000 (0.3863) + 150 + 75 (1.2742) = 631.87 / year
A(n =5) = 1000 (A/P 20%, 5) + 150 + 75 (A/G 20%, 5)
= 1000 (0.3344) + 150 + 75 (1.6405) = 607.44 / year
A(n = = 1000 (A/P 20%, 6) + 150 + 75 (A/G 20%, 6)
. . ) = . / year
A(n = = 1000 (A/P 20%, 7) + 150 + 75 (A/G 20%, 7)
= 1000 (0.2774) + 150 + 75 (2.2902) = 599.17 / year
A(n = ) = 1000 (A/P 20%, 8) + 150 + 75 (A/G 20%, 8)
= 1000 (0.2605) + 150 + 75 (2.8364) = 599.77 / year
A(n = = 610.83 / year
A(n = = 619.04 / year
A(n = = 627.80 / year
Replacement at n = year = 6

53. 6
AnnualCost Years
Year of Replacement