Engineering economics formula sheet

Engineering Economics Formula Sheet

1. ©Haris H.
Engineering Economics Formula Sheet
The future amount of present amount � = � (1+�)
�

The present value of a future amount: � = � (1+�)
−�
=�
1
(1+??????)
??????

The factor (1+i)
-n
is sometimes called the present worth factor,���(�,�). Thus, P = F(1+i)
-n
= F PWF(i,n)
Future Value of a Series of Payments
The future value, F, of a series of equal annuities A, that accrue interest at a rate, I, over n periods is:
��
� =  
i
1i)(1A
n

Present Value of a Series of Annuities
�
� = present value of n payments of amount A = present amount that is equal to a series of payments, A, for n years
��
�= 




 

i
i)(11
A
n =
(1+�)
�
−1
�(1+�)
�
Uniform Gradient Series Annual Equivalent Amount
Annual equivalent amount of a series with an amount of A1 at the end of 1
st
year & with an equal increment (G)
�=�1+�
(1+??????)
??????
−??????�−1
�(1+??????)
??????
−??????

Revenue-Dominated cash flow analysis
P = Initial investment Rn = Net revenue at the end of nth year S = Salvage value at the end of nth year
��=−�+�
1
1
(1+�)
1
+⋯+�
�
1
(1+�)
�
+�
1
(1+�)
�

Future Worth Criterion Cost-Dominated cash flow analysis
��=�(1+�)
�
+�
1(1+�)
�−1
+�
1(1+�)
�−2
+⋯+�
�(1+�)
�−�
+�
�−�
Rate of Return (IRR): I��=??????
�+
�????????????
�????????????−�????????????
(I
H−I
L)
If IRR > MARR, accept the project. If IRR = MARR, remain indifferent. If IRR < MARR, reject the project.
Depreciation
Straight Line Depreciation Method:
&#3627408439;
&#3627408481;=
&#3627408451;−??????
&#3627408475;
&#3627408437;
&#3627408481;=&#3627408451;−&#3627408481;[
&#3627408451;−??????
&#3627408475;
]=&#3627408451;−&#3627408481;&#3627408439;
&#3627408481;
Declining Balance Depreciation Method
&#3627408439;
&#3627408481;=?????? ×&#3627408437;
&#3627408481;−1= ?????? (1 − ??????)
&#3627408481;−1
×&#3627408451;= ??????×
&#3627408437;??????
1−&#3627408446;
&#3627408437;
&#3627408481;=(1−??????)×&#3627408437;
&#3627408481;−1=(1 − ??????)
&#3627408481;
×&#3627408451;
Sum-of-years' digits method
&#3627408439;
&#3627408481;=
&#3627408475;−&#3627408481;+1
??????(??????+1)
2
(&#3627408451;−&#3627408454;) &#3627408437;
&#3627408481;=(&#3627408451;−&#3627408454;)
(&#3627408475;−&#3627408481;)
&#3627408475;
(&#3627408475;−&#3627408481;+1)
(&#3627408475;+1)
+&#3627408454;
Sinking Fund method of depreciation
&#3627408439;
&#3627408481;=(&#3627408451;−&#3627408454;)[
??????
(1+??????)
??????
−1
](1+&#3627408470;)
&#3627408481;−1
&#3627408437;
&#3627408481;=&#3627408451;− (&#3627408451;−&#3627408454;)[
??????
(1+??????)
??????
−1
]
(1+??????)
??????
−1
??????
=&#3627408451;−&#3627408439;
&#3627408481;
(1+??????)
??????
−1
??????(1+??????)
??????−1

Conventional Benefit / Cost (B/C) Ratio with Present Worth
&#3627408437;
&#3627408438;
&#3627408453;&#3627408462;&#3627408481;&#3627408470;&#3627408476;=
&#3627408463;&#3627408466;&#3627408475;&#3627408466;&#3627408467;&#3627408470;&#3627408481;&#3627408480;−&#3627408439;&#3627408470;&#3627408480;&#3627408463;&#3627408466;&#3627408475;&#3627408466;&#3627408467;&#3627408470;&#3627408481;&#3627408480;
&#3627408438;&#3627408476;&#3627408480;&#3627408481;
=
&#3627408437;−&#3627408439;
&#3627408438;

Make or Buy Decisions
Formula for Purchase model (EOQ) and TC for each model are given as:
&#3627408440;&#3627408450;&#3627408452;=√
2(&#3627408436;&#3627408475;&#3627408475;&#3627408482;??????&#3627408473; ??????&#3627408480;????????????&#3627408466; ??????&#3627408475; &#3627408482;&#3627408475;??????&#3627408481;&#3627408480;)(&#3627408450;&#3627408479;&#3627408465;&#3627408466;&#3627408479; &#3627408438;&#3627408476;&#3627408480;&#3627408481;)
(&#3627408436;&#3627408475;&#3627408475;&#3627408482;??????&#3627408473; &#3627408438;??????&#3627408479;&#3627408479;????????????&#3627408475;?????? &#3627408438;&#3627408476;&#3627408480;&#3627408481; &#3627408477;&#3627408466;&#3627408479; &#3627408482;&#3627408475;??????&#3627408481;)
&#3627408452;
1=√
2&#3627408438;0&#3627408439;
&#3627408438;??????
&#3627408455;&#3627408438;=&#3627408439;&#3627408451;+
&#3627408439;&#3627408438;0
&#3627408452;1
+
&#3627408452;1&#3627408438;??????
2

Manufacturing model
&#3627408452;
2=√
2&#3627408438;0&#3627408439;
&#3627408438;??????(1−&#3627408479;/&#3627408472;)
&#3627408455;&#3627408438;=&#3627408439;&#3627408451;+
&#3627408439;&#3627408438;0
&#3627408452;2
+
&#3627408452;2&#3627408438;??????(&#3627408472;−&#3627408479;)
2&#3627408472;

Break-even point
&#3627408437;&#3627408440;&#3627408451;=
&#3627408441;&#3627408438;
&#3627408454;&#3627408466;????????????&#3627408470;&#3627408475;&#3627408468; &#3627408464;&#3627408476;&#3627408480;&#3627408481;/&#3627408482;&#3627408475;&#3627408470;&#3627408481; −&#3627408457;&#3627408462;&#3627408479;&#3627408470;&#3627408462;&#3627408463;??????&#3627408466; &#3627408438;&#3627408476;&#3627408480;&#3627408481;/&#3627408456;&#3627408475;&#3627408470;&#3627408481;
=&#3627408459;=
&#3627408441;&#3627408438;
&#3627408451;−&#3627408457;



0 1 2 3 n
A