help: fxbcr dialog:

Title

fxbcr: Benefit-Cost Ratio (BCR)

Table of Contents

Syntax

Options

Description

References

*** Applications

(1) (CIF) Cash InFlow (Benefit)

(2) (COF) Cash OutFlow (Cost)

(3) (NCF) Net Cash Flow

(4) Nominal and Real Discount / Interest Rate

(4-1) (IR) Interest Rate

(4-2) (DR) Discount Rate

(4-3) (SR) Simple Discount / Interest Rate

(4-4) (Rn) Nominal Discount Rate

(4-5) (Rr) Real Discount Rate

(4-6) (FVF) Future Value Factor

(4-7) (PVF) Present Value Factor

(4-8) (EAR) Effective Annual Rate

(4-9) Discount Rate Converter

(6) Inflation and Deflation

(7) (BCR) Benefit-Cost Ratio (Profitability Index) (PI)

(8) (CBR) Cost-Benefit Ratio

*** Examples

Authors

Syntax

fxbcr lhs = rhs [if] [in] , [ dr(#) ddr def(#) inf(#) period(#)

list print sac(#) sap(#)]

Options

lhs Cash InFlow (Benefit)

rhs Cash OutFlow (Cost)

dr(#) Discount Rate (Integer Number) i.e, (8) that means (8 % or 0.08)
dr(#) default = (10%)

ddr Decimal Discount Rate, i.e, (7.6) that means (7.6 % or 0.076)

def(#) Use Deflation to Convert Cash Flows from Nominal to Real Values
Inflation Rate (Integer Number) i.e, (8) that means (8 % or 0.08)
inf(#) default = (0%)

inf(#) Use Inflation to Convert Cash Flows from Real to Nominal Values
Inflation Rate (Integer Number) i.e, (8) that means (8 % or 0.08)
inf(#) default = (0%)

sap(#) Sensitivity Analysis Scenario to Decrease/Increase Cash Inflow (Benefit)
sap(#) default = (10%)

sac(#) Sensitivity Analysis Scenario to Increase/Decrease Cash Outflow (Cost)
sac(#) default = (10%)

list Add UnDiscounted and Discounted Cash Flow Variables to Data List:

print Display UnDiscounted and Discounted Cash Flow Values:
(CIFu): UnDiscounted Cash Inflow (Benefit or Revenue)
(COFu): UnDiscounted Cash Outflow (Investment or Cost)
(NCFu): UnDiscounted Net Cash Flow
(CIFd): Discounted Cash Inflow (Benefit)
(COFd): Discounted Cash Outflow (Cost)

period(#) Period for Seasonal Discount Rate; default is (1)
pe(#) must be:
pe(1) Yearly Rate
pe(2) Half-Yearly Rate
pe(3) Third-Yearly Rate
pe(4) Quarter-Yearly Rate
pe(12) Monthly Rate
pe(7) Weekly Rate
pe(365) Daily Rate

*** Important Notes:
fxbcr generates some variables names starting with prefix "_":
So, you must avoid to include variables names with these prefixes

Description

fxbcr estimates Benefit-Cost Ratio (BCR).
fxbcr can estimate many projects at once, for comparison.
fxbcr can estimate seasonal data.

References

Frank J. Fabozzi & Pamela P. Peterson (2003)
"Financial Management and Analysis, 2nd Edition",
John Wiley & Sons, Inc..

Applications

(1) (CIF) Cash InFlow (Profit - Benefit)

* Definition:
* (CIF) = Summation of Cash Inflow values (Profit - Benefit)

(2) (COF) Cash OutFlow (Cost- Investment)

* Definition:
* (COF) = Summation of Cash Outflow values (Cost- Investment)

(3) (NCF) Net Cash Flow

* Formula:
(NCF) = (CIF) Cash InFlow (Benefit) - (COF) Cash OutFlow (Cost)
(NCF) = CIF - COF

* Definition:
* (NCF) = Summation of Net Cash Flow values

* Note:
1- (NCF) Must be Negative Number at least in First Observation
2- (NCF) Summation must be Positive

* Example:
clear all
sysuse fxbcr.dta, clear
fxbcr p1 = k1 , pe(1)

Suppose you have investment with the following expected cash flows, with discount rate (0.08)

+------+------------------------+-------------------------------+
| | (UnDiscounted Values) | (Discounted Values) |
| Time |------------------------+-------------------------------+
| | Cost Profit NCF | Cost Profit NCF |
| | COFu CIFu NCFu | COFd CIFd NCFd |
|------+------------------------+-------------------------------|
| 0 | 500 400 -100 | 500 400 -100 |
| 1 | 30 60 30 | 27.778 55.556 27.778 |
| 2 | 40 70 30 | 34.294 60.014 25.720 |
| 3 | 50 110 60 | 39.692 87.322 47.630 |
|------+------------------------+-------------------------------|
| Sum | 620 640 20 | 601.763 602.891 1.128 |
+------+------------------------+-------------------------------+

+---+------------------------+------------------------+-------------------------+
| T | COFd | CIFd | NCFd (NPV) |
|---+------------------------+------------------------+-------------------------+
| 0 | 500*(1+0.08)^0= 500 | 400*(1+0.08)^0= 400 | 400 - 500 =-100 |
| 1 | 30*(1+0.08)^1= 27.778 | 60*(1+0.08)^1= 55.556 | 55.556 - 27.778= 27.778 |
| 2 | 40*(1+0.08)^2= 34.294 | 70*(1+0.08)^2= 60.014 | 60.014 - 34.294= 25.720 |
| 3 | 50*(1+0.08)^3= 39.692 | 110*(1+0.08)^3= 87.322 | 87.322 - 39.692= 47.630 |
|---+------------------------+------------------------|-------------------------+
| Sum = 601.763 | = 602.891 | = 1.128 |
+----------------------------+------------------------+-------------------------+

(4) Nominal and Real Discount / Interest Rate

(4-1) (IR) Interest Rate

* Definition:

* The rate that will be between the commercial banks and their customers, whether they are individuals or companies

(4-2) (DR) Discount Rate

* Definition:

* The rate that will be between the Central Bank and Domestic Commercial Banks. This means that the central bank takes from commercial banks to cover liquidity needs.

* the interest rate, which the Central Bank lends to Domestic Commercial Banks.

* the interest rate at which future value are discounted to present value and vice versa.

(4-3) (SR) Simple Discount / Interest Rate

* Formula:
SR = Pmt x R * n

where:
Pmt= Payment
FV = Future Value
R = Discount Rate
n = Number of Periods

* Definition:

* Simple Discount / Interest Rate is used to calculate the interest accrued on a loan or savings account that has simple interest.
The simple interest formula is fairly simple to compute and to remember as principal times rate times time.

* The borrower pays the lender interest at regular periods within the term of the loan plus the principal and a single interest period payment at the end of the term.
In this case interest accrues only on the original principal sum and does not compound.

* Example:
SR = Pmt x R * n
= 100 * 0.08 * 4 = 32

FV = Pmt + SR
FV = 100 + 32 = 132

FV = Pmt x (1+ R * n )
= 100 * (1 + 0.08 * 4) = 132

Investment $100 this year at 8% interest rate over 4 years will give $132

(4-4) (Rn) Nominal Discount Rate

* Formula:
* Real Discount Rate (Rr):
Rr = (1 + Rn) ÷ (1 + F) – 1
Rr = (Rn- F) ÷ (1 + F)
Rr =~ Rn – F

where:
Rn = Nominal Discount Rate
Rr = Real Discount Rate
F = Inflation Rate

* Definition:

* Nominal Discount Rate is the rate before taking inflation into account.

* Nominal Discount Rate is the rate before removing inflation

* Example:
*** if Nominal Discount Rate (Rn = 8%), Inflation Rate (F = 5%)
* Real Discount Rate (Rr):
Rr = (1 + Rn) ÷ (1 + F) – 1 = (1 + 8%) ÷ (1 + 5%) – 1 = 2.857%
Rr = (Rn- F) ÷ (1 + F) = (8% - 5%) ÷ (1 + 5%) = 2.857%
Rr =~ Rn – F = 8% - 5% = 3.000%

(4-5) (Rr) Real Discount Rate

* Formula:
*** if Real Discount Rate (Rr = 8%), Inflation Rate (F = 5%)
* Nominal Discount Rate (Rn):
Rn = (1 + Rr) x (1 + F) - 1 = (1 + 8%) x (1 + 5%) – 1 = 13.400%
Rn = (Rr+ F) + (Rr x F) = (8% + 5%) x (8% x 5%) = 13.400%
Rr = (Rn+ F) x (1 + F) = (8% + 5%) x (1 + 5%) = 13.650%
Rn~= Rr + F = (8% + 5%) = 13.000%

where:
Rn = Nominal Discount Rate
Rr = Real Discount Rate
F = Inflation Rate

* Definition:

* Real Discount Rate is the rate after taking inflation into account.

* Real Discount Rate is the rate after removing inflation (deflation)

* Real Discount Rate is the rate that has been adjusted to remove the effects of inflation to reflect the real cost of capital, and the real yield to the lender.
The real interest rate of an investment is calculated as the amount by which the nominal interest rate is higher than the inflation rate.

* Real Discount Rate approximation is: Nominal Discount Rate - Inflation Rate.

Rr ~= Rn - F

* For example if Nominal Discount Rate (Rn = 5%), and Inflation Rate (F 3%), and the starting balance is $1000. Using the real rate of return formula would return a real rate of 1.942%.

Rr = [(1 + 0.05)/ (1 + 0.03)] - 1 = 0.01942 = 1.942%

With a $1000 starting balance, the individual could purchase $1019.42 of goods based on today's cost.

= 1000 * (1 + 0.01942) = 1019.42

This example of real rate of return formula can be checked by multiplying $1019.42 by (1.03), inflation rate plus one, which results in a $1050 balance which would be the normal return on a 5% yield.

= 1019.42 * (1 + 0.03) = 1050
= 1000.00 * (1 + 0.05) = 1050

* Example:
Rr = [(1 + Rn) ÷ (1 + F)] - 1
Rr = ([(1 + Rn) ÷ (1 + F)] - 1) x 100
Rr = [(1 + 0.05) / (1 + 0.03)] - 1 = 0.01942
Rr = ([(1 + 0.05) / (1 + 0.03)] - 1)* 100 = 1.942

(4-6) (FVF) Future Value Factor

* Formula:
FVF = (1 + R)^n

where:
R = Discount Rate
n = Number of Periods

* Definition:

Interest Rate Factor = V x (1 + R) = 1*1.10 = $1.10 ($ tomorrow /$ today)

Discount Rate Factor = V ÷ (1 + R) = 1/1.10 = $0.91 ($ today /$ tomorrow)

(4-7) (PVF) Present Value Factor

* Formula:
PVF = 1/(1 + R)^n

where:
R = Discount Rate
n = Number of Periods

(4-8) (EAR) Effective Annual Rate

* (EAR) or Effective Interest/Discount Rate (EIR)

* Formula:
EAR = (1 + R/n)^n - 1

where:
R = Periodic Interest Rate (day, week, month, ... etc.)
n = Number of Periods in the Year

* Definition:

* The equivalent simple annual interest rate resulting from the compounding frequency for a nominal annual interest rate.

* Example:
if annual interest rate (R=10%),
if there is Semi-Annual compounding, then (n=2)

Effective Annual Rate:
EAR = (1 + R/n)^n - 1
= (1 + 0.10/2)^2 - 1
= 1.05^2 - 1
= 0.1025 or 10.25%

----------------------------------------------------------
Frequency | Rate | t | Formula | Effective Annual Rate
----------------------------------------------------------
Annual | 10% | 1 | R | 10.00%
Semi-Annual | 10% | 2 | (1+R/2)^2-1 | 10.25%
Qua.-Annual | 10% | 4 | (1+R/4)^4-1 | 10.38%
Monthly | 10% | 12 | (1+R/12)^12-1 | 10.47%
Daily | 10% | 365 | (1+R/365)^365-1 | 10.5156%
Continuous | 10% | | exp^R-1 | 10.5171%
----------------------------------------------------------

-------------------------------------------
* Quarter-Effective Annual Rate (R = 0.08)
-------------------------------------------
Time | PMT | NFV | Diff.
-------------------------------------------
| (1) | (2) | (3)
-------------------------------------------
1 | 1.0000 | 1.02000 | 0.02000
2 | 1.0200 | 1.04040 | 0.02040
3 | 1.0404 | 1.06121 | 0.02081
4 | 1.0612 | 1.08243 | 0.02122
-------------------------------------------
Sum | | | 0.08243
-------------------------------------------

(1) = Beginning Value in Period (m)
(2) = Ending Value in Period (m) = [(1 + R/m)^n]
(3) = (2) - (1)
n = Total Number of Periods in the Year
m = Period Number (m) in the Year

EAR = (0.02000 + 0.02040 + 0.02081 + 0.02122)
= 0.08243 = 8.243%

EAR = (1.08243 - 1) / 1 = 0.08243 = 8.243%

EAR = (1 + R/n)^n - 1
= (1 + 0.08/4)^4 - 1
= 0.08243 = 8.243%

(4-9) Discount Rate Converter

* Formula:
-----------------------------------------------------------------------------------------------
From \ To | Month | Quarter-Year | Half-Year | Year |
-----------------------------------------------------------------------------------------------
Month |((1+R/12)^1-1)*12 |((1+R/12)^3-1)*4 |((1+R/12)^6-1)*2 |((1+R/12)^12-1)*1 |
Quarter-Year|((1+R/4)^(1/3)-1)*12 |((1+R/4)^1-1)*4 |((1+R/4)^2-1)*2 |((1+R/4)^4-1)*1 |
Half-Year |((1+R/2)^(1/6)-1)*12 |((1+R/2)^(1/2)-1)*4|((1+R/2)^(1/1)-1)*2|((1+R/2)^2-1)*1 |
Year |((1+R/1)^(1/12)-1)*12|((1+R/1)^(1/4)-1)*4|((1+R/1)^(1/2)-1)*2|((1+R/1)^(1/1)-1)*1|
-----------------------------------------------------------------------------------------------

* Interest Rate Converter enables you to convert interest rate payable at any frequency into an equivalent rate in another frequency.
For instance, you can convert interest rate from annual to semi annual or monthly to annual, quarterly etc.

* If the cash flows are NOT yearly but at any other uniform intervals like monthly, quarterly, semi annual, etc, IRR needs to be annualized with appropriate factor to calculate effective annual (IRR);

* to calculate Interest Rate (R) or (IRR) for monthly cash flows, we have to first calculate IRR for these cash flows using IRR function and then we need to annualize the result by using the factor [(1+IRR)^12]-1,
where IRR is the IRR calculated for montly cash flows.

for seasonal cash flow, the period transformations will be:
----------------------------------------------------------------------------
| Year | Half-Year | Third-Year | Quarter-Year | Month | Week | Day |
| 1 | 2 | 3 | 4 1 2.167 | 52.143 | 365 |
----------------------------------------------------------------------------

(6) Inflation and Deflation

* Inflation: convert value in present time (2015) to equivalent value in future time (2020)

* Deflating: convert value in future time (2020) to equivalent value in present time (2015)

- if Nominal Discount Rate (Rn) > Inflation Rate (F)
==> Real Discount Rate (Rr) == Positive

- if Nominal Discount Rate (Rn) < Inflation Rate (F)
==> Real Discount Rate (Rr) == Negative

** Irving Fisher’s (1930) Equation

generalized relationship between real discount rate of and nominal discount rate is expressed as follow under Fisher’s equation:

(1 + Rn) = (1 + Rr) × (1 + F)

where:
Rn = Nominal Discount Rate
Rr = Real Discount Rate
F = Inflation Rate

Nominal Cash Flows = Real Cash Flows × (1 + F)^t
Real Cash Flows = Nominal Cash Flows ÷ (1 + F)^t

-------------------------------------------------------------------
*** if Nominal Discount Rate (Rn = 8%), Inflation Rate (F = 5%)
* Real Discount Rate (Rr):
Rr = (1 + Rn) ÷ (1 + F) – 1 = (1 + 8%) ÷ (1 + 5%) – 1 = 2.857%
Rr = (Rn- F) ÷ (1 + F) = (8% - 5%) ÷ (1 + 5%) = 2.857%
Rr = Rn – F = 8% - 5% = 3.000%

-------------------------------------------------------------------
*** if Real Discount Rate (Rr = 8%), Inflation Rate (F = 5%)
* Nominal Discount Rate (Rn):
Rn = (1 + Rr) x (1 + F) - 1 = (1 + 8%) x (1 + 5%) – 1 = 13.400%
Rn = (Rr+ F) + (Rr x F) = (8% + 5%) x (8% x 5%) = 13.400%
Rr = (Rn+ F) x (1 + F) = (8% + 5%) x (1 + 5%) = 13.650%
Rn = Rr + F = (8% + 5%) = 13.000%

-------------------------------------------------------------------
*** (Rnr): Convert Nominal to Real Cash Flow Variables:
NCFu_n = UnDiscounted Nominal Net Cash Flow
NCFu_r = UnDiscounted Real Net Cash Flow (Deflated)
NCFd_n = Discounted Nominal Net Cash Flow
NCFd_r = Discounted Real Net Cash Flow (Deflated)
Nominal Discount Rate (Rn = 8%)
Inflation Rate ( F = 5%)
-------------------------------------------------------------------
Deflation Method (1) | Deflation Method (2)
-------------------------------------------------------------------
| F(5%) |NCFu_n| NCFu_r | Rn(8%)| NCFd_r | Rnr |NCFu_n| NCFd_r
t |---------------------------------------------------------------
| (1) | (2) | (3) | (4) | (5) | (6) | (7) |(8)
-----------------------------------|-------------------------------
0 | 1 |-100 |-100 | 1 |-100 | 1 | -100 |-100
1 | 0.952 | 30 | 28.571 | 0.926 | 26.455 | 0.882 | 30 | 26.455
2 | 0.907 | 30 | 27.211 | 0.857 | 23.329 | 0.778 | 30 | 23.329
3 | 0.864 | 60 | 51.830 | 0.794 | 41.145 | 0.686 | 60 | 41.145
-------------------------------------------------------------------
NPV -9.0715 | NPV -9.0715
IRR1 3.3842 % | IRR1 8.5534 %
IRR2 8.5534 % | IRR2 3.3842 %
-------------------------------------------------------------------
(1) = 1/(1+F)^t | Rnr =(1+Rn)x(1+F)-1=13.4%
(3) = (1) x (2) | (6) = 1/(1+Rrn)^t
(4) = 1/(1+Rn)^t | (8) = (6) x (7)
(5) = (3) * (4) | IRR2= (1+IRR1) ÷ (1+F)-1
IRR2= (1+IRR1) x (1+F)-1 |
-------------------------------------------------------------------

-------------------------------------------------------------------
*** (Rrn): Convert Real to Nominal Cash Flow Variables:
NCFu_n = UnDiscounted Nominal Net Cash Flow
NCFu_r = UnDiscounted Real Net Cash Flow (Deflated)
NCFd_n = Discounted Nominal Net Cash Flow
Nominal Discount Rate (Rn = 8%)
Inflation Rate ( F = 5%)
------------------------------------------------------------
No Inflation | Inflation
----------------------------|-------------------------------
| Rn(8%)| NCFu_n| NCFd_n | F(5%) | NCFu_r| Rrn | NCFd_n
t -------------------------|-------------------------------
| (1) | (2) | (3) | (4) | (5) | (6) | (7)
----------------------------|-------------------------------
0 | 1 | -100 | -100 | 1 |-100 | 1 | -100
1 | 0.926 | 30 | 27.778 | 0.952 | 28.57 | 0.972 | 27.778
2 | 0.857 | 30 | 25.720 | 0.907 | 27.21 | 0.945 | 25.720
3 | 0.794 | 60 | 47.630 | 0.864 | 51.83 | 0.919 | 47.630
----------------------------|--------------------------------
NPV 1.1279 | NPV 1.1279
IRR1 8.5534 % | IRR1 3.3842 %
IRR2 3.3842 % | IRR2 8.5534 %
----------------------------|--------------------------------
(1) = 1/(1+Rn)^t | (4) = 1/(1+F)^t
(3) = (1) x (2) | (5) = (2) x (4)
| (6) = 1/(1+Rrn)^t
Rrn = (Rn-F)/(1+F)= 2.86% | (7) = (4) x (6)
--------------------------------------------------------------------

--------------------------------------------------------------------------------------
NCFu_n = UnDiscounted Nominal Net Cash Flow
NCFu_r = UnDiscounted Real Net Cash Flow (Deflated)
NCFd_n = Discounted Nominal Net Cash Flow
NCFd_r = Discounted Real Net Cash Flow (Deflated)
Nominal Discount Rate (Rn = 8%)
Inflation Rate ( F = 5%)
--------------------------------------------------------------------------------------
| No Inflation | Nominal to Real | Real to Nominal
t |-----------------------------------------------------------------------------------
|Rn(8%) |NCFu_n| NCFd_n | F(5%) | NCFu_r |Rn(8%) | NCFd_r | NCFd_r | NCFd_n | NCFu_n
--------------------------------------------------------------------------------------
| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
--------------------------------------------------------------------------------------
0 | 1 | -100 | -100 | 1 | -100 | 1 | -100 | -100 |-100 | -100
1 | 0.926 | 30 | 27.778 | 0.952 | 28.571 | 0.926 | 26.455 | 26.455 | 27.778 | 30
2 | 0.857 | 30 | 25.720 | 0.907 | 27.211 | 0.857 | 23.329 | 23.329 | 25.720 | 30
3 | 0.794 | 60 | 47.630 | 0.864 | 51.830 | 0.794 | 41.145 | 41.145 | 47.630 | 60
--------------------------------------------------------------------------------------
- | | 20 | 1.1279 | | 7.6126 | |-9.0715 |-9.0715 | 1.1279 | 20
--------------------------------------------------------------------------------------
(1) = 1/(1+Rn)^t | (4) = 1/(1+F)^t | (8) = (7)
(3) = (1) x (2) | (5) = (2) x (4) | (9) = (8) ÷ (4)
| (6) = 1/(1+Rn)^t | (10)= (9) ÷ (1)
| (7) = (5) x (6) |
--------------------------------------------------------------------------------------

Rnr =(1+Rn)x(1+F)-1=13.4%

(1) = 1/(1+Rn)^t [Rn = 0.8%)]
(3) = (1) x (2)
(4) = 1/(1+F)^t
--------------------------------------------------------
(5) = (2) x (4)
(6) = 1/(1+Rnr)^t [Rnr = (Rn-F)/(1+F) = 2.86%]
(7) = (5) x (6)
--------------------------------------------------------
(8) = (1+Rrn)^t [Rrn = (1+Rnr) * (1+F) - 1 = 0.8%]
(9) = (7)
(10)= (8) x (9)
--------------------------------------------------------

(7) (BCR) Benefit-Cost Ratio (Profitability Index) (PI)

* Profitability Index (PI) = Benefit-Cost Ratio (BCR)

* Formula:
(BCR) = (CIF) Cash InFlow (Benefit) ÷ (COF): Cash OutFlow (Cost)

* Definition:

* (BCR) Benefit-Cost Ratio or Profitability Index (PI) is ratio of present value of future operating cash inflows to present value of investment cash flows.
(PI) tells us whether investment would increase owners’ wealth.
Because (PI) does not give us a dollar measure of the increase in value, we cannot use it to choose among mutually exclusive projects.
But (PI) does help us to rank projects when there is capital rationing.

* Decision Rule:
1- if (BCR>1): Accept Project (Investment is Expected to Increase Profit)
Investment Returns more than $1 in present value for every $1 invested.

2- if (BCR<1): Regect Project (Investment is Expected to Decrease Profit)
Investment Returns less than $1 in present value for every $1 invested

3- if (BCR=1): Accept or Regect Project (Investment is Expected Not to Change Profit)
Investment Returns $1 in present value for every $1 invested

* (PI) Advantages:

1. Tells whether an investment increases the firm's value

2. Considers all cash flows of the project

3. Considers the time value of money

4. Considers the risk of future cash flows (through the cost of capital)

5. Useful in ranking and selecting projects when capital is rationed

* (PI) Disadvantages:

1. Requires an estimate of the cost of capital in order to calculate the profitability index

2. May not give the correct decision when used to compare mutually exclusive projects.

* Example:
(BCR) = (CIF) Cash InFlow (Benefit) ÷ (COF): Cash OutFlow (Cost)
(BCRu)= [(30.000 + 30.000 + 60.000) ÷ 100] = 120.0000 ÷ 100 = 1.2000 = (120.00 %)
(BCRd)= [(27.778 + 25.720 + 47.630) ÷ 100] = 101.1279 ÷ 100 = 1.0113 = (101.13 %)

(8) (CBR) Cost-Benefit Ratio

* Formula:
(CBR) = (COF): Cash Outflow (Cost) ÷ (CIF) Cash Inflow (Benefit)

* Definition:

* (CBR) Cost-Benefit Ratio is the inverse of Profitability Index (PI), it is the ratio of present value of investment cash flows to present value of the future operating cash inflows. (CBR) tells us whether investment would increase owners’ wealth.
Because (CBR) does not give us a dollar measure of the increase in value, we cannot use it to choose among mutually exclusive projects.
But (CBR) does help us to rank projects when there is capital rationing.

* Decision Rule:
1- if (CBR<1): Accept Project (Investment is Expected to Increase Profit)
Investment Returns more than $1 in present value for every $1 invested.

2- if (CBR>1): Regect Project (Investment is Expected to Decrease Profit)
Investment Returns less than $1 in present value for every $1 invested

3- if (CBR=1): Accept or Regect Project (Investment is Expected Not to Change Profit)
Investment Returns $1 in present value for every $1 invested

* (CBR) Advantages:

1. Tells whether an investment increases the firm's value

2. Considers all cash flows of the project

3. Considers the time value of money

4. Considers the risk of future cash flows (through the cost of capital)

5. Useful in ranking and selecting projects when capital is rationed

* (CBR) Disadvantages:

1. Requires an estimate of the cost of capital in order to calculate the profitability index

2. May not give the correct decision when used to compare mutually exclusive projects.

* Example:
(CBR) = (COF): Cash Outflow (Cost) ÷ (CIF) Cash Inflow (Benefit)
(CBRu)= [100 ÷ (30.000 + 30.000 + 60.000)] = 100 ÷ 120.0000 = 0.8333 = (83.33 %)
(CBRd)= [100 ÷ (27.778 + 25.720 + 47.630)] = 100 ÷ 101.1279 = 0.9888 = (98.88 %)

Examples

clear all

sysuse fxbcr.dta, clear

fxbcr p1 = k1 , pe(1) dr(8) print list

fxbcr p1 = k1 , pe(1) dr(8) print list inf(5)

fxbcr p1 = k1 , pe(1) dr(8) print list def(5)

fxbcr p1 = k1 , pe(1) dr(8) print list

fxbcr p1 = k1 , pe(1) dr(8) print list sac(1) sap(-1)

----------------------------------------------------------

fxbcr p1 p2 p3 p4 p5 = k1 k2 k3 k4 k5 , print list

----------------------------------------------------------

fxbcr p1 = k1 , pe(1) print list

fxbcr p1 = k1 , pe(12) print list

fxbcr p1 = k1 , pe(1) dr(8) print list

fxbcr p1 = k1 , pe(1) dr(8) print list sac(5) sap(5)

fxbcr p1 = k1 , pe(1) dr(8) print list sac(5) sap(-5)

clear all
sysuse fxbcr.dta, clear
fxbcr p1 = k1 , pe(1) print list

========================================================================================
*** Benefit-Cost Ratio (BCR) ***
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========================================================================================
*** Benefit-Cost Ratio (BCR) for Project (1): [ p1 = k1 ]
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* (AN): Number of Periods = 4 (Year)
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* (ADR): Discount Rate (8.000 %) = 0.0800 (Year)
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*** Criterion *** * UnDiscount * | * Discount * (adr= 8.00 %)
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1- (CIF): Cash Inflow (Benefit) = 640.000 | 602.891
2- (COF): Cash Outflow (Cost) = 620.000 | 601.763
3- (NCF): Net Cash Flow = 20.000 | 1.128
----------------------------------------------------------------------------------------
4- (BCR): Benefit-Cost Ratio = 1.200 (120.00 %) | 1.011 (101.13 %)(Year)
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5- (CBR): Cost-Benefit Ratio = 0.833 ( 83.33 %) | 0.989 ( 98.88 %)(Year)
----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------
*** UnDiscounted and Discounted Cash Flow Values ***

+-----------------------------------------------------------------------------+
| Time CIF_u COF_u NCF_u CIF_d COF_d NCF_d |
|-----------------------------------------------------------------------------|
| 0.000 400.000 500.000 -100.000 400.000 500.000 -100.000 |
| 1.000 60.000 30.000 30.000 55.556 27.778 27.778 |
| 2.000 70.000 40.000 30.000 60.014 34.294 25.720 |
| 3.000 110.000 50.000 60.000 87.322 39.692 47.630 |
|-----------------------------------------------------------------------------|
| 6.000 640.000 620.000 20.000 602.891 601.763 1.128 |
+-----------------------------------------------------------------------------+
* (CIF_u) & (CIF_d): UnDiscounted & Discounted Cash INFlow (Benefit)
* (COF_u) & (COF_d): UnDiscounted & Discounted Cash OUTFlow (Cost)
* (NCF_u) & (NCF_d): UnDiscounted & Discounted Net Cash Flow (Benefit-Cost)
----------------------------------------------------------------------------------------

Authors

- Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
Email: emadstat@hotmail.com
WebPage at IDEAS: http://ideas.repec.org/f/psh494.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm

- Sahra Khaleel A. Mickaiel
Professor (PhD Economics)
Cairo University - Faculty of Agriculture - Department of Economics - Egypt
Email: sahra_atta@hotmail.com
WebPage at IDEAS: http://ideas.repec.org/f/pmi764.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/pmi764.htm

FXBCR Citation

Mickaiel, Sahra Khaleel A. & Emad Abd Elmessih Shehata (2016)

FXBCR: "Stata Module to Estimate Benefit-Cost Ratio (BCR)"

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