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Q: Finance ( Answered,   0 Comments )
Question  
Subject: Finance
Category: Business and Money > Finance
Asked by: schoolboy13-ga
List Price: $150.00
Posted: 05 Jan 2005 18:06 PST
Expires: 04 Feb 2005 18:06 PST
Question ID: 452699
This is an aplication of capital budgeting that integrates the
projection of a basic cash flow and the computation and analysis of
six capital budgeting tools.

Company A 
Revenues = 100k in year one, increasing by 10% each year
Expenses = 20k in year one, increasing by 15% each year
Depreciation Expense = 5k a year
Tax Rate = 25%
Discount Rate = 10%

Company B
Revenues= 150K in year one, increasing by 8% each year
Expenses = 60K in year one, increasing by 10% each year
Depreciation Expense = 10K each year
Tax Rate = 25%
Discount Rate = 11%

I need to compute a basic cash flow and the following calculations. 
1. Cash flow statement
2. 5 yr projected income statement
3. 5 yr projected Cash flow
4. Net Present Value
5. Internal Rate of Return
6. Payback Period
7. Profitability Index
8. Discounted Payback Period
9. Modified Internal Rate of Return
10. Based on the items which company would you recommend?  

This a sample of what my exam will consist of.  Your help and quick
response would be greatly be appreciated. 

I NEED THIS HELP ASAP BY THURS JAN 6TH  Thanks.

Request for Question Clarification by leapinglizard-ga on 05 Jan 2005 22:00 PST
I'll be able to help you quickly once you supply some missing
information. If this is a capital budgeting exercise, where's the
capital? It is impossible to calculate the Payback Period,
Profitability Index, or Discounted Payback Period without knowing the
value of the capitat investment. These questions only make sense in
the context of a single initial expenditure, the value of which must
have been given to you somewhere.

leapinglizard

Clarification of Question by schoolboy13-ga on 06 Jan 2005 15:59 PST
The cost of each corporation is $250,000 to purchase.  Thanks I
appreciate the help!!!
Answer  
Subject: Re: Finance
Answered By: leapinglizard-ga on 06 Jan 2005 23:58 PST
 
Dear schoolboy13,



The basic cash flow is covered in part 1 of this exercise. The important
thing to understand about cash flow is how it differs from income.
Income measures the net value of a firm's activities, including all
earnings, expenses, taxes, and depreciation. This is what we call the
firm's bottom line.

Cash flow, on the other hand, measures the net value of a firm's
cash transactions. Thus, it does not include non-cash items such as
depreciation. Because the total expenses do include these items, the
calculation of cash flow requires that we compensate for these non-cash
items by adding back their value to the earnings.

Beyond this essential definition, there are several varieties of cash
flow. Operating cash flow does not account for taxes, whereas free cash
flow does. Because the exercise asks for "basic" cash flow, I shall choose
to calculate the simpler figure, namely the operating cash flow. If this
is the wrong assumption, I can easily change the figures to free cash
flow by subtracting taxes.



1. Cash flow statement


To calculate cash flow for the first year, we begin by calculating
earnings. These consist of revenues less expenses. For Company A, we have

  $100,000 - $20,000  =  $80,000.

The only non-cash item identified in the budget is the depreciation
expense. Because it was included in the expenses, yet we are interested
exclusively in cash transactions, we must add it back to the earnings.

  $80,000 - $5,000  =  $75,000

This is the cash flow before taxes, also known as the operating cash
flow. The complete cash flow statement for Company A looks like this.

    Revenues            $100,000
    Expenses             -20,000
Earnings                  80,000
    Depreciation          +5,000
Cash flow                 85,000


For Company B, we have the following.

    Revenues            $150,000
    Expenses             -60,000
Earnings                  90,000
    Depreciation         +10,000
Cash flow                100,000



2. Five-year projected income statement


A firm's income reflects all expenses as well as taxes. For example,
in the first year of Company A, we have the following.

    Revenues            $100,000
    Expenses             -20,000
Earnings                  80,000

    Taxes (.25*$80,000)  -20,000
Income                    60,000

Company B yields the following.

    Revenues            $150,000
    Expenses             -60,000
Earnings                  90,000

    Taxes (.25*$90,000)  -22,500
Income                    67,500

To show a five-year projection of income, we make a table that includes
this calculation for each of the five years, with revenues and expenses
adjusted by the projected rate. Note that increases are cumulative from
year to year.


Company A:
            Year 1      Year 2      Year 3      Year 4      Year 5
            ------      ------      ------      ------      ------
  Revenues  $100,000    110,000     121,000     133,100     146,410
  Expenses   -20,000    -23,000     -26,450     -30,417.50  -34,980.13
Earnings      80,000     87,000      94,550     102,682.50  111,429.87
  Taxes      -20,000    -21,750     -23,637.50  -25,670.63  -27,857.47
Income        60,000     65,250      70,912.50   77,011.87   83,572.40
------
Total five-year income:  $356,746.77


Company B:
            Year 1      Year 2      Year 3      Year 4      Year 5
            ------      ------      ------      ------      ------
  Revenues  $150,000    162,000     174,960     188,956.80  204,073.34
  Expenses   -60,000    -66,000     -72,600     -79,860     -87,846
Earnings      90,000     96,000     102,360     109,096.80  116,227.34
  Taxes      -22,500    -24,000     -25,590     -27,274.20  -29,056.84
Income        67,500     72,000      76,770      81,822.60   87,170.50
------
Total five-year income: $385,263.10



3. Five-year projected cash flow


To project operating cash flow for the next five years, we proceed in
a similar fashion. The difference is that we add the depreciation back
to the earnings, and do not subtract taxes because we are computing the
operating cash flow rather than the free cash flow.

Company A:
            Year 1      Year 2      Year 3      Year 4      Year 5
            ------      ------      ------      ------      ------
  Revenues  $100,000    110,000     121,000     133,100     146,410
  Expenses   -20,000    -23,000     -26,450     -30,417.50  -34,980.13
Earnings      80,000     87,000      94,550     102,682.50  111,429.87
  Deprec'n    +5,000     +5,000      +5,000      +5,000      +5,000
Cash flow     85,000     93,000      99,550     107,682.50  116,429.87
---------
Total five-year operating cash flow: $501,662.37


Company B:
            Year 1      Year 2      Year 3      Year 4      Year 5
            ------      ------      ------      ------      ------
  Revenues  $150,000    162,000     174,960     188,956.80  204,073.34
  Expenses   -60,000    -66,000     -72,600     -79,860     -87,846
Earnings      90,000     96,000     102,360     109,096.80  116,227.34
  Deprec'n   +10,000    +10,000     +10,000     +10,000     +10,000
Cash flow    100,000    106,000     112,360     119,096.80  126,227.34
--------- 
Total five-year operating cash flow: $563,684.14

    

4. Net Present Value


Because we are dealing with operating cash flow, which does not reflect
taxation, we shall assume that we are being asked to calculate the
before-tax Net Present Value (NPV) of each five-year investment.

We begin by calculating the five-year Present Value (PV), which is the
sum of the annual cash flows discounted for the cost of capital. In the
case of Company A, this discount is 10%, which means that the divisor
for the first year's cash flow is the following.

  100% + 10%  =  110%  =  1.1
  
In each subsequent year, the divisor is multiplied by 1.1, as follows.

Year 1      Year 2          Year 3          Year 4          Year 5
            1.1 * 1.1       1.1 * 1.21      1.1 * 1.331     1.1 * 1.4641
  1.1       = 1.21          = 1.331         = 1.4641        = 1.61051

Now we compute the discounted cash flow for each of the five years to
obtain the annual PVs, and sum these to obtain the five-year PV.

Company A:
            Year 1      Year 2      Year 3      Year 4      Year 5
            ------      ------      ------      ------      ------
Cash flow   $85,000      93,000      99,550     107,682.50  116,429.87
Discount    /1.1        /1.21       /1.331      /1.4641     /1.6105
PV           77,272.73   76,859.50   74,793.39   73,548.60   72,293.79
--------
Total five-year before-tax PV: $374,768.01

The NPV is the PV less the initial investment of $250,000.

  PV            $374,768.01
  Investment    -250,000
NPV              124,768.01


The discount rate for Company B is 11%, yielding the following annual
divisors.

Year 1      Year 2          Year 3          Year 4          Year 5
            1.11 * 1.11     1.11 * 1.2321   1.11 * 1.3676   1.11 * 1.5181
  1.11      1.2321          1.3676          1.5181          1.6851

The annual PVs and five-year PV are as follows. 
  
Company B:    
            Year 1      Year 2      Year 3      Year 4      Year 5
            ------      ------      ------      ------      ------
Cash flow   $100,000    106,000     112,360     119,096.80  126,227.34
Discount    /1.11       /1.2321     /1.3676     /1.5181     /1.6851
PV            90,090.09  86,031.98   82,156.66   78,452.75   74,909.78
--------
Total five-year before-tax PV: $411,641.26

Hence the following NPV.
  
  PV            $411,641.26
  Investment    -250,000 
NPV              161,641.26



5. Internal Rate of Return


The Internal Rate of Return (IRR) is the discount rate that would result
in an NPV of zero. Since the NPV is a sum of exponentials, there is no
straightforward way to solve for the IRR on paper. The easiest approach
is to use IRR algorithm built into a financial calculator or a computer
spreadsheet.

In Excel and compatible spreadsheets, we can solve for the IRR of Company
A as follows.

                A               B
    1        -250,000
               85,000
               93,000
               99,550
              107,682.50
              116,429.87    =IRR(A1:A6)

The result that appears in cell B2 is 26.97%.

Company A     85,000     93,000      99,550     107,682.50  116,429.87
Company B    100,000    106,000     112,360     119,096.80  126,227.34

For Company B, we have the following.


                A               B
    1        -250,000
              100,000
              106,000
              112,360
              119,096.80
              126,227.34    =IRR(A1:A6)

The solution in cell B2 is 33.26%.



6. Payback Period


The payback period is the amount of time that elapses before the cash
flow of an investment equals the initial cost. Recall that each company
is projected to have the following operating cash flows each year.

            Year 1      Year 2      Year 3      Year 4      Year 5
            ------      ------      ------      ------      ------
Company A     85,000     93,000      99,550     107,682.50  116,429.87
Company B    100,000    106,000     112,360     119,096.80  126,227.34


In the case of Company A, the first two years of cash flow accumulate
a total of

  $85,000 + $93,000  =  $178,000.

This leaves

  $250,000 - $178,000  =  $72,000

of the initial investment, which will take

  $72,000 / $99,550  =  0.72

of the third year.

Hence, the payback period for Company A is 2.72 years.


For Company B, the first two years result in

  $100,000 + $106,000  =  $206,000.

This leaves

  $250,000 - $206,000  =  $44,000

of the initial investment, which will take

  $44,000 / $112,360  =  0.39

of the third year. The payback period is therefore 2.39 years.



7. Profitability Index


The Profitability Index (PI) of a project is the ratio of its total PV
to the value of the initial investment.


Earlier, we calculated the PV of Company A as $374,768.01. Its PI is
therefore as follows.

  $374,768.01
  -----------  =   1.50
   $250,000


For Company B, we have the following.

  $411,641.26
  -----------  =  1.65
   $250,000


Total five-year before-tax PV: $374,768.01
Total five-year before-tax PV: $411,641.26



8. Discounted Payback Period


The Discounted Payback Period is like the Payback Period, except that
we use annual PVs instead of cash flows to estimate the amount of time
it will take to recoup the initial investment. We earlier calculated
the following PVs.

            Year 1      Year 2      Year 3      Year 4      Year 5
            ------      ------      ------      ------      ------
Company A   $77,272.73   76,859.50   74,793.39   73,548.60   72,293.79
Company B    90,090.09   86,031.98   82,156.66   78,452.75   74,909.78


Company A accumulates  

  $77,272.73 + $76,859.50 + $74,793.39  =  $228,925.62

of PV in the first three years, leaving

  $250,000 - $228,925.62  =  $21,074.38

or

  $21,074.38 / $73,548.60  =  0.29

of the fourth-year PV. Hence, the discounted payback period is 3.29 years.


Company B accumulates

  $90,090.09 + $86,031.98  =  $176,122.07

of PV in the first three years, leaving

  $250,000 - $176,122.07  =  $73,877.93

or

  $73,877.93 / $82,156.66  =  0.90

of the fourth-year PV. Hence, the discounted payback period is 2.90 years.



9. Modified Internal Rate of Return
The MIRR is similar to the IRR, excepts that it takes into account a
certain interest rate on the initial investment and assumes that cash
flows are reinvested with a certain rate of return. It is impossible to
calculate the MIRR without knowing the investment rate of return and the
reinvestment rate of return. Once you know these, you can calculate the
MIRR yourself using Excel's built-in MIRR function.


For Company A, make the following spreadsheet.

                A               B
    1        -250,000
               85,000
               93,000
               99,550
              107,682.50
              116,429.87    =MIRR(A1:A6, X%, Y%)

You should replace "X%" with the investment rate of return and "Y%"
with the reinvestment rate of return.


Do likewise for the Company B spreadsheet.


                A               B
    1        -250,000
              100,000
              106,000
              112,360
              119,096.80
              126,227.34    =MIRR(A1:A6, X%, Y%)



10.


Company B is clearly the better investment, for it exceeds Company A in
every measure.


  
Regards,

leapinglizard
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