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 |