Hi!!
Rate of Return. Steady As She Goes, Inc. will pay a year-end dividend
of $3 per share. Investors expect the dividend to grow at a rate of 4
percent indefinitely.
a. If the stock currently sells for $30 per share, what is the
expected rate of return on the stock?
The Gordon Growth Formula, also known as The Constant Growth Formula,
for stock valuation assumes that a company grows at a constant rate
forever, and states that:
P0 = D1 / (K - g)
Where:
P0 = Today's Price
D1 = The next dividend
K = Rate of Return
g = Growth Rate
Then:
K = D1/P0 + g =
= $3/$30 + 0.04 =
= 0.1 + 0.04 =
= 0.14 or 14%
The expected rate of return on the stock is 14% .
b. If the expected rate of return on the stock is 16.5 percent, what
is the stock price?
Again we can use the constant growth formula:
P0 = D1 / (K - g)
Where:
P0 = Today's Price
D1 = The next dividend
K = Rate of Return
g = Growth Rate
Then
P0 = D1 / (K - g) =
= $3 / (0.16 - 0.04) =
= $3 / 0.12 =
= $25
If the expected rate of return on the stock is 16.5 percent, the stock
price is $25.
For further reference see:
"Basis for Valuation of Financial Securities":
http://www.ssc.uwo.ca/bacs/courses/310/peters/VALUATION%20OF%20FINANCIAL%20SECURITIES%20FOR%20FINAL%20EXAM.pdf
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Refer to two projects with the following cash flows:
Year Project A Project B
0 ?$200 ?$200
1 80 100
2 80 100
3 80 100
4 80
What is the payback period of each project?
Payback Period (PB) calculation give us an idea on how long it will
take for a project to recover the initial investment.
If Y is the year before the full recovery of the investment I, U is
the unrecovered cost at the start of last year and CFi is the CF of
the year Y+1 then:
PB = Y + U/CFi
Project A:
The initial investment is $200 and you will recover it during the 3rd year, then:
Y = 2
and
U = $200 - $80 - $80 = $40
Then:
PB(A) = 2 + $40/$80 = 2 + 0.5 = 2.5 years
For the project A the payback period is 2 years and six months.
Project B:
The initial investment is $200 and you will recover it during the 2nd year, then:
Y = 1
and
U = $200 - $100 = $100
Then:
PB(B) = 1 + $100/$100 = 1 + 1 = 2 years
For the project B the payback period is exactly 2 years.
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Cash Flows and Working Capital.
A house painting business had revenues of $16,000 and expenses of
$9,000. There were no depreciation expenses. However, the business
reported the following changes in working capital:
Beginning End
Accounts receivable $1,200 $4,500
Accounts payable 700 300
Calculate net cash flow for the business for this period.
First thing you must remember is that Net working capital (often
referred to simply as working capital) is the difference between a
company?s short-term assets and liabilities:
net working capital = Current assets minus current liabilities.
The principal short-term assets are cash, accounts receivable
(customers?unpaid bills), and inventories of raw materials and
finished goods. The principal short-term liabilities are accounts
payable (bills that you have not paid), notes payable, and accruals
(liabilities for items such as wages or taxes that have recently been
incurred but have not yet been paid).
Then the current working capital (working capital at end of this year) is:
Current WC = $4,500 - $300 = $4,200
And the previous year working capital (working capital at the
beginning of this year) is:
Previous Year WC = $1,200 - $700 = $500
Recall the formula to calculate the cash flow of one year:
CF = R - E - T - ChWC
where:
CF = cash flow
Ri = total revenues of the year
E = expenses of the year
D = depreciations for the year
T = taxes for the year = t*(R - E - D) with t = tax rate
ChWCi = Working Capital Change for the year =
= Current WC - Previous Year WC
Since taxes are not mentioned in the statement we must ignore this
part of the formula, then for this problem:
CF = R - E - ChWC =
= R - E - (Current WC - Previous Year WC) =
= $16,000 - $9,000 - ($4,200 - $500) =
= $16,000 - $9,000 - $3,700 =
= $3,300
The net cash flow for this period is $3,300.
See for references:
"How To Prepare a Cash Flow Statement: Indirect Method":
http://www.finetuning.com/articles/p3-932-how-to-prepare-a-cash-flow-statement.html
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Project Evaluation.
Kinky Copies may buy a high-volume copier. The machine costs $100,000
and will be depreciated straight-line over 5 years to a salvage value
of $20,000. Kinky anticipates that the machine actually can be sold in
5 years for $30,000. The machine will save $20,000 a year in labor
costs but will require an increase in working capital, mainly paper
supplies, of $10,000. The firm?s marginal tax rate is 35 percent and
the discount rate is 8 percent.
Should Kinky buy the machine?
The initial investment is $100,000 for the copier plus $10,000 in
working capital, for a total outlay of $110,000.
Depreciation expense = ($100,000 - $20,000)/5 = $16,000 per year
The project saves $20,000 in annual labor costs, so the net operating
cash flow (including the depreciation tax shield) is, for years 1 to
5:
CF = $20,000 * (1 - 0.35) + ($16,000 * 0.35) = $18,600
In addition, due project termination at year 5, the copier is sold for
$30,000, which generates net-of-tax proceeds of:
$30,000 - (0.35 * $10,000) = $26,500
And the working capital associated with the project is freed up, which
releases another $10,000 in cash.
Then, non-operating cash flow in year 5 totals $36,500.
The NPV is PV of the cash flows - Initial Investment (I) :
NPV = PV of Cash Flows - I
then:
NPV = [$18,600 * annuity factor(8%, 5 Years)] + [$36,500/(1.08)^5] - I =
= $18,600 * 3.993 + $36,500/1.469 - $110,000 =
= $74,269.80 + $24,846.83 - $110,000 +
= $99,116.63 - $110,000 = -$10,883.37
Since the project's NPV is negative, Kinky?s should not buy the new copier.
For references on annuity factors and annuity PV see:
"Annuities":
http://www.netmba.com/finance/time-value/annuity/
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I hope that this helps you. Feel free to request for a clarification
if you need it.
Regards,
livioflores-ga |
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