Problem 1. (2 points) Net Working Capital should be considered in project cash flows
because:
(a)
(b)
(c)
(d)
Firms must invest cash in short–term assets to produce finished goods
They are sunk costs
Firms need positive NPV projects for investment
None of the above
Solution: (a) only.
Problem 2. (3 points) A company has forecasted sales in the first 3 months of the year
as follows (figures in millions): January, $60; February, $120; March, $240. 60% of sales
are usually paid for in the month that they take place and 40% in the following month.
Receivables at the end of December were $24 million. What are the forecasted collections
on accounts receivable in March?
Solution:
0.6 · $240 million + 0.4 · $120 million = $192 million.
Problem 3. (3 points) Given the following data: Sales = $4,000, Cost of goods sold
= $1,600, Average total assets = $1,600, Average inventory = $200, calculate the asset
turnover ratio.
Solution:
Asset turnover =
$4, 000
sales
=
= 2.5.
average total assets
$1, 600
Problem 4. (3 points) Given the following data: EBIT = $140, Depreciation = $40,
Interest = $20, Dividends = $10, calculate the Times–Interest–Earned ratio.
Solution:
T imes–Interest–Earned =
EBIT
$140
=
= 7.
interest payments
$20
Problem 5. (2 points) When a firm improves (lowers) its days in inventories it generally:
(a)
(b)
(c)
(d)
Requires additional cash investment in inventory
Releases cash locked up in inventory
Does not alter its cash position
A firm cannot reduce its inventories
Solution: (b) only.
Problem 6. (3 points) Given a book value per share of $10 and a market value of $24,
what is the market value added of a firm with 5,000,000 outstanding shares?
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Solution:
M V A = ($24 − $10) · 5 million = $70 million.
Problem 7. (3 points) Given the following data: Plowback ratio = 50%, Return on
equity = 30%, equity to net assets ratio = 60%, calculate the internal growth rate for the
firm.
Solution:
Internal growth rate = plowback ratio × ROE ×
equity
= 0.5 · 0.3 · 0.6 = 0.09 or 9%.
net assets
Problem 8. (2 points) What is accounts receivable?
(a)
(b)
(c)
(d)
Money owed to the business from customers
A business owes money to the customers
A business owes money to a bank
A business owes money to government
Solution: (a) only.
Problem 9. (2 points) Assets are listed on the balance sheet in order of:
(a)
(b)
(c)
(d)
Decreasing liquidity
Decreasing size
Increasing size
Relative life
Solution: (a) only.
Problem 10. (2 points) Total uses of funds are calculated as:
(a) investments in net working capital + investments in fixed assets
(b) investments in fixed assets + dividend paid to shareholders
(c) investments in net working capital + investments in fixed assets + dividend paid to
shareholders
(d) investments in net working capital + investments in fixed assets – dividend paid to
shareholders
Solution: (c) only.
Problem 11. (3 points) Given the following data: current assets = 500, current liabilities
= 250, inventory = 200, account receivables = 200, calculate the current ratio.
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Solution:
Current ratio =
current assets
500
=
= 2.
current liabilities
250
Problem 12. (3 points) Given a book value per share of $10 and a market value of $24,
what is the market capitalization of a firm with 2,000,000 outstanding shares?
Solution:
M arket capitalization = market value × number of outstanding shares =
= $24 × 2, 000, 000 = $48, 000, 000.
Problem 13. (4 points) The following are known as current assets:
(a)
(b)
(c)
(d)
(e)
Cash
Marketable securities
Receivables
Inventories
Payables
Solution: (a), (b), (c) and (d) only.
Problem 14. (3 points) Given the following data: current assets = 500, current liabilities
= 250, inventory = 200, account receivables = 200, calculate the quick ratio.
Solution:
Quick ratio =
current assets − inventory
500 − 200
=
= 1.2.
current liabilities
250
Problem 15. (3 points) Given the following data: annual sales = 3,200, cost of good
sold = 1,600, average receivables = 200, calculate the average collection period.
Solution:
Average collection period =
average receivables
=
daily sales
200
= 22.8 days.
3200/365
Problem 16. (15 points) The table below contains spot and six–month futures prices
for several commodities and financial instruments. There may be some money–making
opportunities. See if you can find them, and explain how you would trade to take advantage
of them. The interest rate is 6%, or 3% over the six–month life of the contracts.
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Commodity
Magnoosium
Oil
Biotech stock index
Allen Wrench Co.
common stock
Spot Price
$2,800 per ton
$0.44 per barrel
$140.2
$58
Futures Price
$2,812 per ton
$0.56 per barrel
$142
$62
Comments
Net convenience yield = 4% per year
Net convenience yield = 0.5% per month
Dividend = 0
Cash dividend = $2.4 per year
Solution: To check whether futures are correctly priced, we use the following basic
relationships for commodities and for financial futures, respectively:
Ft = S0 (1 + rf + storage costs − convenience yield)t ,
Ft = S0 (1 + rf − y)t .
This gives the following:
Magnoosium
Oil
Biotech stock index
Allen Wrench stock
Actual
Futures
Price
$2,812
$0.56
$142
$62
Value of Future
$2,828 (= 2, 800 · (1.03 − 0.02))
$0.44 (= 0.44 · (1.03 − 0.03))
$144.41 (= 140.2 · 1.03)
$58.54 (= 58 · (1.03 − 1.2/58))
Where the futures are overpriced (i.e., oil and Allen Wrench stock), it pays to borrow,
buy the goods on the spot market, and sell the future. Where they are underpriced (i.e.,
magnoosium and Biotech stock index), it pays to buy the future, sell the commodity on
the spot market, and invest the receipts in a six–month account.
Problem 17. Buffelhead’s stock price is $220 and could halve or double in each six–
month period (equivalent to a standard deviation of 98%). Suppose that you own a one–
year American put option on Buffelhead stock with an exercise price of $220. The interest
rate is 20% a year.
(a) (20 points) Calculate the value of the put.
(b) (5 points) Now compare the value with that of an equivalent European put option.
Solution:
(a) The possible prices of Buffelhead stock and the associated American put option values
(shown in parentheses) are:
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Let p equal the probability of a rise in the stock price. Then, if investors are risk–
neutral:
p · 100 + (1 − p) · (−50) = 10 ⇒ p = 0.4.
If the stock price in month 6 is $110, and if the American put option is not exercised,
it will be worth:
0.4 · $0 + 0.6 · $165
= $90.
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On the other hand, if it is exercised after 6 months, it is worth $110. Thus, the investor
should exercise the put early.
Similarly, if the stock price in month 6 is $440, and if the American put option is not
exercised, it will be worth $0. On the other hand, if it is exercised after 6 months, it
will cost the investor $220. The investor should not exercise early.
Finally, the value today of the American put option is:
0.4 · $0 + 0.6 · $110
= $60.
1.1
(b) Unlike the American put in part (a), the European put can not be exercised prior
to expiration. We noted in part (a) that, if the stock price in month 6 is $110, the
American put would be exercised because its value if exercised (i.e., $110) is greater
than its value if not exercised (i.e., $90). For the European put, however, the value
at that point is $90 because the European put can not be exercised early. Therefore,
the value of the European put is:
0.4 · $0 + 0.6 · $90
= $49.09.
1.1
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