Problem_Set__3_Solutions
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Finance
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Jan 9, 2024
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Fin 401
Problem Set #3
Book vs. Market Values
Solutions
1.
If a firm is offered payment terms of “1/15, net/30”, what is the implicit annual interest
rate on the trade credit if the firm pays in 30 days rather than 15 days?
1.01%*(365/15) = 24.6%
(i.e., in losing the 1% discount, the firm effectively pays 1.01% interest ($1 of interest
on a “loan” of $99).
To annualize, multiply by the number of 15 day periods in the
year, because it is postponing payment for 15 days.)
2.
Firm ABC has 20 million shares outstanding at a price of $40/share.
They currently
have no debt outstanding.
a.
What does ABC’s market value balance sheet look like?
b.
ABC decides to raise money by issuing $200 million of bonds.
Assume that this
transaction has no impact on the equity value.
What will the market value balance
sheet look like after the transaction?
What will be the effect of the transaction on
the accounting balance sheet?
Market value balance sheet
Accounting balance sheet:
Cash goes up by $200 million
Debt (probably long-term debt) goes up by $200 million
c.
Explain each change in the market value balance sheet due to the debt issuance.
Assets:
$800 million
Debt:
0
Equity:
$800 million ($40 * 20 million)
Assets:
$1 billion
Debt:
$200 million
Equity:
$800 million ($40 * 20 million)
The market value of assets will increase by $200 million because ABC will receive
$200 million in cash from investors.
In exchange, investors will get debt claims
worth $200 million, so the market value of debt will increase by $200 million.
3.
Firm XYZ has 10 million shares outstanding at a price of $50/share.
The market value
of its debt is $300 million of debt.
a.
What does XYZ’s market value balance sheet look like?
b.
XYZ wants to raise money by issuing 2 million new shares.
Assume this has no
effect on the market value of debt.
What does the market value balance sheet look
like if they issue those shares at $50/share?
What effect would this transaction
have on the accounting balance sheet?
Market value balance sheet
Accounting balance sheet:
Cash would increase by $100 million, as would equity (paid-in-capital).
c.
Explain each change in the market value balance sheet due to the stock issuance.
XYZ will receive $100 million in cash, which increases the market value of assets
by $100 million.
Since the value of debt is unaffected, the increased asset value
flows through entirely to equity value.
d.
What effect would the stock issuance have on shareholder wealth?
None.
Shares were worth $50 both before and after the stock issuance.
4.
The Sheinhardt Wig Company has 15 million shares outstanding at a price of $60/
share.
The firm has $500 million of debt, which we’ll assume for now is both the
market and book value of its debt.
Assets:
$800 million
Debt:
$300 million
Equity:
$500 million ($50 * 10 million)
Assets:
$900 million
Debt:
$300 million
Equity:
$600 million ($50 * 12 million)
2
a.
What does Sheinhardt’s market value balance sheet look like?
b.
Now imagine that Sheinhardt signs a contract with an important new customer, and
we see its stock price increase by 10%.
The firm’s bond prices also increase by
2%.
What does the new market value balance sheet look like?
What effect would
this news have on the accounting balance sheet?
Market value balance sheet
The accounting balance sheet is unaffected by the signed contract.
c.
Explain the changes in the market value balance sheet. and why they differ from
any changes in the accounting balance sheet.
A contract with an important customer is an economic asset.
The market value of
that asset can be seen in the increase in asset market value for Sheinhardt ($100
million).
Bond prices change because of changes in credit risk or changes in prevailing
market interest rates.
In this case, the new contract most likely improved investors’
perceptions of the credit risk, since Sheinhardt’s future cash flows look more
promising.
Movements in equity values are caused by changes in the value of the assets. Debt
value increased somewhat ($10 million).
Equity holders, as the residual claimants,
get the rest ($90 million).
d.
Why does the market value balance sheet respond differently than the accounting
balance sheet?
A contract with an important customer is not one of the assets that accountants
recognize.
This is one example of an economic asset that is not an accounting
asset.
Assets:
$1.4 billion
Debt:
$500 million
Equity:
$900 million ($60 * 15 million)
Assets:
$1.5 billion
Debt:
$510 million
Equity:
$990 million ($66 * 15 million)
3
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