Suggested Solutions to Questions and Problems
1.
P.V. Ltd.
Income Statement for Year 2
Accretion of discount (10% × 286.36)
$28.64
P.V. Ltd.
Balance Sheet
As at Time 2
Financial Asset
Cash
Shareholders’ Equity
$315.00
Opening balance
Net income
$286.36
28.64
Capital Asset
Present value
0.00
$315.00
$315.00
,Note that cash includes interest at 10% on opening cash balance of $150.
2.
Suppose that P.V. Ltd. paid a dividend of $10 at the end of year 1 (any portion of year 1 net
income would do). Then, its year 2 opening net assets are $276.36, and net income would be:
P.V. Ltd.
Income Statement
For Year 2
Accretion of discount (10% × 276.36)
P.V.’s balance sheet at time 2 would be:
P.V. Ltd.
Balance Sheet
As at Time 2
Financial Asset
Shareholders’ Equity
Cash: (140 + 14 + 150)
$304.00
Opening balance:
$276.36
(286.36 - 10.00 dividend)
Capital Asset, at
Present value
Net income
27.64
0.00
$304.00
$304.00
Thus, at time 2 the shareholders have:
Cash from dividend
$10.00
Interest at 10% on cash dividend, for year 2
Value of firm per balance sheet
, 1.00
304.00
$315.00
This is the same value as that of the firm at time 2, assuming P.V. Ltd. paid no dividends (see
Question 1). Consequently, the firm’s dividend policy does not matter to the shareholders under
ideal conditions. It may be worth noting that a crucial requirement here, following from ideal
conditions, is that the investors and the firm both earn interest on financial assets at the same
rate. 3.
Year 1
At time 0, you know that if the bad economy state is realized, ex post net income for year 1 will
be a loss of $23.97. If the good economy state is realized, ex post net income will be $76.03.
Since the probability of each state is 0.50, expected net income for year 1, evaluated at time 0,
is:
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