Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 2
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 Shareholders’ Equity
Cash $315.00 Opening balance $286.36
Net income 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) $27.64
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, Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 2
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 Net income 27.64
Present value 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 1.00
Value of firm per balance sheet 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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,Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 2
0.50 (-23.97) + 0.50 (76.03)
= -11.98 + 38.01
= $26.03.
This agrees with the direct calculation of accretion of discount for year 1 in
Example 2.2.
Year 2
Assume that you are at time 1, after the state realization for year 1 has been
observed. Suppose the year 1 state realization is bad economy. Then expected
net income for year 2 is accretion of discount on opening net asset value of
$236.36:
236.36 × .10 = 23.64
Note that this amount includes $10 interest on opening cash balance of $100.
Now suppose the state realization for year 1 is good economy. Expected net
income for year 2 then is:
336.36 × .10 = 33.64,
including interest income of $20 on opening cash balance.
Thus expected net income for year 2 is $23.64 or $33.64, depending on which
state is realized in period 1.
The above assumes the year 2 expected net income is calculated after year 1
state realization is observed. The question could also be interpreted as asking for
expected year 2 net income before the state realization is observed at time 1.
Then, expected year 2 net income would be, at time 1:
0.50 (23.64) + 0.50 (33.64)
= 11.82 + 16.82
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, Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 2
= $28.64
Expected net income is also called accretion of discount because the firm’s
expected future cash flows are one year closer at year end than at the beginning.
Consequently, the opening firm value is rolled forward or “accreted” at the 10%
discount rate used in the present value calculations.
Note: further discussion of accretion of discount would bring out:
The amount of accretion of discount is driven by the principle of arbitrage, and
risk-neutral valuation. Under these conditions, the market will force a beginning of
year valuation of the firm such that the expected net income is 10% of this value.
To illustrate, the present value of the firm at time 0 is $260.33 and expected net
income is $26.03 for year 1. Similarly, the present value of the firm at time 1 is
$236.36 or $336.36 depending on state realization, and expected net income for
year 2 is $23.64 or $33.64. In each case the market expects the firm to earn 10%
on opening value. This 10% of opening value is accretion of discount.
Copyright © 2012 Pearson Canada Inc
14
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 Shareholders’ Equity
Cash $315.00 Opening balance $286.36
Net income 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) $27.64
Copyright © 2012 Pearson Canada Inc
11
, Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 2
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 Net income 27.64
Present value 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 1.00
Value of firm per balance sheet 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:
Copyright © 2012 Pearson Canada Inc
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,Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 2
0.50 (-23.97) + 0.50 (76.03)
= -11.98 + 38.01
= $26.03.
This agrees with the direct calculation of accretion of discount for year 1 in
Example 2.2.
Year 2
Assume that you are at time 1, after the state realization for year 1 has been
observed. Suppose the year 1 state realization is bad economy. Then expected
net income for year 2 is accretion of discount on opening net asset value of
$236.36:
236.36 × .10 = 23.64
Note that this amount includes $10 interest on opening cash balance of $100.
Now suppose the state realization for year 1 is good economy. Expected net
income for year 2 then is:
336.36 × .10 = 33.64,
including interest income of $20 on opening cash balance.
Thus expected net income for year 2 is $23.64 or $33.64, depending on which
state is realized in period 1.
The above assumes the year 2 expected net income is calculated after year 1
state realization is observed. The question could also be interpreted as asking for
expected year 2 net income before the state realization is observed at time 1.
Then, expected year 2 net income would be, at time 1:
0.50 (23.64) + 0.50 (33.64)
= 11.82 + 16.82
Copyright © 2012 Pearson Canada Inc
13
, Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 2
= $28.64
Expected net income is also called accretion of discount because the firm’s
expected future cash flows are one year closer at year end than at the beginning.
Consequently, the opening firm value is rolled forward or “accreted” at the 10%
discount rate used in the present value calculations.
Note: further discussion of accretion of discount would bring out:
The amount of accretion of discount is driven by the principle of arbitrage, and
risk-neutral valuation. Under these conditions, the market will force a beginning of
year valuation of the firm such that the expected net income is 10% of this value.
To illustrate, the present value of the firm at time 0 is $260.33 and expected net
income is $26.03 for year 1. Similarly, the present value of the firm at time 1 is
$236.36 or $336.36 depending on state realization, and expected net income for
year 2 is $23.64 or $33.64. In each case the market expects the firm to earn 10%
on opening value. This 10% of opening value is accretion of discount.
Copyright © 2012 Pearson Canada Inc
14
