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

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)

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$27.64

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

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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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...