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Different bases of accounting, such as current value accounting and historical cost$-$based accounting, do not affect total earnings over the life of the firm, but only the timing of the recognition of those earnings. In effect, over the life of the firm, the firm "earns what it earns", and different bases of accounting will all produce earnings that add up to this total.

If this is so$,$ then we would expect that the longer the time period over which we aggregate a firm's historical cost earnings; the closer the resulting total will be to economic income; that is$,$ the earnings total that would be produced over the same periods under ideal conditions.

Easton, Harris, and Holson $(1992,$ EHO$)$ and Warfield and Wild $(1992$; WW$)$ studied the long$-$run agreement of earnings with economic income. EHO proxied economic income by the return on the firm's shares over varying periods of time, up to $10$ years. When EHO compared this proxy with aggregate hstorical cost$-$based earnings for similar periods, the comparison improved as the time period lengthened. WW studied a similar phenomenon for shorter periods. They found, for example, that the association between economic and accounting income for quarterly time periods was, on average, about $1/10$ of their association for an annual period, consistent with mixed measurement model$-$based net income lagging behind economic income in its recognition of relevent economic events.

Required

a$.$ From the information in Example $2\mathrm{.}1,$ calculate total net income over the two$-$year life of the firm, assuming that P$.$V$.$ Ltd$.$ uses historical cost accounting with straight$-$line amortization for its capital asset, while retaining all other assumptions. Verify that total net income over the life of P$.$V$.$ Lted equals the total economic net income that P$.$V$.$ Ltd would report using present value amortization.

b$.$ Do the same for Example $2\mathrm{.}2.$ Continue the assumptions about P$.$V$.$ Ltd from part a$,$ while assuming that the state realization is bad and good, in years $1$ and $2$ respectively.

c$.$ Use the fact that accruals reverseto explain why total net income over the two years in parts a and b above are the same under economic and straight$-$line amortization. Are these results consistent with the empirical results of EHO and WW outlined above?

d$.$ If all accounting methods produce the same total net income over a sufficiently long period, why does the accounting policy choice and its full disclosure matter to investors?

I am attaching screenshots of Problem $2\mathrm{.}1$ so that you can please calculate the actual answers. Thank you! Example $2\mathrm{.}1$

Illustration of the Present Value Model Under Certainty

Consider P$.$V$.$ Ltd$.,$ a one$-$asset firm with no liabilities. Assume that the asset will generate

end$-$of$-$year cash flows of $$150$ each year for two years and then will have zero value.

Assume also that the interest rate in the economy is $10$ percent. Then, at time $0($the begin$-$

ning of the first year of the asset's life$),$ the present value of the firm's future cash flows,

denoted by $P{A}_0,$ is

$P{A}_0=\frac{\text{\$}150}{1\mathrm{.}10}+\frac{\text{\$}150}{{1\mathrm{.}10}^2}=$$$136\mathrm{.}36+$$$123\mathrm{.}97=$$$260\mathrm{.}33$

We can then prepare a present value$-$opening balance sheet as follows:

P$.$V$.$ Ltd$.$

Balance Sheet

Time $0$

Capital asset, at present value

$$260\mathrm{.}33$

Shareholders' equity

$$260\mathrm{.}33$

The firm's income statement for year $1$ is

P$.$V$.$ Ltd$.$

Income Statement

For Year $1$

Accretion of discount

Since future net revenues are capitalized into asset value, net income is simply interest

on the opening asset value, just as income from a savings account is interest on the open$-$

ing account balance. ${?}^1$ Thus, net income for the year is equal to $P{A}_{0}10\%=$

$$260\mathrm{.}3310\%=$$$26\mathrm{.}03.$ This amount is called accretion of discount. The term arises

because the stream of cash receipts is one year closer at the end of the year than it was at

the beginning. ${?}^2$

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