A farmer expects irrigation system will increase real operating receipts by $32,000 per year but will also increase real operating expenses by $8,000. Suppose that the inflation rate is 5% and the marginal tax rate is 20%. (i) What is the nominal net return at the end of year 3?

a. $29,172 b. $22,800

c. $27,783 d. $24,000

(ii) Calculate the nominal after-tax net return at the end of year 4.

a. $28,800 b. $27,360

c. $34,560 d. $23,338

(i) Option (c) $27,783 (ii) $23,338 option (d)

Explanation:

Given that:

Real receipts = 32,000

Real expenses =$8,000

Inflation rate =5%

Marginal tax rate = 20%

(1) Now,

The  receipts (nominal)for year 3 is  = Real receipts ( 1 + Inflation rate ^)3

Nominal Expenditure for year 3 = Real Expenditure ( 1 + Inflation rate )^3

The  receipts (nominal)for year 3 = Real receipts ( 1 + Inflation rate )^3

= $ 32,000 ( 1.05 ^)3

= $ 32,000 ( 1.1576 )

= $ 37,044

Thus,

The receipts  (nominal)for year 3 = Real receipts ( 1 + Inflation rate )^3

= $ 8000 ( 1.05 )3

= $ 8000 ( 1.1576)

= $ 9261

The nominal net return = Nominal receipts - Nominal Expenditure

= $ 37,044 - $ 9,261

= $ 27,783

(ii) We find the nominal after-tax net return at the end of year 4

Thus,

Nominal receipts for year 4 = Real receipts ( 1 + Inflation rate )4

= $ 32,000 ( 1.05 )4

= $ 32,000 ( 1.2155 )

= $ 38,896

Now,

Nominal receipts for year 4 = Real receipts ( 1 + Inflation rate )^4

= $ 8000 ( 1.05 )^4

= $ 8000 ( 1.2155)

= $ 9724

So,

Nominal net return = Nominal receipts - Nominal Expenditure

= $ 38,896 - $ 9,724

= $ 29,712

After Tax net return = Nominal net return ( 1 - tax rate )

= $ 29,712 ( 1 - 0.2)

= $ 29,712 (0.8)

= $ 23,338

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