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