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21 June, 20:21

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

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  1. 21 June, 20:36
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    (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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