17C) Mr. Agirich has the opportunity to purchase some farm land at $3,000/acre.

Question

17C)

Mr. Agirich has the opportunity to purchase some farm land at $3,000/acre. He expects that real land prices will increase at 5% per year and inflation will be 2%. His pretax risk adjusted discount rate is 14%. Assume that the land will be sold in 10 years and the marginal tax rate is 23%. The effective interest rate on land loans is 6%.

Calculate the after-tax risk adjusted discount rate.

            a.         14%                 b.       10.7%

            c.          6%                  d.         4.6%

            e. None of the answers are correct

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(ii)       Calculate the real price of land in 10 years.

                        a.         $3,657                        b.        $8,291

c.        $4,887                        d.        $5,373

e. None of the answers are correct

            Enter Response Here:

(iii)      Calculate the nominal price of land in 10 years.

                        a.         $4,458                        b.        $6,550

c.          $10,019            d.       $5,957

e. None of the answers are correct

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(iv)      Calculate the after-tax terminal value of the land.

            a.         $5,957                         b.       $5,277

            c.          $4,887                        d.         $3,000

            e. None of the answers are correct

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(v)       Calculate the Present Value of the after-tax terminal value.

                        a.         $2,140                        b.        $1,756

c.        $1,896                         d.        $1,077

e. None of the answers are correct

            Enter Response Here:

(vi)      What is the approximate maximum bid price for this land?

                        a.         $5,140                        b.        $4,756

c.          $4,077                       d.       $4,896

e. None of the answers are correct

Explanation / Answer

i) After tax risk adjusted discount rate

After tax risk adjusted discount rate = Pre tax risk adjusted discount rate * (1 - Tax)

= 14% * (1 - 23%)

= 10.78%

Correct answer is option b i.e. 10.7%

ii) Real price of land in 10 years

Future value = Initial investment * ((1 + growth rate) ^ number of years)

= 3000 * ((1 + 5%)^10) = $ 4886.68

Correct answer is option c i.e. $4887

iii) Nominal price of land in 10 years

Nominal rate = [(1 + growth rate) / (1 + inflation rate)] - 1

= [(1 + 5%) / (1 + 2%)] - 1 = 0.0194 *100 = 1.94%

Future value = Initial investment * (1 + nominal rate)^number of yeras

= 3000 * ( 1 + 1.94%) ^ 10

= $ 3635.5

Correct answer is option e i.e. none of the above

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