A farmer has the opportunity to purchase an advanced guidance system for precision farming. This is the advertisement:
New Outback MAX Guidance System
Outback MAX™ with Outback ConnX™ — introducing the next generation Outback Guidance® system that redefines simplicity in precision farming.
The farmer believes that the guidance system that can be purchased for $5,500 will improve corn production by 220 bushels per year. He plans to keep the Guidance system for 8 years. At the end of 8years he believes he can sell it for $1,000. The farm’s accountant has done some preliminary work. The marginal tax rate is 25%, the pre-tax risk adjusted discount rate is 8% and inflation is assumed to be zero. The account calculates the present value of the tax savings from depreciation to be $1,067.31, and the present value of the after-tax terminal value to be $470.56. The price of corn is expected to be $4.30/bushel over the 8 years.
(i) Calculate the additional after-tax net returns from corn production if the farmer purchases the guidance system.
A. $900
B. $709
C. $270
D. $750
E. None of these answers
Enter Response Here:
(ii) Calculate the after-tax risk adjusted discount rate.
A. 6.0%
B. 12%
C. 3.6%
D. 1.25%
E. None of these answers
Enter Response Here:
(iii) Calculate the present value of the additional after-tax net returns from corn production if the farmer purchases the guidance system.
A. $5,932
B. $1,779
*C. $4,406
D. $2,963
E. None of these answers
Enter Response Here:
(iv) Calculate the NPV of the guidance system.
A. $156
B. $1100
C. $445
D. $444
E. None of these answers
Enter Response Here:
(v) Calculate the break-even improvement in corn production (yield) if the farmer purchases the guidance system.
A. $150
B. $198
C. $140
D. $170
E. None of these answers
Please help by explaining the process.
Answer (i):
Correct answer is:
B. $709
Explanation:
The farmer believes that the guidance system will improve corn production by 220 bushels per year. The marginal tax rate is 25%.
The price of corn is expected to be $4.30/bushel over the 8 years.
Hence:
After-tax net returns from corn production if the farmer purchases the guidance system = (220 * $4.30) * (1 - 25%)
= $946 * 75%
= $709.50
Closest option is B and other options A, C and D are incorrect.
Answer (ii):
Correct answer is:
A. 6.0%
Explanation:
Given:
The marginal tax rate is 25%, the pre-tax risk adjusted discount rate is 8%.
Hence:
After-tax risk adjusted discount rate = 8% * (1 - 25%) = 6%
Option A is correct and other options B, C and D are incorrect.
Answer (iii):
Correct answer is:
C. $4,406
Explanation:
Present value of the additional after-tax net returns = Annual after-tax net returns from corn production * PV of $1 annuity for 8 years at 6% rate
= 709.50 * (1 - 1/ (1 + 6%) ^8)/ 6%
= $4,405.85
or $4,406
Option C is correct and other options A, B and D are incorrect.
Answer (iv):
Correct answer is:
D. $444
Explanation:
Given:
Initial investment = $5,500
Present value of the tax savings from depreciation = $1,067.31
Present value of the after-tax terminal value = $470.56
We calculated in answer iii above:
Present value of the additional after-tax net returns = $4,405.85
Hence:
NPV = $4,405.85 + $1,067.31 + $470.56 - $5,500
= $443.72
or $444
Option D is correct and other options A, B and C are incorrect.
Answer (v):
Correct answer is:
B. 198
Explanation:
At break-even improvement in corn production (yield), NPV will be zero.
Present value of after-tax net returns from corn production will be = $4,405.85 - $443.72 = $3962.13
After tax annual improvement in corn production in dollars = 3962.13 / ((1 - 1/ (1+6%) ^8)/6%) = $638.05
Before tax annual improvement in corn production in dollars = 638.05 / (1 - 25%) = $850.73
Break-even improvement in corn production (yield) in units = 850.73 / 4.30 = 198 Bushels
Option B is correct and other options A, C and D are incorrect.
A farmer has the opportunity to purchase an advanced guidance system for precision farming. This is...
A farmer has the opportunity to purchase an advanced guidance system for precision farming. This is the advertisement: New Outback MAX Guidance System Outback MAX™ with Outback ConnX™ — introducing the next generation Outback Guidance® system that redefines simplicity in precision farming. The farmer believes that the guidance system that can be purchased for $5,500 will improve corn production by 220 bushels per year. He plans to keep the Guidance system for 8 years. At the end of 8years he...
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