Question

A farmer has the opportunity to purchase The Pioneer Appli-Pro Super Low Volume (SLV) Applicator System which is a new way to apply inoculant to silage using low volumes of inoculant. Microbial inoculants can make silage fermentation more efficient, thereby preserving more nutrients and dry matter, and sometimes improve animal performance. Some inoculants have also been designed to specifically improve aerobic stability. This is important because a large portion of dry matter (DM) lost in a silo is actually due to aerobic spoilage. The farmer believes that this new inoculant system can be purchased for $2,000 and it will cost $1.25/ton for the inoculant. He believes this process will reduce silage spoilage and save $620/year in feed costs (after any application, labor or chemical costs). He plans to keep the inoculant system for 6 years. At the end of 6 years he believes he will scrap the system and it will be worthless. The farm’s accountant has done some preliminary work. The marginal tax rate is 25%, the pre-tax risk-adjusted discount rate is 10% and inflation is assumed to be zero. The accountant calculates the present value of the tax savings from depreciation to be $391.15, and the present value of the after-tax terminal value to be $0. i.

1. How much money does the farmer save after taxes each year if he purchases SLV applicator?

A. $620

B.      $465

C.        $155

D.        $750

E.         None of these answers

2. Calculate the after-tax risk adjusted discount rate.

A.      7.5%

B.        10%

C.        2.5%

D.        1.25%

E.         None of these answers

3. Calculate the present value of the after tax savings if the farmer purchases the SLV applicator.

A.        $3,368

B.        $711

C.      $2,183

D.        $2,790

E.         None of these answers

4.Calculate the NPV of the Inoculant System.

A.        $379

B.        $711

C.        $1,659

D.      $574

E.         None of these answers

5. Calculate the break-even pre-tax reduction in feed costs due to the reduction of silage spoilage

A. $439

B. $457.06

C. $600

D. $308

E.   None of these answers

Answer 1

1	Farmer saves after taxes each year
	Pretax savings	$620
	Tax @ 25%	$155
	After taxes savings	$465
2	After tax risk adjusted discount rate
	Pre-tax risk adjusted discount rate	10%
	Less: Tax @ 25%	2.5%
	After tax risk adjusted discount rate	7.5%
3	Present value of after tax savings
	After tax savings	$465
	After tax risk adjusted discount rate	7.50%
	PV of annuity of $1 for 6 years @ 7.5%	4.6938
	Present value of after tax savings	$2,182.62
		$2,183
4	NPV of Inoculant System
	Present value of after tax savings	$2,182.62
	Present value of tax saving from depreciation	$391.15
	Total Cash Saving	$2,573.77
	Less: Initial Cash outflow	$2,000
	NPV of Inoculant System	$573.77
		$574