Question

Creamy Dairy is a family-owned dairy located in upstate New York.
They are trying to decide how to process their corn into feed for
their livestock. Because they are dairy farmers (and good ones at
that), financial choices have a mystical quality about them, so they
could use your help. The farm is currently earning $300,000 per
year, and an improvement could provide additional revenue. Each
of the options will result in an additional (above the current dairy
earnings) yearly pre-tax cash flow of $100,000 for 15 years starting
at time 1:
• Option 1: Subcontract the feed process at a cost of $75,000 per
year starting at time 1.
• Option 2: Upgrade the current feed facilities at a cost of $200,000
for equipment and yearly maintenance cost of $25,000.
• Option 3: Build a new facility for $300,000 with no maintenance
required for 10 years then $15,000 for the remaining useful life.
Creamy Dairy uses the cost of capital of 4%. Assume no short-term
debt, a market rate of 8%, risk-free rate of 2.5%, and marginal tax rate
of 35%. Create an Excel model (use the blank template provided in
Table 3.4), and determine the NPW/AEW of the three options.

Problem 3-11 from Engineering Economics of LCCA by Farr and Faber

Answer 1

In order to check which of the three options is better for the purpose of earning additional revenue of $ 100,000 (pre-tax) for 15 years we will calculate the net present cost for all the 3 options by taking cost of captial as required rate of return.
Formula for calculating PV (present value) = ,
Where R_t=net cash inflow-outflows during a single period t.
i=discount rate or required rate of return
t= number of time periods
Therefore, PV of cost incurred under all the 3 options is as follows:-

OPTION 1: {75000*(1-0.35)} * PV factor
=48750*10.29646
=$ 501,952.42
OPTION 2: =200,000 +[ {25000*(1-0.35)} * PV factor]
=200,000+ 16,250*10.29646
=$ 367,317.48
OPTION 3: =300,000 + PV of [$15,000 *(1-0.35)] incurred for 5 years after the completion of 10th year.
= 300,000 + {9750* 3.007491}
=$ 329,323.04

Now, we will calculate PV of post tax marginal cash inflow in the similar manner:-
PV of cash inflow = {100,000(1-.035)} * 10.29646
= $ 669,269.90

Therefore, from the above we can see that the most optimum option for Creamy Dairy will be Option 3 as the incremental cost incurred for earning additional revenue is the least and heance maximising profit of the dairy.

So, OPTION 3 is to be choosen by Creamy Dairy.