Question

The Tillamook County Creamery Association manufactures Tillamook Cheddar Cheese. It sells the cheese in four​ varieties: aged 2​ months, 9​ months, 15​ months, and 2 years. At the shop in the​ dairy, it sells 2 pounds of each variety for the following​ prices: $ 8.00$8.00​, $ 9.50$9.50​, $ 11.50$11.50​, and $ 12.00$12.00​, respectively. Consider the cheese​ maker's decision whether to continue to age a particular​ 2-pound block of cheese. At 2​ months, he can either sell the cheese immediately or let it age further. If he sells it​ now, he will receive $ 8.00$8.00 immediately. If he ages the​ cheese, he must give up the $ 8.00$8.00 today to receive a higher amount in the future. What is the IRR​ (expressed in percent per​ month) of the investment of giving up $ 80.00$80.00 today by choosing to store 20 pounds of cheese that is currently 2 months old and instead selling 10 pounds of this cheese when it has aged 9​ months, 6 pounds when it has aged 15​ months, and the remaining 4 pounds when it has aged 2​ years?

Answer 1

Let the IRR be 12*r% p.a. i.e.r% every month

Now, The decision to store 20 pounds will result in a net loss of $80 today

and will result in cashflows of $47.5 after 7 months, $34.5 after 13 months and $24 after 22 months

As we know that by discounting the cashflows at IRR , NPV =0

-80+47.5/(1+r)^7 + 34.5/(1+r)^13+24/(1+r)^22 = 0

Solving the above equation for r using SOLVER tool of Excel, we get

r = 0.023805 or 2.38%

So, the IRR of the decision to store is 2.38% per month