23. A farmer has two storage facilities for grain; a modem silo and an old shed. Grain stored in the silo is perfectly preserved, but grain stored in the shed suffers a 10% loss through spillage, spoilage, and rodent damage. The farmer's current crop is 10,000 bushels. The capacity of the silo is 6,000 bushels, while the shed can store the remaining crop. Suppose grain sells today for S1 per bushel, and will sell next year for $1.22 per bushel 23a. Above what interest rate wll the farmer elect to sell all 10,000 bushels today He wil elect to sell all 10,000 bushels today if the interest rate is above: 23b. Below what interest rate will the farmer elect to store all 10,000 bushels and sell them next year? He will elect to store a 10,000 bushels and sell them next year if the interest rate is below:
| Bushels available | 10000 | ||
| Sale proceed if sold today | 10000*1 | ||
| 10000 | |||
| If sold after 1 year | |||
| Bushels avaialble | |||
| Stored in Silo | 6000*100% | ||
| Stored in Shed | 4000*90% | ||
| Stored in Silo | 6000 | ||
| Stored in Shed | 3600 | ||
| Total | 9600 | ||
| Sale price | 1.22 | ||
| Total Sale proceed | 11712 | ||
| Which rate becomes 10000 equals to 11712 in 1 year | |||
| 11712= | 10000*(1+r) | ||
| 1+r= | 1.1712 | ||
| r= | 17.12% | ||
| Interest rates | Action | ||
| Less than 17.12% | Hold on and sell after 1 year | ||
| 17.12% | Indifferent | ||
| More than 17.12% | Sell today and invest in bank | ||
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