A certain wine costs $3 a bottle to produce. It improves in taste if stored prop

Question

A certain wine costs $3 a bottle to produce. It improves in taste if stored properly for a period of time. When it is newly bottled, people are willing to pay only $2 a bottle to drink it. But the amount that people are willing to pay to drink a bottle of this wine will rise by $3 a year for the next 50 years. Storage costs, not including interest, are $.50 per year. If the interest rate is 5% and the wine is kept by rational investors, how old will it be when it is drunk and what will be its price at that time?

Explanation / Answer

We have Cost of wine $3 and WTP is increasing additively by $3 where storge cost is $0.5 per year

Hence Present worth of Bottle is calculated for each year and it increases at the begining and decreases afterwards

We found that after 16 years it will decrease in present worth than previous year

Hence the bottle should be 16 years old and worth $50

Price Year 1.05 PW 1 2.5 2.380952 2 4.5 4.081633 3 7.5 6.478782 4 10.5 8.638376 5 13.5 10.5776 6 16.5 12.31255 7 19.5 13.85829 8 22.5 15.22889 9 25.5 16.43753 10 28.5 17.49653 11 31.5 18.4174 12 34.5 19.21089 13 37.5 19.88705 14 40.5 20.45525 15 43.5 20.92424 16 46.5 21.30219 17 49.5 21.29394 18 52.5 21.04523 19 55.5 20.77191 20 58.5 20.4769 21 61.5 20.16289

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