You are planning to invest in fine wine. Each case costs $80, and you know from

Question

You are planning to invest in fine wine. Each case costs $80, and you know from experience that the value of a case of wine held for t years is $100sqrtT. One hundred cases of wine are available for sale, and the interest rate is 10 percent. How many cases should you buy, how long should you wait to sell them, and how much money will you receive at the time of their sale? You should

A. buy all 100 cases of wine and sell them in 5.00 years, receiving $55.86 at the time of the sale.

B. buy all 100 cases of wine and sell them in 5.00 years, receiving $223.61 at the time of the sale.

C. buy all 100 cases of wine and hold them indefinitely.

D. buy none of the wine.

E. buy all 100 cases of wine and sell them immediately for $100.

Suppose that at the time of purchase, someone offers you $200 per case immediately. Should you take the offer?

ou should take /not take the offer.

How would your answers change if the interest rate were only 5 percent?

If you buy the wine, then the optimal time to sell would be after _____ years.(Enter a numeric response rounded to two decimal places.)

In turn, the net present value when buying the wine and then selling after 10.00 years would be $____per case.

Therefore, you should not buy/ buy the wine to be resold in 10.00 years.

Furthermore, if someone offers you $200 per case immediately, you should take/not take the offer.

Explanation / Answer

1) B. Buy all 100 cases of wine and sell them in 5.00 years, receiving $223.61 at the time of the sale.

Five years from today, the value of $80 would be equal to $80x(1 + 10%)^5 = $128.84

And you could sell the wine case for 100sqrt(5) = 100x(5)^0.5 = $223.61

2) You should take the offer to sell the case for $200 immediately. Because $223.61 five years hence is worth $223.61/(1+10%)^5 = $138.84 today. So you would make a profit by selling immediately for $200.

3) If interest rate is 5%, the future value of $80 would be equal to $102.10 in five years. So if you can sell the wine case in five years for $223.61, your profit margin would only increase.

4) The optimal time to sell would be after 8.50 years. After 8.50 years, your profit would be maximum at $111.69.

Using solver function, you would be able to calculate the following table.

5) NPV of profit per wine case after 10 years would be $41.92.

After 10 years, the wine case cost would be $80x(1+10%)^10 = $207.50 and sale price would be 100xsqrt(10) = $316.23. Net Profit = $108.73. PV of Net Profit = $108.73/(1+10%)^10 = $41.92.

I/Y N Cost FV 10% 5 $80 $ 128.84 PV Sale Price 100SQRT(5) $      223.61 138.8422

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