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A vintner is deciding when to release a vintage of sauvignon blanc. If it is bottled and released​ now, the wine will be worth $ 2.6 million. If it is barrel aged for a further​ year, it will be worth 25​% ​more, though there will be additional costs of $ 975 comma 000 incurred at the end of the year. If the interest rate is​ 7%, what is the present value of the difference in the benefit the vintner will realize if he releases the wine after barrel aging it for one year or if he releases the wine​ now?

Respuesta :

Answer:

a. PV of one year future net benefit is $2,126,168.22

b. The PV of now is $2,600,000

c. The difference between the two PVs is $473,831.78.

d. It is better to release the vintage of sauvignon blanc now.

Explanation:

a. What is the present value of the difference in the benefit the vintner will realize if he releases the wine after barrel aging it for one year?

Benefit in one year = $2,600,000 + ($2,600,000 × 25%) = $3,250,000

Cost in one year =  $975,000

Net Benefit in one year = Benefit in one year - Cost in one year

Net Benefit in one year = $3,250,000 - $975,000 = $2,275,000

Present value (PV) =  $2,275,000 ÷ (1.07^1) = $2,126,168.22

b. What is the present value if he releases the wine​ now

The present value is $2,600,000

c. Difference between the two PVs

Difference = PV of b - PV of a = $2,600,000 - $2,126,168.22 = $473,831.78.

d. Decision

 Since the PV of releasing the vintage of sauvignon blanc is $473,831.78 higher than the PV of releasing it in a year, it is better to release it now.

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