The current price of silver is $ 31.00 per ounce.The effective lease rate and risk free rate are 1.0% and 3.5%,respectively.If the cost to mine one ounce of silver is a constant $25.00,what is the value of an option to wait and mine the silver later?
A) $13.50
B) $14.50
C) $15.50
D) $16.50

Question

Quizplus · Accepted Answer

The value of the option to wait and mine the silver later can be calculated using the formula for the value of a real option, which is based on the Black-Scholes model. The key factors in this calculation are the current price of silver, the cost to mine, the risk-free rate, and the effective lease rate. The formula to calculate the net present value (NPV) of mining the silver now is: NPV = (Spot Price - Cost to Mine) - (Spot Price - Cost to Mine) / (1 + Risk-Free Rate - Effective Lease Rate). Plugging in the values: NPV = ($31.00 - $25.00) - ($31.00 - $25.00) / (1 + 0.035 - 0.01) = $6.00 - $6.00 / 1.025 = $6.00 - $5.85 = $0.15. The value of the option to wait is then the current price minus the cost to mine plus the NPV of waiting, which is $31.00 - $25.00 + $0.15 = $6.15. However, this calculation does not directly lead to any of the provided options, suggesting a misunderstanding in the application of the formula or the interpretation of the question. The correct approach involves understanding the option value as related to the opportunity to mine silver later at potentially more favorable conditions, taking into account the cost of delay (considering the risk-free rate and lease rate). The provided options and the calculation do not align with standard financial models for such a scenario, indicating a need for a more detailed explanation or a different approach to calculating the option's value based on the given parameters.

The Current Price of Silver Is $ 31