# Question

The stock price of XYZ is $100. One million shares of XYZ (a negligible fraction of the shares outstanding) are buried on a tiny, otherwise worthless plot of land in a vault that would cost $50 million to excavate. If XYZ pays a dividend, you will have to dig up the shares to collect the dividend.

a. If you believe that XYZ will never pay a dividend, what would you pay for the land?

b. If you believe that XYZ will pay a liquidating dividend in 10 years, and the continuously compounded risk-free rate is 5%, what would you pay for the land?

c. Suppose that XYZ has a 1% dividend yield and a volatility of 0.3. At what price would you excavate and what would you pay for the land?

a. If you believe that XYZ will never pay a dividend, what would you pay for the land?

b. If you believe that XYZ will pay a liquidating dividend in 10 years, and the continuously compounded risk-free rate is 5%, what would you pay for the land?

c. Suppose that XYZ has a 1% dividend yield and a volatility of 0.3. At what price would you excavate and what would you pay for the land?

## Answer to relevant Questions

Repeat Problem 17.6, only assume that after the stock is excavated, the land has an alternative use and can be sold for $30m. Let t = 1. What is E(St |St < $98)? What is E(St |St < $120)? How do both expectations change when you vary t from 0.05 to 5? Let σ = 0.1. Does either answer change? How? If x ∼ N(2, 5), what is E(ex)? What is the median of ex? An options trader purchases 1000 1-year at-the-money calls on a non-dividend paying stock with S0 = $100, α = 0.20, and σ = 0.25. Assume the options are priced according to the Black-Scholes formula and r = 0.05. a. Use ...Suppose S0 = 100, r = 0.06, σS = 0.4 and δ = 0. Use Monte Carlo to compute prices for claims that pay the following: a. S21 b.√S1 c. S1-2Post your question

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