1. Suppose you are considering buying a gold deposit. It will cost $1 million pe
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Question
1. Suppose you are considering buying a gold deposit. It will cost $1 million per year to construct a mine so that gold can be extracted. The construction period lasts 3 years. In the fourth year, production starts. Each year the mine operates, it will yield a profit (total revenue minus total cost) of $500,000. Costs are paid and profits are received at the beginning of the respective year. What will you pay for the gold deposit if: a. Interest rates are 10% and gold can be extracted for 6 years? b. Interest rates are 5% and gold can be extracted for 10 years? 2. What is the difference between private ownership and open access?
2. What is the difference between private ownership and open access?
Explanation / Answer
a. First calculate the Present value of the total cost
PV of Total Cost = Price paid for Gold deposit + 1000000/1.1 + 1000000/(1.1)^2 + 1000000/(1.1)^3
= P of Gold Deposit + $ 2,486,851.99
PV of Returns with 4th year as base = 500000/1.1 + 500000/(1.1)2 + 500000/(1.1)3 +500000/(1.1)4 + 500000/(1.1)5 + 500000/(1.1)6
= $ 2,177,630.35
PV of Returns at base year = $ 2,177,630.35/1.10^4 = $ 1,487,350.83
For profit total returns should be greater then or equal to total cost
P of Gold Deposit + $ 2,486,851.99 <= $ 1,487,350.83
P of Gold Deposit = - $999501.16
Similarly for r = 5% , t = 10
PV of Total Cost = Price paid for Gold deposit + 1000000/1.05 + 1000000/(1.05)^2 + 1000000/(1.05)^3
= P of Gold Deposit + $ 2,723,248.03
PV of Returns with 4th year as base = 500000/1.05 + 500000/(1.05)2 + 500000/(1.05)3 +500000/(1.05)4 + 500000/(1.05)5 + 500000/(1.05)6 + 500000/(1.05)7 + 500000/(1.05)8 + 500000/(1.05)9 + 500000/(1.05)10
= $3,860,867.46
PV of Returns at base year = 3,860,867.46/1.05^4 = $3,860,867.46
For profit total returns should be greater then or equal to total cost
P of Gold Deposit + $ 2,723,248.03 <= $3,860,867.46
P of Gold Deposit <= 1137619.43
The difference between private ownership and open access is that in case of Private Property is owned by an entity which may be asingle individual or group of Individuals and Access, use, and exclusion are controlled by this entity Whereas in case of open acess, the Acess, use and exclusion are not controlled by anybody, it is free for acess and use by everyone.
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