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The northern district of the municipality of Montblanc is exposed to the risk of...
Apr 19, 2024
The northern district of the municipality of Montblanc is exposed to the risk of avalanches. The probability of avalanche is 1/1200 per year
. When an avalanche occurs, it completely destroys all the homes in the northern neighborhood but causes no other damage, death or injury. There are 200 houses in the northern neighborhood and their average price is 180,000.a)Istheconstructionatacostof300,000 of a barrier that would eliminate the risk of avalanches justified? (15 points
Answer
Yes, the construction of the barrier is economically justified.
Solution
a
Expected Annual Loss Calculation: The expected annual loss (EAL) from avalanches is calculated by multiplying the probability of an avalanche by the total potential loss
b
EAL = Probability of Avalanche × Total Value at Risk: Using the given data, EAL = \frac{1}{1200} × 200 × \$180,000
c
EAL Calculation: EAL = \frac{1}{1200} × 200 × \$180,000 = \$30,000
d
Cost-Benefit Analysis: Compare the EAL to the cost of the barrier. If the EAL is greater than or equal to the annualized cost of the barrier, the construction is justified
e
Barrier Justification: Since the EAL of \$30,000 per year is greater than the annualized cost of the barrier assuming a reasonable discount rate and lifespan for the barrier, the construction is justified
Key Concept
Expected Annual Loss (EAL) and Cost-Benefit Analysis
Explanation
The decision to build the barrier is justified if the expected annual loss from avalanches exceeds the annualized cost of the barrier. In this case, the EAL of \$30,000 is higher than the annualized cost of a \$300,000 barrier over its lifespan, assuming a reasonable discount rate.
The northern district of the municipality of Montblanc is exposed to the risk of avalanches. The probability of avalanche is 1/1200 per year
. When an avalanche occurs, it completely destroys all the homes in the northern neighborhood but causes no other damage, death or injury. There are 200 houses in the northern neighborhood and their average price is 180,000.a)Istheconstructionatacostof300,000 of a barrier that would eliminate the risk of avalanches justified? (15 points
According to real estate experts, the construction of the barrier would have the effect of increasing the average price of houses located in the northern district by $1,500. Should we therefore increase the advantage provided by the barrier? (10 points)
YES
NO
Justify your answer.
Assume that:1) the lifespan of the houses and the fence is infinite;
2)the social discount rate is “i”;
3) the construction of the barrier would last 1 day
假设：1）房屋和栅栏的寿命是无限的；
2）社会贴现率为“i”；
3）屏障的建造将持续1天
Answer
YES, the increase in the average price of houses due to the construction of the barrier should be considered in the economic justification.
Solution
a
Expected Annual Loss Without Barrier: Calculate the expected annual loss due to avalanches without the barrier
The expected annual loss is the product of the probability of the event and the total loss if the event occurs. Using the given data, the expected annual loss is $\frac{1}{1200} \times 200 \times \$180,000 = \$30,000$.
b
Expected Annual Benefit of the Barrier: Calculate the expected annual benefit of the barrier in terms of increased house prices
The expected annual benefit is the total increase in house prices due to the barrier. The increase for each house is $1,500, so for 200 houses, the total increase is $1,500 \times 200 = \$300,000. Since the houses and the barrier have an infinite lifespan, this is a perpetual benefit. The present value of this perpetual benefit is $\frac{\$300,000}{i}$, where $i$ is the social discount rate.
c
Economic Justification: Compare the cost of the barrier to the sum of the expected annual loss without the barrier and the present value of the increased house prices
The cost of the barrier is \$300,000. The economic justification requires that the cost of the barrier be less than or equal to the sum of the expected annual loss without the barrier and the present value of the increased house prices. Since the expected annual loss is \$30,000 and the present value of the increased house prices is $\frac{\$300,000}{i}$, the barrier is justified if $\$300,000 \leq \$30,000 + \frac{\$300,000}{i}$.
Key Concept
Economic Justification of Investment
Explanation
The construction of the barrier is economically justified if the cost is less than or equal to the sum of the expected annual loss without the barrier and the present value of the increased house prices due to the barrier.
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