Question

file:///C:/Users/ESTHER/AppData/local/Temp/ES-3083_su%202020%20Final.pdf + А. 6. The probability of weather-related crop damage during the growing season in a typical year is given by the following table. If the interest rate is 5%, what is the expected present worth of crop damage over the next 5 years? (10 points) Value of Crop Damage SO $100,000 $200,000 $300,000 Probability 60% 20% 15% 5%

Answer 1

Expected crop damage per year = $0*60% + $100000*20% + $200000*15% + $300000*5% = 65000

Thus, crop damage over the next 5 years are:

Year	Expected Crop damage
1	$65,000
2	$65,000
3	$65,000
4	$65,000
5	$65,000

The expected Present value of the crop damage occurring in each of the 5 years is:

Expected Present Value = Expected Crop damage /(1+r)^n

Where,

n = nth Year

r=5%

Interest rate = 5%
Year	Expected Crop damage	Expected Present value
1	$65,000	$61,905
2	$65,000	$58,957
3	$65,000	$56,149
4	$65,000	$53,476
5	$65,000	$50,929

Hence, the expected present worth of the crop damage over the next 5 years is the sum total of the expected present value of the crop damage occurring in each of the 5 years.

Thus, the expected present worth is:

Interest rate = 5%
Year	Expected Crop damage	Expected Present value
1	$65,000	$61,905
2	$65,000	$58,957
3	$65,000	$56,149
4	$65,000	$53,476
5	$65,000	$50,929
	Expected PW	281415.9836

Thus, the expected present worth of the crop damage over the next 5 years is $281415.9836