A venture capitalist is considering investing \(\$ 400,000\) in a business start-up. It is expected that the start-up will generate annual receipts of \(\$ 80,000\) over a 10 -year period. However, there is uncertainty with respect to the annual receipts. The standard deviation for annual receipts is estimated to be \(\$ 5,000\) each year. MARR is 10 percent/year. For the following questions, determine an analytical solution:

a. Determine the expected value and standard deviation of present worth assuming annual receipts are statistically independent.

b. Determine the expected value and standard deviation of present worth assuming annual receipts are perfectly correlated.