For tax reasons, your client wishes to purchase an annuity that pays $$120,000$ each year for $10$ years, with the first payment in one year. At an interest rate of $6\%$ and focusing on time value of money without consideration of any fees, how much would the client need to invest now?

Equivalent problem structure $($in neutral time$-$value$-$of$-$money terms$)$: What is the present value of an annuity that pays $$120,000$ each year for $10$ years, assuming a discount rate of $6\%$ and the first payment occurs one year from now?

Equivalent problem structure $($as a borrower$)$: How much could you borrow today in exchange for paying back $$120,000$ each year for $10$ years, assuming an interest rate of $6\%$ and the first payment occurs one year from now?

Please round your answer to the nearest hundredth.

Please round your answer to the nearest hundredth.

Equivalent problem structure $($in neutral time$-$value$-$of$-$money terms$)$: What is the present value of a series of payments received each year for $11$ years, starting with $$65,000$ paid one year from now and the payment growing in each subsequent year by $7\%?$ Assume a discount rate of $10\%.$

Please round your answer to the nearest hundredth.

Please round your answer to the nearest hundredth.

Assume all cash flows occur at the start of each year $($i$.$e$.,$ immediate, one year from now, two years from now,..., nine years from now$).$ Also assume that the choice can be implemented immediately so that for the MBA alternative the current year is the first year of business school.

What is the net present value of the more attractive choice?

Please round your answer to the nearest dollar.

For each generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year $($i$.$e$.,$ immediate, one year from now,..., four years from now$).$

What is the net present value of the more attractive generator?

Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.

For the local utility option, consider five years of electricity purchases. For the generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year $($i$.$e$.,$ immediate, one year from now,..., four years from now$).$

What is the net present value of the more attractive choice?

Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.