$7.$ Unequal project lives

Galaxy Corp. has to choose between two mutually exclusive projects. If it chooses project A$,$ Galaxy Corp. will have the opportunity to make a similar investment in three years. However, if it chooses project B$,$ it will not have the opportunity to make a second investment. The following table lists the cash flows for these projects. If the firm uses the replacement chain $($common life$)$ approach, what will be the difference between the net present value $($NPV$)$ of project A and project B$,$ assuming that both projects have a weighted average cost of capital of $13\%?$

Cash Flow

Project A Project B

Year $0$: $$$$20,000$ Year $0$: $$$$45,000$

Year $1$: $11,000$ Year $1$: $10,000$

Year $2$: $17,000$ Year $2$: $17,000$

Year $3$: $16,000$ Year $3$: $16,000$

Year $4$: $15,000$

Year $5$: $14,000$

Year $6$: $13,000$

$$7,584$

$$13,904$

$$10,112$

$$9,480$

$$12,640$

Galaxy Corp. is considering a three$-$year project that has a weighted average cost of capital of $11\%$ and a NPV of $$22,870.$ Galaxy Corp. can replicate this project indefinitely. What is the equivalent annual annuity $($EAA$)$ for this project?

$$11,699$

$$7,955$

$$9,359$

$$9,827$

$$10,295$