$7.$ 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 $0$: $$$$10,000$ Year $0$: $$$$40,000$

Year $1$: $7,000$ Year $1$: $8,000$

Year $2$: $15,000$ Year $2$: $16,000$

Year $3$: $14000$ Year $3$: $15,000$

Year $4$: $12,000$

Year $5$: $11,000$

Year $6$: $10,000$

$$23,907$

$$14,127$

$$13,040$

$$15,214$

$$21,734$

Galaxy Corp. is considering a three$-$year project that has a weighted average cost of capital of $10\%$ and a NPV of $$85,647.$ Galaxy Corp. can replicate this project indefinitely. What is the equivalent annual annuity $($EAA$)$ for this project?

$$34,440$

$$32,718$

$$43,050$

$$30,996$

$$29,274$