$7.$ 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 $11\%?$

Cash Flow

Project A Project B

Year $0$: $$$$10,000$ Year $0$: $$$$45,000$

Year $1$: $7,000$ Year $1$: $9,000$

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

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

Year $4$: $14,000$

Year $5$: $13,000$

Year $6$: $12,000$

$$21,988$

$$13,193$

$$14,292$

$$16,491$

$$18,690$