You are considering two projects with the following cash flows: $$\begin{array} { l c c }
& \text { Project X } & \text { Project Y } \
\text { Year 1 } & \mathbf { \$ 9 , 0 0 0 } & \mathbf { \$ 7 , 0 0 0 } \
\text { Year 2 } & \mathbf { 8 , 0 0 0 } & \mathbf { 7 , 5 0 0 } \
\text { Year 3 } & \mathbf { 7 , 5 0 0 } & \mathbf { 8 , 0 0 0 } \
\text { Year 4 } & \mathbf { 7 , 0 0 0 } & \mathbf { 9 , 0 0 0 }
\end{array}$$ Which of the following statements are true concerning these two projects?
I.Both projects have the same future value at the end of year 4,given a positive rate of return.
II.Both projects have the same future value given a zero rate of return.
III.Project X has a higher present value than Project Y,given a positive discount rate.
IV.Project Y has a higher present value than Project X,given a positive discount rate.

Question

You are considering two projects with the following cash flows: $$\begin{array} { l c c } 
& \text { Project X } & \text { Project Y } \
\text { Year 1 } & \mathbf { \$ 9 , 0 0 0 } & \mathbf { \$ 7 , 0 0 0 } \
\text { Year 2 } & \mathbf { 8 , 0 0 0 } & \mathbf { 7 , 5 0 0 } \
\text { Year 3 } & \mathbf { 7 , 5 0 0 } & \mathbf { 8 , 0 0 0 } \
\text { Year 4 } & \mathbf { 7 , 0 0 0 } & \mathbf { 9 , 0 0 0 }
\end{array}$$ Which of the following statements are true concerning these two projects?
I.Both projects have the same future value at the end of year 4,given a positive rate of return.
II.Both projects have the same future value given a zero rate of return.
III.Project X has a higher present value than Project Y,given a positive discount rate.
IV.Project Y has a higher present value than Project X,given a positive discount rate.

Quizplus · Accepted Answer

I. This statement is false because the future value of each project will depend on the rate of return used to discount the cash flows. The projects have different cash flows, so they will not have the same future value at any positive rate of return.

II. This statement is true because the future value of each project is simply the sum of its cash flows, and the sums of the cash flows for these two projects are equal. Therefore, at a zero rate of return, the future value of each project is the same.

III. This statement is true because Project X has a higher total cash flow at the beginning of the sequence (Year 1), so it will have a higher present value. Given a positive discount rate, cash flows further in the future are worth less today, so the larger cash flows in the later years of Project Y will not be sufficient to overcome the initial difference in cash flows.

IV. This statement is false because Project X has a higher present value than Project Y, as explained in statement III above.

You Are Considering Two Projects with the Following Cash Flows