The following table gives the available projects (in $millions) for a firm. $\begin{array}{rrrrrrll}
\underline { \mathrm { A }} & \underline { \mathrm { B } } & \underline { \mathrm { C } } & \underline { \mathrm { D } } & \underline { \mathrm { E } } & \underline { \mathrm { F } } & \underline { \mathrm { G } } & \
5.0 & 4.0 & 5.0 & 1.0 & 2.0 & 7.0 & 8.0 & \text { Initial investment } \
1.5 & -0.5 & 1.0 & 0.5 & 0.5 & 1.0 & 1.0 & \mathrm{NPV}
\end{array}$ The firm has only $20 million to invest.What is the maximum NPV that the company can obtain?
A)3.5
B)4.0
C)4.5
D)5.0

Question

Quizplus · Accepted Answer

To maximize the NPV, the company should invest in projects with the highest NPV per dollar invested.

The NPV per dollar for each project is:
- Project A: 1.5/5 = 0.3
- Project B: (-0.5)/4 = -0.125
- Project C: 1/5 = 0.2
- Project D: 0.5/1 = 0.5
- Project E: 0.5/2 = 0.25
- Project F: 1/7 ≈ 0.143
- Project G: 1/8 = 0.125

Based on these calculations, the company should invest in project D and project A (in that order) to maximize the NPV. The total investment in these two projects is 6 million, which is within the available budget of $20 million.

The total NPV for these two projects is 0.5 + 1.5 = 2. The maximum NPV that the company can obtain is therefore 2.0.

Note that project C also has a high NPV per dollar invested, but it would not be possible to invest in this project without going over the budget of $20 million.

The Following Table Gives the Available Projects (In $Millions) for a Firm