Calculation to obtained the maximizes the NPV from the given investment:

The Net Present Value (NPV) of an investment is the amount by which the investment will increase the firm’s value.

Assuming the annual rate interest, “r = 0.10”, the user can compute the NPV for investment 1 as,

NVP = −6 −51+0.1+7(1+0.1)2+9(1+0.1)3=−6−51.1+7(1.1)2+9(1.1)3=−6−51.1+71.21+91.331=−6−4.545+5.785+6.762=2.0018

Now, the user computes the NPV for investment 1 as,

NVP = −8 −31+0.1+9(1+0.1)2+7(1+0.1)3=−8−31.1+9(1.1)2+7(1.1)3=−8−31.1+91.21+71.331=−8−2.727+7.438+5.259=1.97

Therefore, the NPV of investment 1 is larger than investment 2.

Let, “x₁” be the fraction of investment 1 that is undertaken and “x₂” be the fraction of investment 2 that is undertaken.

The objective function is to maximize the NPV of the investment.

Therefore, maximize z = 2x1+ 1.97x2

Constraint 1:

At time 0, $10000 is available for investment

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Chapter 3.6, Problem 1P

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Solution Summary: The author explains how the user calculates the NPV of investment 1 as, cNVP =-6 -51+0.1

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