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I have this problem

An investor enters into an agreement to contribute $7,000$ immediately and $1,000$ at the end of two years in exchange for the receipt of $4,000$ at the end of one year and $5,500$ at the end of three years.

I tried setting up this problem by equating each of their present values: $$7000+1000v^2 = 4000v + 5500v^3 \hspace{.3in} [1]$$ Notice that equation $[1]$ can be set up in two different ways: $$NPV_2(i) = 7000+1000v^2-4000v-5500v^3=0 \hspace{.3in} [2]$$ $$NPV_3(i) = 4000v+5500v^3-7000-1000v^2 = 0 \hspace{.3in} [3]$$

And if I evaluate equation $[2]$ at $i=0.09$ I get $NPV_2(0.09)= -75.05$

while using euation $[3]$ at $i=0.09$ yields $NPV_3(0.09) = 75.05$

Why are they different?

llawliet_78
  • 323
  • Because you can compute the NPV for the investor or the NPV for the other contracting party. The NPV for the investor is the NPV of his/her receipts minus the NPV of his/her contributions. This is what equation [3] yields. The NPV for the other partner is exactly the opposite (negative amount), i.e., the value given by equation [2]. – Gerhard S. Jan 05 '18 at 16:49
  • @GerhardS. woah, I forgot about that xD. Anyways, thanks for pointing that out! – llawliet_78 Jan 05 '18 at 16:57

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