I am working on homework for my Business Finance class, I was trying to look at

Question

I am working on homework for my Business Finance class, I was trying to look at the question in Chapter 8, number 7QP, and there is no solution. My book is Essentials of Corporate Finance 8th Edition, the link to the question is, https://www.chegg.com/homework-help/Essentials-of-Corporate-Finance-8th-edition-chapter-8-problem-7QP-solution-9780078034756.

The question is: Calculating NPV and IRR. A project that provides annual cash flows of $1,930 for eight years costs $7,700 today. Is this a good project if the required return is 8 percent? What if it's 24 percent? At what discount rate would you be indifferent between accepting the project and rejecting it?

Explanation / Answer

Present value of annual cash flows of $1,930 for eight years @ 8%

PV=(1930/0.08)*(1-(1/(1+0.08)^8)

=11091.01

The Net Present value(NPV) of   annual cash flows of $1,930 for eight years @ 8%

=PV-Investment

=11091.01-7,700

=3391.01

=$ 3391(rounded to 2 places)

Present value of  annual cash flows of $1,930 for eight years @ 24%

PV=(1930/0.24)*(1-(1/(1+0.24)^8)=6602.96

The Net Present value(NPV) of   annual cash flows of $1,930 for eight years @ 8%

=PV-Investment

=6602.96-7,700

=-1097.04

Let at r discount rate(is IRR) would you be indifferent between accepting the project and rejecting it at which NPV=0.

PV=(1930/r)*(1-(1/(1+r)^8)

Thus ,Investment=PV at this rate(NPV=0)

=>7,700 =(1930/r)*(1-(1/(1+r)^8)

@r=20%,PV=(1930/.20)*(1-(1/(1+.20)^8)=7405.72

@r=19%,PV=(1930/.19)*(1-(1/(1+.19)^8)=7631.92

@r=18.5%,PV=(1930/.185)*(1-(1/(1+.185)^8)=7749.32

@r=18.7%,PV=(1930/.187)*(1-(1/(1+.187)^8)=7702~7700

Therefore the discount rate would you be indifferent between accepting the project and rejecting it is the IRR is 18.7%.

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