Question

A project that provides annual cash flows of $17,300 for nine years costs $78,000 today. What is the NPV for the project if the required return is 8%? At a required return of 8% should the firm accept this project? What is the NPV for the project if the required return is 20%? At a required return of 20% should the firm accept this project? At what discount rate would you be indifferent between accepting the project and rejecting it? 

Answer 1

At 8%

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

=17300/1.08+17300/1.08^2+17300/1.08^3+17300/1.08^4+17300/1.08^5+17300/1.08^6+17300/1.08^7+17300/1.08^8+17300/1.08^9

=108071.16

NPV=Present value of inflows-Present value of outflows

=108071.16-78000

=$30071.16(Approx)

At 20%

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

=17300/1.2+17300/1.2^2+17300/1.2^3+17300/1.2^4+17300/1.2^5+17300/1.2^6+17300/1.2^7+17300/1.2^8+17300/1.2^9

=69735.72

NPV=Present value of inflows-Present value of outflows

=69735.72-78000

=$-8264.28(Approx)(Negative)

Let discount rate be x%

At this rate;present value of cash flows=78000

78000=17300/1.0x+17300/1.0x^2+............+17300/1.0x^9

Hence x=discount rate=16.62%(Approx)