Question

A new computer system will require an initial outlay of $20,250, but it will increase the firm’s cash flows by $4,500 a year for each of the next 6 years.

A) Calculate the NPV and decide if the system is worth installing if the required rate of return is 8%. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

B) Calculate the NPV and decide if the system is worth installing if the required rate of return is 13%. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

C) How high can the discount rate be before you would reject the project? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

Year	Cashflows	Discounting factor for 8%	Present value@8%	Discounting factor for 13%	Present value@13%	Discounting factor for 8.9%	Present [email protected]%
0	-20250	1	-20250	1	-20250	1	-20250
1	4500	0.93	4,166.67	0.88	3,982.30	0.92	4,132.23
2	4500	0.86	3,858.02	0.78	3,524.16	0.84	3,794.52
3	4500	0.79	3,572.25	0.69	3,118.73	0.77	3,484.41
4	4500	0.74	3,307.63	0.61	2,759.93	0.71	3,199.64
5	4500	0.68	3,062.62	0.54	2,442.42	0.65	2,938.14
6	4500	0.63	2,835.76	0.48	2,161.43	0.60	2,698.02
	NPV		552.96		-2,261.03		-3.04
IRR	8.89%
Ans a. At rate of return of 8%, we get NPV of $552.96 and hence the system is worth installing.
Ans b. At rate of return of 13%, we get NPV of -$2261.03 and hence the system is not worth installing.
NPV is the present value of cash inflows less present value of cash outflows
IRR Explaination:-
Internal rate of return is the rate where NPV of the project is zero. To calculate IRR, we should set NPV is equal to zero and solve for discount rate which is the IRR.
Using trial and error method we guessed the discounting rate to be 8.89% .
Ans c. Internal Rate of Return is the rate at which NPV is zero i.e. no profit no loss. So at IRR of 8.89% the NPV will be zero and anything above this rate will give negative npv as also evident from the calculations above (i.e. Return of 13% gives negative npv). One should not accept the project with negative npv and hence IRR i.e. 8.89 is the highest rate after which one will start rejecting the project.
Also see at return of 8.90% as calculated above we have started getting negative NPV