Question

A-12 Present Value of Cash Flows

Star City is considering an investment in the community center that is expected to return the following cash flows: Use Exhibit A.8.

Year	Net Cash Flow
1	$	32,000
2		62,000
3		92,000
4		92,000
5		112,000

This schedule includes all cash inflows from the project, which will also require an immediate $212,000 cash outlay. The city is tax-exempt; therefore, taxes need not be considered.

Required:

a. What is the net present value of the project if the appropriate discount rate is 24 percent? (Round PV factor to 3 decimal places. Negative amount should be indicated by a minus sign.)

b. What is the net present value of the project if the appropriate discount rate is 14 percent? (Round PV factor to 3 decimal places. Negative amount should be indicated by a minus sign.)

Answer 1

Solution a:

Computation of NPV - Star City
Particulars	Period	PV Factor (24%)	Amount	Present Value
Cash outflows:
Cost of VAN	0	1	$212,000.00	$212,000.00
Present Value of Cash outflows (A)				$212,000.00
Cash Inflows
Annual increase in Cash Inflows:
Year 1	1	0.806	$32,000.00	$25,792.00
Year 2	2	0.650	$62,000.00	$40,300.00
Year 3	3	0.524	$92,000.00	$48,208.00
Year 4	4	0.423	$92,000.00	$38,916.00
Year 5	5	0.341	$112,000.00	$38,192.00
Present Value of Cash Inflows (B)				$191,408.00
Net Present Value (NPV) (B-A)				-$20,592.00

Solution b:

Computation of NPV - Star City
Particulars	Period	PV Factor (14%)	Amount	Present Value
Cash outflows:
Cost of VAN	0	1	$212,000.00	$212,000.00
Present Value of Cash outflows (A)				$212,000.00
Cash Inflows
Annual increase in Cash Inflows:
Year 1	1	0.877	$32,000.00	$28,064.00
Year 2	2	0.769	$62,000.00	$47,678.00
Year 3	3	0.675	$92,000.00	$62,100.00
Year 4	4	0.592	$92,000.00	$54,464.00
Year 5	5	0.519	$112,000.00	$58,128.00
Present Value of Cash Inflows (B)				$250,434.00
Net Present Value (NPV) (B-A)				$38,434.00