Question

Consider the following opportunities: Opportunity 1 requires a $6,050 cash payment now (Year 0) but will result in $17,600 cash received in Year 5. Opportunity 2 requires no cash outlay and results in $3,950 cash received in Year 3 and Year 5.

a. Use a 6 percent discount rate and determine whether Opportunity 1 or Opportunity 2 results in a greater NPV.

b. Use a 10 percent discount rate and determine whether Opportunity 1 or Opportunity 2 results in a greater NPV.

Answer 1

a. Using 6% discount rate

The Present value factor table of 6% is as follows

YEAR	PRESENT VALUE FACTOR @ 6%
0	1
1	0.9434
2	0.8900
3	0.8396
4	0.7921
5	0.7473

OPPORTUNITY 1

PRESENT VALUE (PV) OF CASH OUTFLOW = $6050*1 = $6050

PV OF CASH INFLOW IN YEAR 5 = $17600*0.7473 = $13152.48

NPV = PV OF CASH INFLOW - PV OF CASH OUTFLOW

= $7102.48

OPPORTUNITY 2

PV OF CASH OUTFLOW = NIL

PV OF CASH INFLOW IN YEAR 3 AND 5 = $3950*0.8396 + $3950*0.7473 = $6268.255

NPV = $6268.255

At 6% discount rate OPPORTUNITY 1 has higher NPV.

b. Using 10% discount rate

The Present value factor table of 10% is as follows

YEAR	PRESENT VALUE FACTOR @ 10%
0	1
1	0.9091
2	0.8264
3	0.7513
4	0.6830
5	0.6209

OPPORTUNITY 1

PRESENT VALUE (PV) OF CASH OUTFLOW = $6050*1 = $6050

PV OF CASH INFLOW IN YEAR 5 = $17600*0.6209 = $10927.84

NPV = PV OF CASH INFLOW - PV OF CASH OUTFLOW

= $4877.84

OPPORTUNITY 2

PV OF CASH OUTFLOW = NIL

PV OF CASH INFLOW IN YEAR 3 AND 5 = $3950*0.7513 + $3950*0.6209 = $5420.19

NPV = $5420.19

At 10% discount rate OPPORTUNITY 2 has higher NPV.