Net Present Value-Unequal Lives Al a Mode, Inc., is considering one of two inves
ID: 2579098 • Letter: N
Question
Net Present Value-Unequal Lives
Al a Mode, Inc., is considering one of two investment options. Option 1 is a $25,000 investment in new blending equipment that is expected to produce equal annual cash flows of $7,000 for each of seven years. Option 2 is a $28,000 investment in a new computer system that is expected to produce equal annual cash flows of $9,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $5,000. The computer system has no expected residual value at the end of the fifth year.
Assume there is sufficient capital to fund only one of the projects. Determine which project should be selected, comparing the (a) net present values and (b) present value indices of the two projects, assuming a minimum rate of return of 10%. Use the present value tables appearing above.
a. Determine the net present values of the two projects.
b. Determine the present value indices of the two projects. If required, round the present value index to two decimal places.
Which project should be selected? (If both present value indices are the same, either project will grade as correct.)
SelectBlending EquipmentComputer SystemItem 9
Explanation / Answer
Al a Mode Inc
Blending Equipment
Computer System
Total present value of cash flows
$135,790
$170,595
Less: amount to be invested
$25,000
$28,000
Net present value
$110,790
$142,595
Present value of cash flows for option1:
Annual cash inflows $7,000
Residual value at the end of 5 years = $5,000
Expected minimum rate of return 10%
Though the cash flows are available for 7 years, for comparison with Option 2 the life is taken at 5 years.
Hence, net cash flows for a five a year period = 5 x $7,000 = $35,000
Present value of an annuity at $1 at compound interest for 5 years at 10% = 3.791
Present value of net annual cash flows = $35,000 x 3.791 =$132,685
Present value of residual value = $5,000 x present value of $1 at compound interest at 10% for 5 years
= $5,000 x 0.621 = $3,105
Hence, total net cash inflows of Option 1 Blending Equipment = $132,685 + $3,105 = $135,790
Present value of cash flows for option 2 – Computer System:
Annual cash inflows $9,000
Expected minimum rate of return 10%
Net cash flows for a five a year period = 5 x $9,000 = $45,000
Present value of an annuity at $1 at compound interest for 5 years at 10% = 3.791
Present value of net annual cash flows = $45,000 x 3.791 =$170,595
Hence, total net cash inflows of Option 2 Computer System = $170,595
Present value index = present value of cash inflow/ initial investment
Present value index for Option 1 – Blending Equipment = $132,685/$25,000
= 5.3
Present value index for Option 2 – Computer System = $170,595/$28,000
= 6.09
Blending Equipment
Computer System
Present value index
5.3
6.09
The net present value of cash flows of Computer System ($142,595) is higher than that of the Blending Equipment ($110,790). Also, the present value index of Computer System (6.09) is higher than that of the Blending Equipment (5.3). Hence, the company should choose to invest in Computer System
Select – Computer System
Blending Equipment
Computer System
Total present value of cash flows
$135,790
$170,595
Less: amount to be invested
$25,000
$28,000
Net present value
$110,790
$142,595