Question

Net Present Value-Unequal Lives

Al a Mode, Inc., is considering one of two investment options. Option 1 is a $26,000 investment in new blending equipment that is expected to produce equal annual cash flows of $8,000 for each of seven years. Option 2 is a $27,000 investment in a new computer system that is expected to produce equal annual cash flows of $10,000 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.

Present Value of $1 at Compound Interest
Year	6%	10%	12%	15%	20%
1	0.943	0.909	0.893	0.870	0.833
2	0.890	0.826	0.797	0.756	0.694
3	0.840	0.751	0.712	0.658	0.579
4	0.792	0.683	0.636	0.572	0.482
5	0.747	0.621	0.567	0.497	0.402
6	0.705	0.564	0.507	0.432	0.335
7	0.665	0.513	0.452	0.376	0.279
8	0.627	0.467	0.404	0.327	0.233
9	0.592	0.424	0.361	0.284	0.194
10	0.558	0.386	0.322	0.247	0.162

Present Value of an Annuity of $1 at Compound Interest
Year	6%	10%	12%	15%	20%
1	0.943	0.909	0.893	0.870	0.833
2	1.833	1.736	1.690	1.626	1.528
3	2.673	2.487	2.402	2.283	2.106
4	3.465	3.170	3.037	2.855	2.589
5	4.212	3.791	3.605	3.352	2.991
6	4.917	4.355	4.111	3.784	3.326
7	5.582	4.868	4.564	4.160	3.605
8	6.210	5.335	4.968	4.487	3.837
9	6.802	5.759	5.328	4.772	4.031
10	7.360	6.145	5.650	5.019	4.192

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.

	Blending Equipment	Computer System
Total present value of cash flows	$	$
Less amount to be invested	$	$
Net present value	$	$

b. Determine the present value indices of the two projects. If required, round the present value index to two decimal places.

	Present Value Index
Blending Equipment
Computer System

Which project should be selected? (If both present value indices are the same, either project will grade as correct.)
SelectBlending EquipmentComputer SystemItem 9

Answer 1

a. Determine the net present values of the two projects.

	Blending Equipment	Computer System
Total present value of cash flows	41501	37900
Less amount to be invested	-26000	-27000
Net present value	15501	10900

Working notes for the above answer:

Blending Equipment
Year	Cash flow	PV factor at 10%	Prasent Value
	A	B	C=A*B
1	8000	0.909	7272
2	8000	0.826	6608
3	8000	0.751	6008
4	8000	0.683	5464
5	8000	0.621	4968
6	8000	0.564	4512
7	13000	0.513	6669
Total			41501

Computer System
Year	Cash flow	PV factor at 10%	Prasent Value
	A	B	C=A*B
1	10,000	0.909	9090
2	10,000	0.826	8260
3	10,000	0.751	7510
4	10,000	0.683	6830
5	10,000	0.621	6210
Total			37900

____________________________________________

2

	Present Value Index
Blending Equipment	1.60
Computer System	1.40

Working for the answer

Present value Index =Present value of future cash flow/Amount invested	Blending Equipment	Computer System
Total present value of cash flows A	41501	37900
Amount invested (B)	26000	27000
Present value Index=A/B	1.60	1.40