Question

Net Present Value—Unequal Lives

Project 1 requires an original investment of $73,000. The project will yield cash flows of $14,000 per year for eight years. Project 2 has a calculated net present value of $16,000 over a six-year life. Project 1 could be sold at the end of six years for a price of $60,000.

Use the Present Value of $1 at Compound Interest and the Present Value of an Annuity of $1 at Compound Interest tables shown below.

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

a. Determine the net present value of Project 1 over a six-year life with residual value, assuming a minimum rate of return of 12%. If required, round to the nearest dollar.
$

b. Which project provides the greatest net present value?

Answer 1

Answer:- a)-The net present value of Project 1 is 14974.

Explanation:-

Net present value of Project 1 = Present value of cash inflows – Total outflows

     ={($14000*4.111)+($60000*0.507) - $73000}

     =($57554+$30420) - $73000

     = $87974-$73000

     = $14974

Net present value of Project 2 = $16000.

b)-Project 2 provides the greatest net present value of $16000.

Answer 2

To determine the net present value (NPV) of Project 1 over a six-year life with a residual value, we need to calculate the present value of the cash flows and the residual value, and then subtract the initial investment. Here's the calculation:

Initial investment (outflow): -$73,000

Cash inflows (annual cash flows): $14,000 per year for 6 years (since we are considering a six-year life)

Residual value (cash inflow): $60,000 (to be received at the end of the sixth year)

Discount rate: 12%

Using the Present Value of an Annuity of $1 at Compound Interest table, we find the present value factor for 6 years at a 12% discount rate is 4.111.

Calculating the present value of the cash inflows:

Cash inflows: $14,000 per year Present value factor: 4.111

Present value of cash inflows = $14,000 * 4.111 = $57,554 (rounded to the nearest dollar)

Calculating the present value of the residual value:

Residual value: $60,000 Discount rate: 12% Present value factor for 6 years: 0.507 (from the Present Value of $1 at Compound Interest table)

Present value of the residual value = $60,000 * 0.507 = $30,420 (rounded to the nearest dollar)

Calculating the net present value:

NPV = Present value of cash inflows + Present value of residual value - Initial investment NPV = $57,554 + $30,420 - $73,000 NPV = $15,974 (rounded to the nearest dollar)

Therefore, the net present value of Project 1 over a six-year life with a residual value, assuming a minimum rate of return of 12%, is approximately $15,974.

To determine which project provides the greatest net present value, we need to compare it with the net present value of Project 2. Since the net present value of Project 2 is not provided in the given information, we cannot make a direct comparison and determine which project provides the greatest net present value.