Question

Project 1 requires an original investment of $41,900. The project will yield cash flows of $10,000 per year for five years. Project 2 has a calculated net present value of $11,500 over a three-year life. Project 1 could be sold at the end of three years for a price of $45,000.

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 three-year life with residual value, assuming a minimum rate of return of 15%. If required, round to the nearest dollar.
$

b. Which project provides the greatest net present value?

Answer 1

Answer (a). :

The Net Present Value (NPV) of a project is the sum of all present values of cash inflows that are expected to occur over the life of project minus present values of all cash outflows. So we can say that Net Present Value is difference between Cash Inflow and Cash Outflow.

Net Present Value[NPV] = Present Value of Cash inflow[PVCI] (-) Present Value of Cash Outflow[PVCO]

Project 1 : Given - Original investment = $41,900

Annual cash Inflow = $10,000/ year

Resale Value (at the end of year 3) = $45,000

Rate of Return (r) = 15%

Time Period (i) = 3yrs

Present Value of Cash Inflow =  (Cash flows)/( 1+r)i

= (10000 * 0.870) + (10000 * 0.756) + (55000 * 0.658)

= 8700 + 7560 + 36190

PVCI = 52,450

Present Value of Cash Outflow [PVCO] = Original investment = 41,900

Therefore, NPV = PVCI (-) PVCO

= 52,450 (-) 41,900

= $10,550

Alternatively in tabular form :

Year	Cash Flow	DF @15 %	Dicounted Cash Flow/ Present value of CF
0	(41,900)	1	(41,900)
1	10,000	0.870	8,700
2	10,000	0.756	7,560
3	10,000 + 45,000	0.658	36,190
		NPV	$10,550

Answer (b) : NPV [Project 1] = $10,550

NPV [Project 2] = $11,500

Since the NPV of Project 2 is greater than NPV of Project 1 by $950 [ 11500 - 10550], Project 2 provides the greatest net present value.

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