Question

Alternative Capital Investments

The investment committee of Auntie M's Restaurants Inc. is evaluating two restaurant sites. The sites have different useful lives, but each requires an investment of $900,000. The estimated net cash flows from each site are as follows:

		Net Cash Flows
Year		Wichita		Topeka
1		$310,000		$400,000
2		310,000		400,000
3		310,000		400,000
4		310,000		400,000
5		310,000
6		310,000

The committee has selected a rate of 20% for purposes of net present value analysis. It also estimates that the residual value at the end of each restaurant’s useful life is $0, but at the end of the fourth year, Wichita’s residual value would be $500,000.

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	3.353	2.991
6	4.917	4.355	4.111	3.785	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

Required:

1. For each site, compute the net present value. Use the present value of an annuity of $1 table above. Ignore the unequal lives of the projects. If required, round to the nearest dollar.

	Wichita	Topeka
Present value of annual net cash flows	$	$
Amount to be invested
Net present value	$	$

2. For each site, compute the net present value, assuming that Wichita is adjusted to a four-year life for purposes of analysis. Use the present value of $1 table above. If required, round to the nearest dollar.

	Wichita	Topeka
Total present value of net cash flow	$	$
Amount to be invested
Net present value	$	$

Answer 1

(1) when there is uniform series of cash flow we will use annuity

	wichita	Topeka
Present value of annual net cash flows	$1,031,060	$1,035,600
Amount to be invested	-$900,000	-$900,000
Net present value	$131,060	$135,600

* present value = cash flow*Annuity factor at 20%

=$310,000*3.326

=$1,031,060

** Topeka present value 20% for 4 years

=$400,000*2.589

=$1,035,600

2)

	wichita	Topeka
Present value of annual net cash flows	$1,043,590	$1,035,600
Amount to be invested	-$900,000	-$900,000
Net present value	$143,590	$135,600

present value including salvage = $310,000*2.589+$500,000*0.482

=802,590+241,000

=$1,043,590