An investor paid $8000 to a consulting firm to analyze possible uses for a small parcel of land on the edge of town that can be bought for $30,000. In their report, the consultants suggested four alternatives:Assuming 10% is the minimum attractive rate of return, what should the investor do?

Question

An investor paid $8000 to a consulting firm to analyze possible uses for a small parcel of land on the edge of town that can be bought for $30,000. In their report, the consultants suggested four alternatives:

Terminal Value at End of 20 yr	Uniform Net Annual Benefit	Total Investment Including Land[latex]\underline{*}[/latex]	Alternatives
$ 0	$ 0	$ 0	Do nothing	A
30,000	5,100	50,000	Vegetable market	B
30,000	10,500	95,000	Gas station	C
150,000	36,000	350,000	Small motel	D

* Includes the land and structures but does not include the $8000 fee to the consulting firm.

Assuming 10% is the minimum attractive rate of return, what should the investor do?

Accepted Answer

Alternative A is the “do-nothing” alternative. Generally, one feasible alternative is to remain in the present status and do nothing. The investor could decide that the most attractive alternative is not to purchase the property at all.

Note that if the investor does nothing, then the total venture would appear to be an unsatisfactory one because of the $8000 spent on professional advice. However, because the $8000 is a past cost, it is a sunk cost. The only relevant costs in an economic analysis are present and future costs. Sunk costs are gone and should not be allowed to affect future planning. (Past costs may be relevant in computing depreciation charges and income taxes, but nowhere else.) The past should not deter the investor from making the best decision now.

This problem is one of neither fixed input nor fixed output, so our criterion will be to maximize the present worth of benefits minus the present worth of cost; that is, to maximize net present worth.

Alternative A, Do Nothing

NPW=0

Alternative B, Vegetable Market

[latex]NPW=-50,000+5100(P/A,10\%,20)+30,000(P/F,10\%,20)[/latex]

[latex]=-50,000+5100(8.514)+30,000(0.1486)[/latex]

[latex]=-50,000+43,420+4460[/latex]

[latex]=-\$2120[/latex]

Alternative C, Gas Station

[latex]NPW=-95,000+10,500(P/A,10\%,20)+30,000(P/F,10\%,20)[/latex]

[latex]=-95,000+89,400+4460=-\$1140[/latex]

Alternative D, Small Motel

[latex]NPW=-350,000+36,000(P/A,10\%,20)+150,000(P/F,10\%,20)[/latex]

[latex]=-350,000+306,500+22,290=-\$21,210[/latex]

The criterion is to maximize net present worth. In this situation, one alternative has NPW equal to zero, and three alternatives have negative values for NPW. We will select the best of the four alternatives, namely, the do-nothing Alt. A, with NPW equal to zero.

5-BUTTON SOLUTION

H	G	F	E	D	C	B	A
Answer	Solve for	FV	PV	PMT	n	i	Alternative	1
-$47,878	PV	30,000		5100	20	10%	Vegetable market	2
-$2,122	= -H2+E3	total	50,000					3
								4
-$93,852	PV	30,000		10,500	20	10%	Gas station	5
-$1,148	= -H5+E6	total	-95,000					6
								7
-$328,785	PV	150,000		36,000	20	10%	Small Motel	8
-$21,215	= -H8+E9	total	-350,000					9

Since the total present worth of each action alternative is negative, the best choice is to do nothing. Note that in this case the PV of the positive annual revenue and positive salvage value is negative. To compute the present worth of each alternative, we must subtract the PV values in H2, H5, and H8.

Question 5.9: An investor paid $8000 to a consulting firm to analyze possi...

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