LowTech Manufacturing’s Staged Construction LowTech Manufacturing is building a new office complex next to its manufacturing plant. There are two plans. The first is a five-floor complex, where only three floors are needed for the first 3 to 10 years. The top two floors would remain empty until

Question

LowTech Manufacturing’s Staged Construction
LowTech Manufacturing is building a new office complex next to its manufacturing plant. There are two plans. The first is a five-floor complex, where only three floors are needed for the first 3 to 10 years. The top two floors would remain empty until needed by LowTech. The second is a three-story building whose foundation and first three floors would accommodate adding another two floors later.
Building in two stages reduces the costs now, but total costs will increase substantially. Building in two stages allows flexibility in timing and in the exact design of the upper two floors. A probability distribution for when the space will be needed and data for the profitability estimates are summarized in the table below.
To simplify the calculations, your boss has said to assume that the benefits of having the new space are $1M per floor for each year the floor is needed. LowTech management has identified an interest rate of 10% and an analysis period of 20 years.

Cash Flows
Two Stages	One Stage
Year 0: $15M	$20M	First cost
Year 3, 5, or 10: $12M
$6M	$5M	Salvage value

P(year)	Top 2 Floors Needed (year)
.2	3
.5	5
.3	10

Accepted Answer

First, find the PW for both alternatives with each timing of the second stage. With three floors in use, the benefits are $3M per year for the first 3, 5, or 10 years. With five floors in use, the benefits are $5M per year for the last 17, 15, or 10 years. The E(PW) for each alternative is the weighted average (using probabilities of .2, .5, and .3) for using five floors in 3, 5, or 10 years.

[latex]PW_{one stage, yr. 3}[/latex] = −20M + 5M(P/F,10%,20) + 3M(P/A,10%,3) + 5M(P/A,10%,17)(P/F,10%,3) = $18.34M

[latex]PW_{one stage, yr. 5}[/latex] = −20M + 5M(P/F,10%,20) + 3M(P/A,10%,5) + 5M(P/A,10%,15)(P/F,10%,5) = $15.73M

[latex]PW_{one stage, yr. 10}[/latex] = −20M + 5M(P/F,10%,20) + 3M(P/A,10%,10)+ 5M(P/A,10%,10)(P/F,10%,10) = $11.02M

[latex]E(PW_{one stage})[/latex] = .2(18.34M) + .5(15.73M) + .3(11.02M) = $14.84M

[latex]PW_{two stages, yr. 3}[/latex] = −15M + 6M(P/F,10%,20) + 3M(P/A,10%,3) + 5M(P/A,10%,17)(P/F,10%,3) − 12M(P/F,10%,3) = $14.47M

[latex]PW_{two stages, yr. 5}[/latex] = −15M + 6M(P/F,10%,20) + 3M(P/A,10%,5) + 5M(P/A,10%,15)(P/F,10%,5) − 12M(P/F,10%,5) = $13.43M

[latex]PW_{two stages, yr. 10}[/latex] = −15M + 6M(P/F,10%,20) + 3M(P/A,10%,10) + 5M(P/A,10%,10)(P/F,10%,10) − 12M(P/F,10%,10) = $11.54M

[latex]E(PW_{two stages})[/latex] = .2(14.47M) + .5(13.43M) + .3(11.54M) = $13.07M

The standard deviation of the PW for each alternative is found using the following table.

[latex]P · PW^{2}_{two stage}[/latex]	[latex]PW^{2}_{two stage}[/latex]	[latex]PW_{two stages}[/latex]	[latex]P · PW^{2}_{one stage}[/latex]	[latex]PW^{2}_{one stage}[/latex]	[latex]PW_{one stage}[/latex]	P	N
$41.88	$209.38	$14.47M	$67.27	$336.36	$18.34M	.2	3
90.18	180.36	13.43M	123.72	247.43	15.73M	.5	5
39.95	133.17	11.54M	36.43	121.44	11.02M	.3	10
		E(PW) = $13.07M			E(PW) = $14.84M
[latex]E(PW^{2})[/latex] = $172.01			[latex]E(PW^{2})[/latex] = $227.42

[latex]σ_{one stage} = \sqrt{E(PW^{2}_{one}) − E^{2}(PW_{one})}[/latex]
[latex]= \sqrt{227.4 − 14.84^{2}} = \$2.7M[/latex]

[latex]σ_{two stage} = \sqrt{E(PW^{2}_{two} − E^{2}(PW_{two})}[/latex]
[latex]= \sqrt{172 − 13.07^{2}} = \$1.07M[/latex]

EXHIBIT 19.4 Summary table for Example 19.7: LowTech Manufacturing office complex

Two Stages	One Stage	Attributes
$13.07M	$14.84M	Profitability—E(PW)
$1.07M	$2.69M	Risk—[latex]σ_{PW}[/latex]
Above average	Below average	Flexibility

Question 19.7: LowTech Manufacturing’s Staged Construction LowTech Manufact...

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