Question 19.7: LowTech Manufacturing’s Staged Construction LowTech Manufact...
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 |
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.
PW_{one stage, yr. 3} = −20M + 5M(P/F,10%,20) + 3M(P/A,10%,3) + 5M(P/A,10%,17)(P/F,10%,3) = $18.34M
PW_{one stage, yr. 5} = −20M + 5M(P/F,10%,20) + 3M(P/A,10%,5) + 5M(P/A,10%,15)(P/F,10%,5) = $15.73M
PW_{one stage, yr. 10} = −20M + 5M(P/F,10%,20) + 3M(P/A,10%,10)+ 5M(P/A,10%,10)(P/F,10%,10) = $11.02M
E(PW_{one stage}) = .2(18.34M) + .5(15.73M) + .3(11.02M) = $14.84M
PW_{two stages, yr. 3} = −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
PW_{two stages, yr. 5} = −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
PW_{two stages, yr. 10} = −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
E(PW_{two stages}) = .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.
| P · PW^{2}_{two stage} | PW^{2}_{two stage} | PW_{two stages} | P · PW^{2}_{one stage} | PW^{2}_{one stage} | PW_{one stage} | 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 | ||||||
| E(PW^{2}) = $172.01 | E(PW^{2}) = $227.42 | ||||||
σ_{one stage} = \sqrt{E(PW^{2}_{one}) − E^{2}(PW_{one})}
= \sqrt{227.4 − 14.84^{2}} = \$2.7M
σ_{two stage} = \sqrt{E(PW^{2}_{two} − E^{2}(PW_{two})}
= \sqrt{172 − 13.07^{2}} = \$1.07M
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—σ_{PW} |
| Above average | Below average | Flexibility |