3.34 A foursome of entrepreneurial electrical engineering graduates has a plan to

start a new solar power equipment company based on STE (solar thermal electric)

technology. They have recently approached a group of investors with their idea and

asked for a loan of $5 million. Within the agreement, the loan is to be repaid by

allocating 80% of the company’s profits each year for the first 4 years to the

investors. In the fifth year, the company will pay the balance remaining on the loan

in cash. The company’s business plan indicates that they expect to make no profit for

the first year, but in years 2 through 4, they anticipate profits to be $1.5 million per

year. If the investors accept the deal at an interest rate of 15% per year, and the

business plan works to perfection, what is the expected amount of the last loan

payment (in year 5)?

0 1 2 3 4 5

i = 15%

1.2 1.2 1.2

-5 y

Using Financial Table for i = 15%: Calculating in terms of Present Worth for Year 0

(in millions)

80% of $1.5 million = (1.5) (0.8) = $1.2 million paid for loan from year 2 to year 4

5 = 1.2 (P/A, 15%, 3) (P/F, 15%, 1) + y (P/F, 15%, 5)

5 = 1.2 (2.2832) (0.8696) + y (0.4972)

5 = 2.383 + 0.4972y

y = $ 5.264 million

In conclusion, the 20% profit gained by company in year 2, 3 and 4 are in a

total of $0.9 million, even if the company use the profits to pay the loan at year 5, the

company still has to find another capital of 5.264 – 0.9 = $4.364 million to pay their

loan at year 5. If there are no external sources of money or income to pay the loan,

this method is not economically viable.

In Excel

5.11 The Murphy County Fire Department is considering two options for

upgrading its aging physical facilities. Plan A involves remodeling the fire stations

on Alameda Avenue and Trowbridge Boulevard that are 57 and 61 years old,

respectively. (The industry standard is about 50 years of use for a station.) The cost

for remodeling the Alameda station is estimated at $952,000 while the cost of

redoing the Trowbridge station is $1.3 million. Plan B calls for buying 5 acres of

land somewhere between the two stations, building a new fire station, and selling the

land and structures at the previous sites. The cost of land in that area is estimated to

be $366,000 per acre. The size of the new fire station would be 9000 square feet with

a construction cost of $151.18 per square foot. Contractor fees for overhead, profit,

etc. are expected to be $340,000, and architect fees will be $81,500. (Assume all of

the costs for plan B occur at time 0.) If plan A is adopted, the extra cost for personnel

and equipment will be $126,000 per year. Under plan B, the sale of the old sites is

anticipated to net a positive $500,000 five years in the future. Use an interest rate of

6% per year and a 50-year useful life for the remodeled and new stations to

determine which plan is better on the basis of a present worth analysis.

PWA = -952,000 - 1,300,000 - 126,000(P/A,6%,50)

= -952,000 - 1,300,000 - 126,000(15.7619)

= $-4,237,999.40

= $-4,238,000

952,000 + 1,300,000

126,000 126,000 126,000 126,000

i = 6% 0

1

2

3

50 Plan A

PWB = -5(366,000) - 9000(151.18) - 340,000 - 81,500 + 500,000(P/F,6%,5)

= -3,612,120 + 500,000(0.7473)

= $-3,238,470

Plan B is better on the basis of present worth analysis due to lower cash outflow

(cost).

In Excel

5(366,000) + 9,000(151.18) + 340,000 + 81,500

500,000 i = 6%

0

5

50 Plan B

5.20 Throughout the present worth analyses, the decision between seawater and

groundwater switched multiple times in Examples 5.2 and 5.4. A summary is given

here in $1 million units. The confusion about the recommended source for UPW has

not gone unnoticed by the general manager. Yesterday, you were asked to settle the

issue by determining the first cost Xs of the seawater option to ensure that it is the

economic choice over groundwater. The study period is set by the manager as 10

years, simply because that is the time period on the lease agreement for the building

where the fab will be located. Since the seawater equipment must be refurbished or

replaced after 5 years, the general manager told you to assume that the equipment

will be purchased a new after 5 years of use. What is the maximum first cost that

Angular Enterprises should pay for the seawater option?

To ensure that the seawater option is the economic choice over groundwater, PWs is

set to equal $-33.16, and solve for the Xs.

( )( ⁄ ) (

⁄ )

( ⁄ )

( )( ⁄ )( ⁄ )

( ⁄ )

( )

1.94 1.94 1.94

Xs Xs

0.05Xs

1.94

0.05Xs

1.94

0

1

2

5

6

10 i = 12%

The maximum first cost that Angular Enterprises should pay for the seawater option

is $14.576 million. Seawater option is selected if only if first cost less than $14.576

million.

In Excel

The maximum first cost that Angular Enterprises should pay for the

seawater option is $14.576 million.

Xs, $ =