Question

Question 3 :

A package delivery company is contemplating building a new shipping center. The most recent shipping center, 10,000 square feet large, was built in 2005, at a cost of $500,000. The new shipping center will be 15,000 square feet large. Using the power-sizing cost-estimating model, estimate the cost of building a new shipping center now, using the assumptions below to construct a weighted cost index value for 2005 and for today. Use 0.90 for the cost-capacity factor. The dollar cost of building a shipping center can be broken down into the cost of labor (20%), materials (35%), and equipment (45%). The cost index for labor is 120 in 2005, and 150 today. The cost index for materials is 180 in 2005 and 170 today. The cost index for equipment is 140 in 2005 and 200 today.

Question 4 Milana just deposited $10,000 in her account. Assuming the annual interest rate is 8%, how many years will it take before her account balance reaches $23,000? (Please make sure you use the time value of money Excel functions)

Answer 1

Question 3 :

First we have to break down the Historical Cost of $500,000 into labor (20%), materials (35%), and equipment (45%).

Total Historical Cost = 500,000

Labor(2005) Cost = 500,000 * 20% = 100,000

Material(2005) Cost = 500,000 * 35% = 175,000

Equipment(2005) Cost = 500,000 * 45% = 225,000

As per Cost Indexing, Labor Cost Today / Labor Cost in 2005 = Index Value Today / Index Value in 2005

Labor Cost Today / 100,000 = 150 / 120

=> Labor Cost Today = $125,000

As per Cost Indexing, Material Cost Today / Material Cost in 2005 = Index Value Today / Index Value in 2005

Material Cost Today / 175,000 = 170 / 180

=> Material Cost Today = $165,277.78

As per Cost Indexing, Equipment Cost Today / Equipment Cost in 2005 = Index Value Today / Index Value in 2005

Equipment Cost Today / 225,000 = 200 / 140

=> Equipment Cost Today = $321,428.57

Total Cost of building a new shipping Center based on Indexes = $125,000 + $165,277.78 + $321,428.57 = $611,706.35

However we have to re-scale the shipping center's cost based on size and cost capacity factor.

Cost of NSS = Cost of OSS * [(Size of NSS / Size of OSS)^x]

Here NSS => New Shipping Center, OSS => Old Shipping Center, x = cost-capacity factor i.e power-sizing exponent.

Cost of NSS = $611,706.35 * [(15,000 / 10,000) ^ 0.9]

=$611,706.35 * 1.44 = $ 880,857.14

Question 4:

Deposit Amount = $10,000

Annual Interest Rate = 8%

We can Simply use Excel Function PDURATION(RATE,PRESENTVALUE,FUTUREVALUE) to calculate this :

=PDURATION(8%,10000,23000) => 10.82 years

We can also use the tabular format to calculate approximate period:

Year	Opening Balance	Interest Rate	interest	closing balance
1	10,000	8%	800	10,800
2	10,800	8%	864	11,664
3	11,664	8%	933	12,597
4	12,597	8%	1,008	13,605
5	13,605	8%	1,088	14,693
6	14,693	8%	1,175	15,869
7	15,869	8%	1,269	17,138
8	17,138	8%	1,371	18,509
9	18,509	8%	1,481	19,990
10	19,990	8%	1,599	21,589
11	21,589	8%	1,727	23,316
12	23,316	8%	1,865	25,182