CCP practice question 14 of 25

Money is value. Having money when you need it is very important. Money can also be valuable when used wisely by knowing when to spend and when to…

Money is value. Having money when you need it is very important. Money can also be valuable when used wisely by knowing when to spend and when to conserve Also, planning now for future expenses can be a plus to the company rather than a debit. There are several ways to capitalize money and spending. Basically there is the single payment method that has a compound amount factor and a present worth factor. There is the uniform annual series that has a sinking fund factor, capital recovery factor and also the compound amount factor and present worth factor. At this point, we can assure money is worth 10%. The following question requires your selection of CCC/CCE Scenario 7 (4.8.50.1.1) from the right side of your split screen, using the drop down menu, to reference during your response/choice of responses. If the company needs to repay a loan of $100,000 in 10 uniform annual payments, how much will each payment be?

Answer options

A: $16,380

B: $16,578

C: $15,937

D: $16,273 Correct answer

Correct Answer:

D. $16,273

Explanation

This problem requires the calculation of a uniform annual payment (A) to repay a present loan amount (P). The relationship is defined by the Capital Recovery Factor (CRF). The formula is A = P (A/P, i, n), where P = $100,000, the interest rate i = 10% (0.10), and the number of periods n = 10 years. The formula for the CRF is [i(1+i)^n] / [(1+i)^n - 1]. Calculation: A = $100,000 [0.10(1+0.10)^10] / [(1+0.10)^10 - 1] A = $100,000 [0.10(2.59374)] / [2.59374 - 1] A = $100,000 [0.259374] / [1.59374] A = $100,000 0.162745 A = $16,274.50 This calculated value is closest to $16,273.

Why Incorrect

A. $16,380: This result is incorrect and likely stems from a miscalculation or using an incorrect factor from interest tables, possibly for a different interest rate or period.
B. $16,578: This value is incorrect. It does not correspond to the capital recovery factor for the given interest rate and period.
C. $15,937: This value is too low. It may result from incorrectly using the sinking fund factor (A/F) with an adjustment, which is used to find A given a future value (F).

References

1. AACE International. (2016). Skills & Knowledge of Cost Engineering (6th ed.). Section 2.3, Economic Analysis. The text provides the standard formulas for discrete compounding, including the Capital Recovery Factor (A/P) used here.

2. AACE International. (2019). Recommended Practice No. 10S-90: Cost Engineering Terminology. TCM Framework: 8.2 – Economic Analysis. Defines the principles of time value of money, including present value and uniform series payments.

3. Blank, L., & Tarquin, A. (2018). Engineering Economy (8th ed.). McGraw-Hill. Chapter 4, "Uniform Series and Random Cash Flows," presents the derivation and application of the capital recovery factor (A/P, i, n) with the formula A = P[i(1+i)^n]/[(1+i)^n-1]. The interest tables in Appendix C for i=10% and n=10 show the (A/P) factor as 0.16275.

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