CCP practice question 22 of 25

An agricultural corporation that paid 53% in income tax wanted to build a grain elevator designed to last twenty-five (25) years at a cost of $80,000…

An agricultural corporation that paid 53% in income tax wanted to build a grain elevator designed to last twenty-five (25) years at a cost of $80,000 with no salvage value. Annual income generated would be $22,500 and annual expenditures were to be $12,000. Answer the question using a straight line depreciation and a 10% interest rate. If $50 was invested at 6.0% on January 1, year 1, what would be the value of year-end withdrawals made in equal amounts each year for 10 years and leaving nothing in the fund after the tenth withdrawal?

Answer options

A: $6.80 Correct answer

B: $3.10

C: $5.35

D: $2.22

Correct Answer:

A. $6.80

Explanation

This question is a time value of money problem that requires calculating a uniform series of payments (an annuity) from a given present value. The information about the grain elevator is extraneous and should be disregarded. The correct formula to use is the Capital Recovery Factor (CRF): A = P [i(1+i)^n] / [(1+i)^n - 1], where A is the annual withdrawal, P is the present value ($50), i is the interest rate (6% or 0.06), and n is the number of periods (10 years). Calculation: A = $50 [0.06(1+0.06)^10] / [(1+0.06)^10 - 1] A = $50 [0.10745] / [0.79085] A = $50 0.13587 A ≈ $6.79 The calculated value is $6.79, which rounds to $6.80.

Why Incorrect

B. $3.10: This amount is incorrect and would result from a significant miscalculation or using the wrong time value of money formula, such as a sinking fund factor.
C. $5.35: This answer is incorrect. It is the result of a calculation error, as applying the standard and correct capital recovery formula does not yield this value.
D. $2.22: This value is substantially too low and indicates a fundamental error in applying engineering economic principles or a major calculation mistake.

References

1. AACE International, Skills & Knowledge of Cost Engineering, 6th Ed., (Morgantown, WV: AACE International, 2015). Chapter 8: Economic Analysis, Section 8.1.2, pp. 8.3-8.4. The text provides the formula for the Uniform Series Capital Recovery Factor (A/P, i, n) used for this calculation.

2. Park, C. S., Contemporary Engineering Economics, 6th Ed., (Pearson, 2016). Chapter 4: "Uniform Series and Gradient Series," Section 4.2. The text details the capital recovery factor formula A = P(A/P, i, n) and its application in finding an equivalent uniform payment series from a present sum.

3. Massachusetts Institute of Technology (MIT) OpenCourseWare. (2006). 1.011 Project Evaluation, Lecture 2: Interest and Equivalence. The lecture notes present and explain the Capital Recovery Factor (CRF) formula, A = P [i(1+i)^n / ((1+i)^n - 1)], which is directly applicable to this problem.

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