Subtopic: Cost analysis of implements and tractors
Question Statement:
Which of the following statements regarding the Capital Recovery Factor ($CRF$) method for calculating annual capital depreciation and interest in agricultural machinery economics is/are CORRECT?
Options:
(A) The Capital Recovery Factor converts a present capital expenditure into an equivalent uniform annual series of payments
(B) The formula for $CRF$ with interest rate $i$ and service life $n$ years is $CRF = \frac{i(1 + i)^n}{(1 + i)^n - 1}$
(C) The annual capital recovery cost including salvage value $S$ is calculated as $(C - S) \times CRF + S \times i$
(D) The straight-line method always yields a higher total annual cost than the capital recovery factor method for any positive interest rate
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
- **A is correct:** $CRF$ computes equal annualized ownership capital recovery.
- **B is correct:** Standard financial engineering formula is $CRF(i, n) = \frac{i(1+i)^n}{(1+i)^n - 1}$.
- **C is correct:** The depreciable amount $(C - S)$ amortizes with $CRF$, while salvage capital $S$ bears annual interest $S \times i$.
- **D is incorrect:** The straight-line plus average investment interest method is an approximation that understates true capital cost compared to rigorous compound-interest $CRF$.