A company issues 1000 debentures of ₹ 100 each at a discount of 6% and the debenture are to be repaid by equal installments of ₹ 20,000 at the end of each year, starting from first year, which amount of discount is written off at the end of first year?

Question

Accepted Answer

The correct option is 2:

This problem requires the application of the **Proportionate Outstanding Liability Method** for writing off the Discount on Issue of Debentures, which is an intangible asset that must be amortized over the life of the debentures. Since the debentures are redeemed in equal annual installments of ₹ 20,000, the benefit derived from the debenture issue is linked to the face value of the debentures outstanding at the beginning of each period. First, calculate the total discount: 1,000 debentures \* ₹ 100 face value \* 6% discount = ₹ 6,000. Next, establish the ratio of the outstanding face value at the beginning of each of the five years (₹ 1,00,000, ₹ 80,000, ₹ 60,000, ₹ 40,000, ₹ 20,000), simplifying this ratio to 5:4:3:2:1. The total of the ratios is 15. The amount of discount written off at the end of the first year is calculated by applying the first year's ratio: ₹ 6,000 \* (5/15) = ₹ 2,000. This method ensures the charge to the Profit and Loss Account correctly reflects the period's usage of the funds.

The incorrect option is 1:
Option ₹ 6,000 represents the **total discount** on the issue of all the debentures (1,00,000 \* 6%). It is incorrect because the entire discount is a capital loss that must be written off over the debenture's life, which in this case is five years due to the installment repayment schedule. Writing off the entire amount in the first year would violate the matching principle of accounting by unduly burdening the first year's profit and loss account. This figure is the initial value of the intangible asset, not the amount to be amortized in a single year.

The incorrect option is 3:
Option ₹ 1,200 would be the amount written off if the discount was amortized on a straight-line basis over the five-year redemption period (₹ 6,000 / 5 years = ₹ 1,200/year). This is incorrect because the Straight-Line Method is used only when debentures are redeemed *at the end* of the fixed period, not when they are redeemed in installments. Using this method when the outstanding liability is decreasing annually would result in an overstatement of the write-off in the later years relative to the outstanding capital.

The incorrect option is 4:
Option ₹ 1,600 would correspond to the write-off for the second year based on the 5:4:3:2:1 ratio (₹ 6,000 \* 4/15). This is an incorrect figure for the first year, which requires the largest proportion of the write-off, as the largest amount of capital (₹ 1,00,000) was outstanding during the first year. The write-off amount should decrease each subsequent year as the debenture principal is redeemed, which is why the second year's write-off is lower than the first year's.