Question

1. Ten years ago, your friend’s mum wrote an Indian-Italian fusion cookbook which has become a global bestseller. She has been receiving annual royalties based on revenues reported by the publisher. These revenues started at $1 million in the first year and grew steadily by 5% per year. Her royalty rate has been 15% of the revenues. Recently, she hired an auditor who discovered that the publisher had been under-reporting the revenues. The book had actually earned 10% more in annual revenues than had been reported on her royalty statements. Assuming the publisher pays an interest rate of 4% p.a. on missed annual payments, the money owed by the publisher is closest to: (a)$136,888. b) $150,634. c) $222,976. d) $245,367

Answer 1

c) $222,976.

To calculate the money owed to the publisher, we need to first calculate the underreporting done each year and royalty missed each year.

Royalty underpayment in year 1 = $ 1,000,000 * 1 * 0.10 * 0.15 = $ 15,000

Interest on underpayment = $ 15,000 * 0.04 * 10 years = $ 6,000

Royalty underpayment in year 2 = $ 1,000,000 * 1.05 * 0.10 * 0.15 = $ 15,750

Interest on underpayment = $ 15,750 * 0.04 * 9 years = $ 5,670

Royalty underpayment in year 3 = $ 1,000,000 * 1.103 * 0.10 * 0.15 = $ 16,537.50

Interest on underpayment = $ 16,537.50 * 0.04 * 8 years = $ 5,292

Royalty underpayment in year 4 = $ 1,000,000 * 1.158 * 0.10 * 0.15 = $ 17,364.38

Interest on underpayment = $ 17,364.38 * 0.04 * 7 years = $ 4,862.03

Royalty underpayment in year 5 = $ 1,000,000 * 1.216 * 0.10 * 0.15 = $ 18,232.59

Interest on underpayment = $ 18,232.59 * 0.04 * 6 years = $ 4,375.82

Royalty underpayment in year 6 = $ 1,000,000 * 1.1276 * 0.10 * 0.15 = $ 19,144.22

Interest on underpayment = $ 19,144.22 * 0.04 * 5 years = $ 3,828.84

Royalty underpayment in year 7 = $ 1,000,000 * 1.340 * 0.10 * 0.15 = $ 20,101.43

Interest on underpayment = $ 20,101.43 * 0.04 * 4 years = $ 3,216.23

Royalty underpayment in year 8 = $ 1,000,000 * 1.407 * 0.10 * 0.15 = $ 21,106.51

Interest on underpayment = $ 21,106.51 * 0.04 * 3 years = $ 2,532.78

Royalty underpayment in year 9 = $ 1,000,000 * 1.477 * 0.10 * 0.15 = $ 22,161.83

Interest on underpayment = $ 122,161.83 * 0.04 * 2 years = $ 1,772.95

Royalty underpayment in year 10 = $ 1,000,000 * 1.551 * 0.10 * 0.15 = $ 23,269.92

Interest on underpayment = $ 23,269.92 * 0.04 * 1 years = $ 930.80

Summing up all these values gives us an amount of USD 222,976, therefore "C"