Question

The research group at Company A developed a patent that is anticipated to bring in $550,000 in royalty income each of the next n years. Company B has expressed interest in buying the rights to the patent, and CA is asking $2.5 million. If interest is 8% compounded annually, how many years do the royalties need to last for it to be profitable for Company B to purchase the rights today?

Answer 1

• All working forms part of the answer
• Company B is paying $2.5 million = $2,500,000 for that patent.
• Annual royality income will be $550,000
• Interest rate is 8%
• Company B will be profitable from that year when royality income earned (discounted at PV of 8%) increases more than $2,500,000
• Working

Year	Royality Income $	PV factor @ 8%	PV of income $	Cumulated value of PV of incomes $
1	550000	0.92593	509259	509259
2	550000	0.85734	471536	980796
3	550000	0.79383	436608	1417403
4	550000	0.73503	404266	1821670
5	550000	0.68058	374321	2195991
6	550000	0.63017	346593	$2,542,584

• As seen above, till year 5, ‘B’ would have earned $2195991 of income which is still less than $2500000. But in Year 6, the cumulative income discounted at PV is $2542584, which exceeds $2.5 million.
• Hence, royalities should atleast last for 6 years, to be profitable for Company B to purchase rights today.