Question

Royalty payments (discrete end of period) for the next 15 years will be $5,000 per year for the first 5 years, $9,000 per year for the next 4 years and $12,000 per year for the last 6 years. What uniform annual payment for the next 15 years is equivalent to the described non-uniform series of royalty payments assuming 10% is compounded annually?

Answer 1

In order to solve this question, we would first calculate present value of all non uniform payment.

Present value = Sum of present value of all non uniform payments discounted @ 10 %

Present Value = 5000/(1+0.1)^1 + 5000/(1+0.1)^2 + 5000/(1+0.1)^3 + 5000/(1+0.1)^4 + 5000/(1+0.1)^5 + 9000/(1+0.1)^6 + 9000/(1+0.1)^7 + 9000/(1+0.1)^8 + 9000/(1+0.1)^9 + 12000/(1+0.1)^10 + 12000/(1+0.1)^11 + 12000/(1+0.1)^12 + 12000/(1+0.1)^13 + 12000/(1+0.1)^14 + 12000/(1+0.1)^15

Present Value = 58832.7355

58832.7355 = Uniform annual payment * (1/(1+0.1)^1 +1/(1+0.1)^2 +1/(1+0.1)^3 +1/(1+0.1)^4 +1/(1+0.1)^5 + ........ 1/(1+0.1)^15 )

58832.7355 = Uniform annual payment * 7.6061

Uniform annual payment = 7734.94 Answer