Question

A 30-year security has a price of $10,860.71. The security pays $600 at the end of each of the next 10 years, $1,200 at the end of years 11-15, and then it pays a different fixed cash flow amount at the end of each of the following 10 years (i.e., years 16-25). Finally, in years 26-30 it again pays $600 per year at year end. Interest rates are 6.0%. What is the annual cash flow amount between years 16 and 25?

Answer 1

Price of security is the PV of cash flows.

Given,

Price= $10,860.71

There are 4 cash flows as follows-

(A ): $600 at the end of years 1to 10 (10 years)

(B ): $1200 at the end of years 11 to 15 (5 years after 10 years from now)

(C ): Fixed sum (Let it be P) at the end of years 16 to 25 (10 years after 15 years from now)

(D ): $600 at the end of years 26 to 30 (5 years after 25 years from now)

Interest rate= 6%

Therefore,

10860.71= 600(PVIFA 6%, 10) + 1200(PVIFA 6%,5)*(PVIF 6%, 10) + P(6%, 10*(PVIF 6%, 15) + 600*(PVIFA 6%, 5)*(PVIF 6%, 25)

10860.71= 600* 7.360087 +1200* 4.212364* 0.558395 + P* 7.360087* 0.417265 + 600* 4.212364* 0.232999

10860.71= 4,416.05+ 2,822.59+ P* 3.071107 + 588.88 = 7827.52+ 3.071107P

Therefore, fixed sum during years 16 to 25 (P) = (10860.71-7827.52)/3.071107 = $987.65