Question

What is the present value of a perpetuity that pays you annual, end-of-year payments of $950.00? Use a nominal rate (monthly compounding) of 7.75%. (Hint: use EAR).

Answer 1

Answer:

Present value of perpetuity is $12,242.27

Explanation:

Nominal rate is compounded monthly so the effected rate will be different due to monthly compounding effect.

Effective annual rate is calculated as follows

EAR = [ ( 1 + r )^n ] - 1

EAR = [ ( 1 + 0.0775/12 )^12 ] - 1

EAR = [ ( 1.0775 )^12 ] - 1

EAR = 7.76%

Present value of perpetuity = Cash flow / discount rate

Present value of perpetuity = $950 / 7.76%

Present value of perpetuity = $950 / 0.0776

Present value of perpetuity = 12,242.27