Question

A senior executive is offered a buyout package by his company that will pay him a monthly benefit for the next 20 years. Monthly benefits will remain constant within each of the 20 years. At the end of each 12-month period, the monthly benefits will be adjusted upwards to reflect the percentage increase in the CPI. You are given: The first monthly benefit is R and will be paid one month from today. The CPI increases 3.2% per year forever. At an annual effective interest rate of 6%, the buyout package has a value of 100,000. Calculate R.

Answer 1

R is 545.72.

Step-by-step explanation:

This can be calculated using the formula for calculating the present value (PV) of a growing annuity as follows:

PVga = (R / (r - g)) * (1 – ((1 + g) / (1 + r))^n) .................... (1)

Where;

PVga = Present value of the growing annuity or the value of the buyout package = 100,000

R = The first monthly benefit = ?

r = Monthly effective interest rate = annual effective interest rate / 12 = 6% / 12 = 0.06 / 12 = 0.005

g = monthly growth rate of monthly benefits = Annual CPI / 12 = 3.2% / 12 = 0.032 / 12 = 0.00266666666666667

n = number of months = Number of years * Number of months in a year = 20 * 12 = 240

Substituting the values into equation (1), we have:

100,000 = (R / (0.005 - 0.00266666666666667)) * (1 - ((1 + 0.00266666666666667) / (1 + 0.005))^240)

100,000 = (R / 0.00233333333333333) * 0.427568259925511

100,000 / 0.427568259925511 = R / 0.00233333333333333

233,880.784362762 = R / 0.00233333333333333

R = 233,880.784362762 * 0.00233333333333333

R = 545.721830179777

Rounding to 2 decimal places, we have:

R = 545.72

Therefore, R is 545.72.