Question

Please provide a detail calculation using formula, financial calculator or excel.

22. Assume the following regarding a growing annuity valuation problem:

Your salary at the end of the last year that you work is $90,000.

You would like your income stream to begin at the end of your first year of retirement with a payment equal to 70% of your last working year’s salary. (Assume all amounts are “end of year” payments.)

You plan to be retired for 25 years.

You would like your retirement income will grow at a constant rate equal to a 3.5% (to compensate for expected inflation).

Using a discount rate of 8%, what is the present value at the beginning of your first year of retirement, (i.e. one period prior to the first retirement payment) of your projected 25 year retirement income stream?

a. 960,730

b. 916,893

c. 672,511

d. 211,573

e. 3,308,543

f. 483,107

Answer 1

Current Salary = 90,000

First year retirement income = 90,000 x 70% = 63,000

Using PV of growing annuity formula

PV = P / (r - g) x [1 - ((1 + g) / (1 + r))^n]

= 63,000 / (8% - 3.5%) x [1 - (1.035/1.08)^25]

= $916,893