Junior's Road to Retirement: A Time Value of Money Case.

Problem:

Today, Junior turns 30 years old. Junior also starts a new job today. His monthly net salary, payable at the end of the month, is Ghc2,000. Junior’s boss has been impressed by Junior’s competences during the interview, and has offered him a monthly raise of 0.1%, effective as of Junior’s second month on the job.

Junior’s average monthly expenses are currently Ghc750, but Junior expects his monthly expenses to grow at an annual effective rate of 1%, starting next month (i.e. Junior’s second month on his new job). Junior’s expenses will continue to grow at that rate until Junior retires. There are no other expenses. Junior saves 80% of his disposable income (that is, his salary, minus expenses).

Junior invests all his savings in a security that guarantees a 6% effective annual return. Besides the savings described here, Junior has no other savings. The adequate rate of return to calculate the present and future value of cash flows is 6%, annual effective.

On the day Junior turns 65 years old, he will retire. Junior will invest all his accumulated savings and the proceeds from the sale of the condo in a security that guarantees a return of 3% effective annual. Junior is convinced that he will die on the day of his 88th birthday. He wishes to leave a Ghc100,000 bequest to the Lost Cats Trust. Junior will also buy one gold ring on each of his 75th and 85th birthdays. Each ring costs Ghc10,000.

Given his financial situation, what will be Junior’s monthly gross revenue (i.e. before expenses) during retirement, if we assume that Junior wishes this monthly revenue to be constant? Junior lives in a tax paradise where the tax rate is zero percent (0%).

Solution:

Junior turns 30 today

Net Salary = Ghc2000.00 payable at the end of the month

Monthly raise = 0.1%

Yearly raise = 0.1%*12 = 1.2%

Monthly expenses = Ghc750.00

Monthly expenses expected to grow at an annual effective rate of 1%.

Savings = 80% of (Net salary-expenses)

Therefore: Salary growth per annum – Expenses growth per annum = Growth in Savings  (1.2%) – (1%) = 0.2%

Savings = 80% (Ghc2000.00 – Ghc750.00)

              80% (Ghc1, 250.00)

                   = Ghc1000.00

Savings = Ghc1000.00 *12 (for a year)

Savings = Ghc12, 000.00

Growing Annuity for savings in 6% security.

FV = Pmt (1+r) ^n – (1+g) ^n / (r-g)

Where pmt is the periodic savings of Ghc12, 000.00

r is 6% security rate

g is the 0.2% growth in savings yearly.

n is the number of years (35 years); Number of years from now till retirement at 65 (65 -30) = 35

FV = 12,000.00 [(1+0.06) ^35 – (1+0.002)^35/0.06-0.002]

FV = 12,000.00 [(1+0.06) ^35 – (1+0.002)^35/0.058]

FV = 12,000.00 (7.686 – 1.0724/0.058)

FV = 12,000.00 (6.6136/0.058)

FV = 12,000.00 (114.02759)

FV = GHc1, 368,331.08 the savings at retirement

Now we are calculating the future value of his accumulated savings.

PV = Ghc1, 368,331.08

r = 3%

n = 88 – 55 = 23years

Therefore FV = PV (1+r) ^n

FV = 1,368,331.08 (1+0.03) ^23

FV = 1,368,331.08 (1.03) ^23

FV = 1,368,331.08 * 1.9736

FV = Ghc2, 700,538.22

To find the yearly gross revenue = Ghc2, 700,538.22 / 23 = Ghc117, 414.7052

To find the monthly gross revenue = Ghc117, 414.7052 / 12 = Ghc9, 784.558767

Therefore, Junior’s monthly gross revenue = Ghc9, 784.558767

Published by: HR Forum News