Question

Cyrille has just joined college where he will study computer engineering for the next four years.  Luckily, he has also just secured a 10-year contract with a big I.T firm upon graduation. His annual salary is expected to be $180,000 when he starts the job in four years’ time. The salary may be assumed to be paid at the end of the year. He is guaranteed a 4% annual increase in salary during the 10-year contract. Suppose the opportunity cost of capital is 9%. The average tax rate on his annual income is 30%. What is the present value of his disposable income?

Answer 1

Answer:

His Disposable income will be 70% of his income because 30% will be deducted as tax. So, at the end of 4th year his disposable income will be $126,000.

To find the present value of his disposable income we will use following formula and calculate as folllows:

PV at the beginning of year 4=P/(r-g)[1-(1+g/1+r)ⁿ]

Where, P=First payment=$126,000.

r=rate per period=9%=0.09

g=growth rate=4%=0.04

n=number of years=10

PV at the beginning of year 4=$126,000/(0.09-0.04)[1-(1+0.04/1+0.09)¹⁰

=$944,316.62.

PV at the beginning of year 1=$944,316.62/(1+0.09)³=$729,185.70