Question

2. Suppose that you are considering two careers out of college. The two careers both pose interesting challenges and similar quality of life, so your choice is down to financial considerations. Suppose that the real interest rate that you think is reasonable is r=0.05. You are 22 when you start working and plan to retire at age 68 (so the last working year of your life is 67). (a) Job S (for stable) is expected to have constant salary of $55,000 per year. Find the present discounted value. Show your work - what formulas are you using? (b) Job G (for growth) has a salary that starts at $46,000 per year and grows by 1% per year. Find the PDV. (c) Redo part (b) but with growth rate of 2%.

Answer 1

a)

Case of Job S

Regular Constant salary=S=$55000

Discount rate=r=0.05

Time period=n=46 years

Present discounted value=PDV=S*(P/A,0.05,46)

Let us calculate interest factor

$(P/A,r,n)=\frac{1-\frac{1}{(1+r)^{n}}}{r}$

$(P/A,0.05,46)=\frac{1-\frac{1}{(1+0.05)^{46}}}{0.05}=17.880066$

PDV=55000*17.880066=$983403.63

b)

Case of Job G

Starting Salary=S=$46000

Discount rate=r=0.05

Growth rate=g=1%=0.01

Time period=n=46 years

It is a case of annuity growing with constant rate.

$PVg=\frac{S}{r-g}*\left [ 1-\frac{(1+g)^{n}}{(1+r)^{n})} \right ]$

$PVg=\frac{46000}{0.05-0.01}*\left [ 1-\frac{(1+0.01)^{46}}{(1+0.05)^{46})} \right ]$

$PVg=1150000*0.8324766=957348.11$

PDV at 1% growth rate=$957348.11

c)

Case of Job G

Starting salary=S=$46000

Discount rate=r=0.05

Growth rate=g=2%=0.02

Time period=n=46 years

$PVg=\frac{S}{r-g}*\left [ 1-\frac{(1+g)^{n}}{(1+r)^{n})} \right ]$

$PVg=\frac{46000}{0.05-0.02}*\left [ 1-\frac{(1+0.02)^{46}}{(1+0.05)^{46})} \right ]$

$PVg=1533333.33 *0.7364275 =1129188.79$

PDV at 2% growth rate=$1,129,188.79