Question

1.

You start a business that you expect will provide you with income of $87,209 per year for 14 years. Since this is a “start-up” business, it will not begin providing you income until 3 years from now. If market interest rates are 3.58% APR (compounded annually), what is the market value of this business today?

2.

You would like to buy a retirement home in Florence, Italy in 4 years. The type of home you want to buy currently costs $408,294, but you expect the price to rise at 3% per year for the next 4 years.

If your investments earn 6.04% APR compounded annually (nominal), how much do you have to invest in years 1 to 4 to be able to purchase your retirement home?

Answer 1

1.Present value=Cash flows*Present value of discounting factor(rate%,time period)

=87,209/1.0358^3+87,209/1.0358^4+87,209/1.0358^5+87,209/1.0358^6+87,209/1.0358^7+87,209/1.0358^8+87,209/1.0358^9+87,209/1.0358^10+87,209/1.0358^11+87,209/1.0358^12+87,209/1.0358^13+87,209/1.0358^14+87,209/1.0358^15+87,209/1.0358^16

=$882927.59(Approx)

2.We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

Future value of home=408,294*(1.03)^4

=408,294*1.12550881

=$459538.494

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

459538.494=Annuity[(1.0604)^4-1]/0.0604

459538.494=Annuity*4.37721299

Annuity=459538.494/4.37721299

=$104984.27(Approx)