Question

You are offered an investment in a new store. For this problem, assume away taxes. The store will sell furniture, and historically furniture prices have kept pace with inflation. The current revenue from the store is 20K a year. The current nominal interest rate is 7% and inflation is running at 3% a year. You expect this trend to continue for the 10 years of the contract. Should you make the required 140K investment?

Answer 1

yes, thepresent value fo the furnite investment is above their cost.

Step-by-step explanation:

We calculate the present value of the annuity cosnidering the real rate of 4%

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 20,000.00

time 10 years

rate 0.04

`20000 * (1-(1+0.04)^(-10) )/(0.04) = PV\\`

PV $240,122.1425

We could also consider this a growing annuity as we are told that the furnitures prices kept the pace with inflation thus growing at 3% per year

and discount at 7% to know how much can we do:

`(1-(1+g)^(n)* (1+r)^(-n) )/(r - g)`

g 0.03

r 0.07

C 20,600 (the first year we receive 20,000 x 1.03)

n 10

Future value: 320,966.01

Present value:

FV/1.07^10 = 163,162.85

This approach yield 7% and is still above the 140 rquired investment thus, we should consider to approve the investment.