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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?

Respuesta :

TomShelby

Answer:

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

Explanation:

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

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 20,000.00

time 10 years

rate    0.04

[tex]20000 \times \frac{1-(1+0.04)^{-10} }{0.04} = PV\\[/tex]

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:

[tex]\frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}[/tex]

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.

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