Consider an offer to supply 5 paintings per year to an art gallery in Rome for the next five years. The contract is exclusive, meaning that, if you accept it, you cannot sell paintings to other galleries or other clients. The contract also offers a signing bonus of $100,000. If you were to refuse the contract, you estimate that you would be selling 7 paintings a year, at a price of $45,000 each, for the next 5 years. Assume that your required rate of return is 20%. What is the minimum price per painting (assume the same price for each painting) at which you are willing to accept the contract

Question

contestada

Respuesta :

TomShelby TomShelby · Answer 1 · 2020-09-25T02:57:30+02:00

Answer:

I will accept the offer if the price per painting is $56,312.41 or higher.

Explanation:

We will calculate the present value of the other option which is, selling our painting as a freelancer.

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

C 315,000.00

time 5

rate 0.2

[tex]315000 \times \frac{1-(1+0.2)^{-5} }{0.2} = PV\\[/tex]

PV $942,042.8241

Now, we subtract the signing bonus of 100,000

942,042.83 - 100,000 = 842,042.83

And solve for the annual proceeds from the painting we need to equalize the opportunity cost:

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

PV 842,042.83

time 5

rate 0.2

[tex]842042.83 \div \frac{1-(1+0.2)^{-5} }{0.2} = C\\[/tex]

C $ 281,562.03

Now, we divide by the 5 painting per year:

$281,562.03 per year / 5 painting per year = $56,312.41