Art Dreck's paintings are terribly unpopular now.In fact nobody would pay a dime to have one of his paintings on the wall now.But experts believe that 10 years from now, there will be a craze for Dreck paintings.The craze will last for 2 years and then nobody will ever want to see a Dreck again.During this 2-year period, people will be willing to pay $1,100 a year to have an original Dreck on the wall.The interest rate is r.If the experts' belief is widely held among investors, today's market value of Dreck should be about

Question

Quizplus · Accepted Answer

Using the formula for present value of an annuity, we can find the present value of the 2-year period where people are willing to pay $1,100 a year for an original Dreck painting:
PV = 1,100/(1+r) + 1,100/(1+r)^2
PV = 1,100/(1+r)(1+r) + 1,100/(1+r)(1+r)^2
PV = 1,100(1/(1+r) + 1/(1+r)^2)
PV = 1,100((1+r)/(1+r)^2 + 1/(1+r)^2)
PV = 1,100((1+r+1)/(1+r)^2)
PV = 1,100(1+r)/(1+r)^2
PV = 1,100/(1+r)

Then, the present value of the two-year period is divided by (1+r)² to represent the present value of Dreck's paintings 10 years from now:
PV = 1,100/(1+r)^3

Finally, the total present value is the sum of the present value of the two-year period and the present value of the paintings 10 years from now:
PV = 1,100/(1+r) + 1,100/(1+r)^3
PV = 1,100(1/(1+r) + 1/(1+r)^3)

This can be simplified as PV = 1,100/(1+r)(1+r²), which is equivalent to choice (D): 1,100/(1+(1+r)+(1+r²)).

Art Dreck's Paintings Are Terribly Unpopular Now