An automobile company offers a buyer\'s protection plan to new car buyers. For $

Question

An automobile company offers a buyer's protection plan to new car buyers. For $75.00 today, the company will pay all the costs exceeding $50 for any repairs each year for the next five years. A buyer believes the probability of a repair exceeding $50.00 during the first, second, third, fourth, and fifth years are 0.01, 0.025, 0.045, 0.07, and 0.10, respectively. Assume that the occurrence of a repair is statistically independent from year to year, and that MARR is 10% a year. What is the maximum annual amount of a repair (exceeding $50.00) each year for five years that would make the buyer indifferent to the choice between taking the plan and not taking the plan?

Explanation / Answer

Buyer becomes indifferent to the choice when present value of protection i.e. $75 equal to the present value of future repairs.

Present value of future repairs = $75

Let expected annua damage be Rs.x

Expected Value of damage in year 1= x*0.01 = 0.01x

Expected Value of damage in year 1= x*0.025 = 0.025x

Expected Value of damage in year 1= x*0.045 = 0.045x

Expected Value of damage in year 1= x*0.07 = 0.07x

Expected Value of damage in year 1= x*0.1 = 0.1x

Present value of damage = FV/ (1+rate/100)^T

PV = [(0.01x/1.1) + (0.025x/1.1^2) + (0.045x/1.1^3) + (0.07x/1.1^4)+ (0.1x/1.1^5] = 75

= 0.17x = 75

x = $432.36

Maxm annual amount of repair exceedon $50 = 432.36 - 50 = 382.36

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.