Fran runs a small delivery service. The borrowing and deposit rates of interest

Question

Fran runs a small delivery service. The borrowing and deposit rates of interest are identical for her. Her only inputs are her time, gasoline, and a very specialized delivery truck. The truck is so specialize to her needs that it has no scrap value. The price of a new truck is $45,000. As one of these trucks ages, maintenance gets more expensive. The required maintenance at the end of year one costs $3,000, and the maintenance cost increases each year by $3,000: at the end of year two it is $6,000, at the end of year three it is $9,000, and so on. She plans to stay in the business for just seven more years. Because her current truck is now exactly three years old, she must now spend $9,000 on maintenance. She is considering two options: option A, using her current truck for the next seven years; and option B, buying a new truck today, and using it for the next seven years. (a)* What is the present value of costs under option A? Under option B? Which is the better option? (b)* Given that she is going to stay in business for another seven years, should she be considering other options?

Explanation / Answer

a) cost for option A:

(7/2)((2*9000)+(7-1)*3000)=126000

b)cost for option b=

45000+(7/2)((2*3000)+(7-1)*3000)=159000

so,,option a is better

for another 7 year

option a) 126000+ (7/2)((2*30000)+(7-1)*3000)=399000

option b) 159000+ (7/2)((2*24000)+(7-1)*3000)=390000

so here option b is better

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