Question

A college student has been looking for new tires. The student feels that the warranty period is a good estimate of the tire life and that a 10% interest rate is appropriate. Using an annual cash flow analysis, which tire should be purchased?

Answer 1

the student should purchase the tire with the 12 month warranty

Step-by-step explanation:

tire warranty (in months) price per tire

12 $39.95

24 $59.95

36 $69.95

48 $90.00

since the estimated useful life is similar to the warranty, then to determine the present cost of each tire we can use the present value formula:

present value = future value / (1 + discount rate)ⁿ

• $39.95 / 1.1 = $36.32
• $59.95 / 1.1² = $49.55
• $69.95 / 1.1³ = $52.55
• $90.00 / 1.1⁴ = $61.47

Answer 2

A car tire of 36 months warranty at $28.13

Step-by-step explanation:

Tire Warranty (Months) Price Per Tire

12 $39.95

24 $59.95

36 $69.95

48 $90.00

First we define Equivalent uniform annual cost (EUAC) as the annual cost of owning, operating, and maintaining an asset over its entire life. It is often used by firms for capital budgeting decisions, as this enables company to compare the cost-effectiveness of various assets that have unequal lifespans.

The formula for EUAC = P(A/P,I,N)

Where I = 10% and N = 12 , 24 , 36 AND 48 Months

(a) 12 month tire EUAC = $39.95 (A/P, 10%, 1) = $43.95

(b) 24 month tire EUAC = $59.95 (A/P, 10%, 2) = $34.54

(c) 36 month tire EUAC = $69.95 (A/P, 10%, 3) = $28.13

(d) 48 month tire EUAC = $90.00 (A/P, 10%, 4) = $28.40

From the above, the 36 month tire has the lowest EUAC and the one that is advisable for the student to buy.