Pro-rata Share of the Purchase Price

[matt29]

An auto repair shop plans to sell a new brand of car battery with a 4-year warranty. Given:

(i) If the battery fails within 4 years, the shop will refund a pro-rata share of the purchase price at the moment of failure.
(ii) The purchase price of the battery is equal to the sum of the manufacturing cost, loading for profit, and the actuarial present value of the warranty.
(iii) The manufacturing cost of the battery is 50, and profit is equal to 10% of the manufacturing cost.
(iv) The force of failure of the battery is mu(t) = 1/(10-t), 0 <= t < 10.
(v) delta (d) = 0.05

Calculate the purchase price of the battery. The answer is 67.68. I calculated to be E(Z) = 0.217732*P , which I think is correct, but I don't get where the manufacturing cost fits in? Thanks.