Question

Levi Strauss has some of its jean stone-washed under a contract with independent U.S. Garment Corp. If U.S. Garment's operating cost per machine is $30,000 for year 1 and increases by a constant $5,000 per year through year 10, what is the equivalent uniform annual cost per machine for the 10 years at an interest of 10% per year?

Answer 1

Answer:

C  $ 57,282.803

Explanation:

We solve for a growing annuity at arithmetic increases of 5,000

$(a_1+\frac{d}{r} +d \times n) \times \frac{1-(1+r)^{-time} }{rate} - \frac{d \times n}{r}$

a1 = 30,000

d = 5,000

r = 0.10

time = n = 10

$(30,000+\frac{5,000}{0.1} +5,000 \times 10) \times \frac{1-(1+0.1)^{-10}}{0.10} - \frac{5,000 \times 10}{0.10}$

PV $298,793.72

Now, we calculate the installment of this which is the equivalent uniform annual cost

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 298,793.72

time 10

rate 0.14

$298793.723741609 \div \frac{1-(1+0.14)^{-10} }{0.14} = C$

C  $ 57,282.803