Question

To cover the annual maintenance expenses of their fleet of cranes, the newly

formed Hubly Constructions have just deposited $1 million in a business savings

account earning an interest rate of 4.5% per year. The Chief Financial Officer,

Astrid Wilmer, has calculated that this deposit will just cover all the maintenance

expenses under the following assumptions:

Maintenance expenses will grow at a rate of 3% each year.

Maintenance expenses will be paid at the beginning of each year with the first

expense due in exactly 1 years' time.

The life of the fleet of cranes is 31 years (i.e., the last maintenance expense is

due in exactly 30 years' time).

HINT: set up the set of expenses as a growing annuity and solve for the first cash

flow of the annuity.

$50,378

$40,619

$42,623

$30,000

$94,652

Answer 1

Amount of deposit = [First cash flow of annuity / (interest rate - growth rate)] * [ 1 - ((1 + growth) / (1 + interest))^years]

1000000 = [First cash flow of annuity / (4.50% - 3%)] * [ 1 - ((1.03) / (1.045))^30]

1000000 = [First cash flow of annuity / 1.50%] * [ 1 - (0.9856)^30]

1000000 = [First cash flow of annuity / 1.50%] * [ 1 - 0.6481]

1000000 = [First cash flow of annuity / 1.50%] * 0.3519

First cash flow of annuity = 42623 Option C

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