Question

You want to open a garden. The land cost $150 000. You estimate the upkeep will be $5000 each year. An additional $10 000 will be needed every 15 years starting in 15 years. How much would you need to deposit in an account today in order to build and maintain this garden. Assume interest as 8%?

As a note my answer of $195 949.90 was incorrect.

Answer 1

Initial investment (land cost) = $150,000

Annual upkeep cost = $5,000

Additional cost at every 15 years = $10,000

Interest rate = 8%

As the question is regarding opening of a garden, the life of the investment is assumed to be infinite. Also the life of the project is not mentioned in the question.

If we consider the life of the garden is infinite, we need to calculate the Capitalized cost of the project. Capitalized cost is the summation of the first cost and PW of all annual cash disbursements.

Capitalized Cost = Initial cost + PW of annual cash outflows assumed to continue up to infinite period

CC = I + A / Rate of interest

In the given question

CC = $150,000 + [$5,000 + $10,000 (A/F, 8%, 15)] / 0.08

CC = $150,000 + [$5,000 + $10,000 (0.0368)] / 0.08

CC = $150,000 + [$5,000 + $368] / 0.08

CC = $150,000 + [$5,368] / 0.08

CC = $150,000 + $67,100

CC = $217,100

You need to deposit $217,100 in an account today in order to build and maintain this garden for an infinite period.