Question

Now that the IOC has made the decision to postpone the Tokyo Summer 2020 Olympics until next year, one of the sponsoring organizations finds itself with Olympic merchandise that needs to be liquidated. When you heard about this opportunity you became quite excited because you are an avid collector of Olympic merchandise. In fact, when you graduate from Brock University, you plan on opening an Olympic memorabilia shop. The offer from this Olympic sponsor is such that you have the option to purchase the merchandise entirely upfront for $10,500 or to pay $2,750 per year for the next four years (with payments at the beginning of the year). Assuming a discount rate of 7%, is it advisable to pay the cost of the merchandise entirely upfront? Explain. Be sure to show your calculations

Answer 1

Answer:

It is prudent to pay forthright just if the forthright expense is lower than the whole of present estimations of yearly installments.

Present estimation of every yearly installment = yearly installment/(1 + rebate rate)^n

where as

n = number of years after which the yearly installment happens.

Every installment happens toward the start of the year, thus the primary installment happens at year 0, the second at year 1, etc.

Whole of present estimations of yearly installments = ($2,750/(1 + 7%)^0) + ($2,750/(1 + 7%)^1) + ($2,750/(1 + 7%)^2) + ($2,750/(1 + 7%)^3)

On solving the above expression we get

Whole of present estimations of yearly installments = $9,966.87

This is lower than the forthright expense.

In this way,

it isn't fitting to pay the expense of the product altogether forthright in light of the fact that the current estimation of yearly installments is lower than the upfront cost i.e., forthright expense.