Question

1) An insurance provider has required that a company improve its fire suppression system or be forced to pay fees to continue being covered by the insurance policy. Because updating this system is a big undertaking, the company has a grace period of two years before the updates must be completed. However, if they make the updates, the contractor requires that the cost be paid up front. If the company elects to pay the fees rather than update the system, it will incur fees of $1,000,000 at the end of years 2, 3, and 4. How much could the museum afford to pay now to update the system and prevent having to pay the fees? Use an interest rate of 5% per year.

2) If the contractor proposes to do the work if the company pays $725,000 at the end of each of the next four years, should the company take this offer? Use your answer from part a, and continue to use an interest rate of 5% per year.

Answer 1

1. How much could the museum afford to pay now to update the system and prevent having to pay the fees?

Present value of fees = Year 2 fee / (1 + Interest)^2 + Year 3 fee / (1 + Interest)^3 + Year 4 fee / (1 + Interest)^4

Present value of fees = 1000000 / 1.05^2 + 1000000 / 1.05^3 + 1000000 / 1.05^4

Present value of fees = $2593569.55

The museum can afford a fees of $2593569.55 to pay now to upgrade the fire system

2. should the company take this offer?

PV of contractor payments = amount * Present value annuity factor (5%,4)

PV of contractor payments = 725000 * 3.5460

PV of contractor payments = $2570814.12

Present value of fees to pay for non upgradation is higher than PV of Contractor payments

Thus Company should take the Offer of the contractor

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