Question

1. City 1 wants to encourage an electric vehicle research centre to locate in the city. The centre would be a non-profit organization and therefore would not pay taxes. Another community has offered to provide a $10 million, 20 year, 5% loan to be repaid in equal annual installments of $802,426. Ordinarily, the research centre would have to pay 8% interest on its financing. Instead of offering low-cost financing, City 1 is thinking of offering free land. How much must the land be worth for the value of City 1's incentive package to be the same as that of the competing city?

Answer 1

The value of land should be equal to the present value of all the extra annual payments that the research centre will have to pay if they opt for a normal loan over a low cost loan

Annual payment for a loan can be calculated using the PMT function in spreadsheet

PMT(rate, number of periods, present value, future value, when-due)

Where, rate = annual interest

number of periods = loan tenor = 20

present value = loan amount = $10,000,000

future value = value of loan after its tenor = 0

when-due = when is the loan payment made each year = end = 0

Annual payment for the low cost loan = PMT(5%, 20, 10000000, 0, 0) = $802,426

Annual payment for regular loan = PMT(8%, 20, 10000000, 0, 0) = $1,018,522

Difference between both payments = $1,018,522 - $802,426 = $216,096

This difference will be present for 20 years. The present value of all the differences can be calculated using the PV formula in spreadsheet.

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = annual interest = 8%

number of periods = 20

payment amount = yearly difference in payment = $216,096

future value = future value of payments = 0

when-due = when is the loan payment made each year = end = 0

PV = PV(8%, 10, 216096, 0, 0) = $2,121,665

Hence, the value of the land should be $2,121,665