Question

Silver Sun Consulting just bought a new apple orchard for 695,611 dollars. To pay for the apple orchard, the company took out a loan that requires Silver Sun Consulting to pay the bank a special payment of 21,660 dollars in 6 months and also make regular monthly payments forever. The first regular payment is expected in 1 month and all subsequent regular payments are expected to increase by 0.34 percent per month forever. The interest rate on the loan is 1.14 percent per month. What is the payment expected to be in 1 month?

Answer 1

Value of Apple orchard = $695,611

Company has taken loan for purchase of Apple orchard in which company has to pay one special payment after six month and regular monthly payment forever.

Value of special payment = $21,660

Monthly Interest rate = 1.14%

Present value of special payment = $21,660 / (1 + 1.14%) ^ 6

= $21,660 / 1.070379

= $20,235.82

Present value of special payment is $20,235.82.

So, present value of perpetuity = $695,611 - $20,235.82

= $675,375.18.

So, present value of perpetuity is $675,375.18.

Now, Value of first payment is calculated below using following formula:

Present value = First Payment / (Interest rate - Growth rate)

$675,375.18 = First Payment / (1.14% - 0.34%)

First Payment = $675,375.18 × 0.80%

= $5,403.00

So, value of first payment is $5,403.00