Red Royal Food just bought a new skating rink. To pay for the skating rink, the

Question

Red Royal Food just bought a new skating rink. To pay for the skating rink, the company took out a loan that requires Red Royal Food to pay the bank a special payment of 18,690 dollars in 4 month(s) and also pay the bank regular payments.   The first regular payment is expected to be 1,770 dollars in 1 month and all subsequent regular payments are expected to increase by 0.45 percent per month forever. The interest rate on the loan is 1.96 percent per month. What was the price of the skating rink?

Explanation / Answer

First payment in 1 month (Cf1)= 1,770

expected growth rate(g) = 0.45% = 0.0045

Interest rate per month (r) = 1.96% = 0.0196

Since this is a perpetuity the present value of this = Cf1/(r-g) = 1,770/(0.0196-0.0045) = 117,218.543

Now there is a special payment tat happens in 4 months. Its present value = 18,690/(1+0.0196)^4 = 17,293.782

Total present value = 117,218.543+ 17,293.782 = 134,512.325

Price of the skating ring = $134,512.33 (Rounded to 2 decimals)

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