Question

(Complex stream of cash flows​)

Roger Sterling has decided to buy an ad agency and is going to finance the purchase with seller financing—that ​is, a loan from the current owners of the agency. The loan will be for $2,200,000 financed at an APR of 6 percent compounded monthly. This loan will be paid off over 6 years with​ end-of-month payments, along with a $500,000 balloon payment at the end of year 6. That​ is, the $2.2 million loan will be paid off with monthly​ payments, and there will also be a final payment of $500,000 at the end of the final month. How much will the monthly payments​ be?  

a. How much of the loan will be paid off by the final $500,000 payment?

b. Determine how much of the loan must be paid off by the monthly payments by subtracting the present value of the balloon payment from the loan amount.

c. Determine the monthly payments needed to pay off the portion of the loan that is not paid off by the final balloon payment.

Answer 1

Given loan amount = $2,200,000

APR = 6%

Compounded monthly

Implies monthly rate i = 0.06/12 = 0.005time period = 6 years

N= number of payments = 6 years * 12 months = 72

Balloon payment at end of six years = $500,000

a.

Present value of final balloon payment = Balloon payment * [1/ ((1+i)^N)] =

500,000 * [1/ ((1+0.005)^72)] =500,000 * 0.6983024303 = =349151.2152 = $349,151 (answer rounded off to nearest integer)

Therefore Loan to be paid off at the final payment = $349,151

b.

Loan must be paid off by the monthly payments by subtracting the present value of the balloon payment from the loan amount = $2,200,000 - $349,151 = $1,850,849

Therefore Loan to be paid off in monthly payments = $1,850,849

c.

Amount of monthly payments needed = load to be paid in monthly payments * [(i*((1+i)^N))/(((1+i)^N)-1)]

[(i*((1+i)^N))/(((1+i)^N)-1)] = capital recovery factor = (0.005*(1.005^72))/((1.005^72)-1) = 0.01657288789

Amount of monthly payments needed = $1,850,849 *0.01657288789 = $30673.91298 = $30,674 (answer rounded off to nearest integer)

Therefore Monthly payments needed = $30,674