Question

In 2009 the Lagersmith company purchased an industrial plant for $10,000,000. In 2019 the Johnston Beer Company will acquire the plant for $15,000,000 with a loan at 85% LTV at 7% for 30 years. Because of tax and accounting considerations, the Lagersmith company has offered to provide seller held financing (second mortgage) of $10,000,000 at 3.5% for 30 years but only if they can get a higher price on the sale. The bank has agreed that should the Johnston Beer Company choose to use the second mortgage option, the bank will provide 33% of the purchase price and allow the remainder of the purchase price to financed by the Lagersmith provided second mortgage. At what price would the Johnston Beer Company be indifferent between financing the entire purchase through a bank or using bank debt and the seller held second mortgage? (Indifferent means the monthly expense to the Johnston Beer Company is exactly the same in either scenario).

Answer 1

First let's find out the monthly expenses under pure bank financing i.e. bank debt:

In 2019 the Johnston Beer Company will acquire the plant for $15,000,000 with a loan at 85% LTV at 7% for 30 years.

The monthly expense can be calculated using the PMT function of excel. Inputs for PMT function will be:

Rate = interest rate per period of 1 month = 7% / 12 = 0.583333%

Period = Nos. of months in 30 years = 12 x 30 = 360

PV = - Loan amount = - LTV x Purchase cost = - 85% x 15,000,000 =  12,750,000

Hence, monthly expense = PMT (Rate, Period, PV) = PMT (0.583333%, 360, - 12750000) = $84,826.07

Let's now consider the case of mix financing. Let's assume P is the indifference price.

The bank has agreed that should the Johnston Beer Company choose to use the second mortgage option, the bank will provide 33% of the purchase price and allow the remainder of the purchase price to financed by the Lagersmith provided second mortgage.

Bank Loan amount = 33% x P = 0.33P

So, this will translate into monthly payment of an amount, A such that PV of annuity of A over N = 360 period s and R = 0.583333% = Loan amount

That is, A / R x [1 - (1 + R)^-N] = A / 0.58333% x [1 - (1 + 0.58333%)^-360] =  150.3076A = 0.33P

Hence, A = 0.33P /  150.3076 =  0.0021955P

Maximum amount financed by the Lagersmith = $ 10,000,000

Interest rate, i = 3.5% / 12 = 0.2916667%; N = 360 periods

Hence, the monthly payment, B will be such that, B / i x [1 - (1 + i)^-N] = B / 0.2916667%; x [1 - (1 +  0.2916667%)^-360] =  222.6950B = 10,000,000

Hence, B = 10,000,000 / 222.6950 = 44,904.47

Hence, total monthly expense under this option = A + B = 0.0021955P + 44904.47

This amount should be equal to monthly expenses under pure bank loan option.

Hence, 0.0021955P + 44904.47 = $84,826.07

Hence, P = ($84,826.07 - 44,904.47) / 0.0021955 = $ 18,183,389

Hence, the price of indifference, P = $18,183,389