Question

A balloon payment is a loan where you pay small amounts of the loan first and then, at the end of the loan, you pay a BIG portion of the acquired debt to liquidate it. Many times, in this type of loan, you pay the interest of the loan first and then, in the last installment, you pay the last part of the interest and the principal. You and your business partners are contemplating the purchase of a commercial building. The conditions for the loan are: $840,000 principal on a 4-year term, with a loan with 7.2% interest, using a balloon payment method (i.e., paying only the interest years 1-3 and the last portion of the interest and the principal in Year 4). You have secured a long-term debt with longer repayment provisions at a lower interest rate of 6.1%, that you can use right now to make the payments of the balloon payment loan. a) What immediate single payment (i.e., present dollars) would be a fair offer to pay all the series of payments for the balloon payment? (Assume that you are going to use the new long-term loan that you secured at a lower interest rate to cover all the payments) b) What if, instead of using a balloon payment method, you can use an equivalent (i.e., using the same interest rates and term) with uniform annual payments? =$

Answer 1

Given,

Principal (P)= $840,000

Interest rate (R1 ) on loan= 7.2%

Interest rate on long term loan for repayment of the earlier loan= 6.1%

Part (a):

For the balloon payment loan, payments due are as follows:

Interest in year 1, 2 and 3 each = P*R = $840,000*7.2% = $60,480

Payment in year 4= Interest for 4^th year + Principal

= $60,480+$840,000= $900,480

Immediate single payment to pay all series of payments using the long term loan is the PV of payments due, discounted at 6.1%

=60,480/(1+6.1%) + 60,480/(1+6.1%)^2 + 60,480/(1+6.1%)^3 +900480/(1+6.1%)^4

= $871,944.40

Part (b):

In the case of uniform annual payments, annual payments will be $249,112.25 as follows:

A B С D E F G 1 Equated Yearly Installments (1) Payments at the end of each year 2 Equal yearly instalment is calculated using the formula I=[P*r*(1+r)^n]/[(1+r)^n-1] 3 Where P= Principal (loan amount), 4 n= Number of installments. 5 r= Rate of interest per year 6 Given that All amounts in $ 7 Principal (loan amount) (P)= 840,000 No. of years (N)= 4 8 Rate of interest (% p.a)=R= 7.2 9 Calculations: Formula Cell reference Value 10 Interest rate per year in decimals (r )= R/100 D10/100 0.072 11 No. of years (n)= 4 12 (1+r)= 1+G10 1.072 13 (1+r)^n= G124G7 1.320623866 14 [(1+r)^n]-1= G13-1 0.320623866 15 P*r*(1+r)^n= D7*410*G13 79871.33141 16 Equated Yearly Insallments (1)= [P*r*(1+r)^n]/[(1+r)^n-1] G15/14 249112.2462 17 Rounded to $ 249,112.25

Immediate single payment to pay all series of payments using the long term loan is the PV of series payments due, discounted at 6.1%.

The immediate single payment = $861,227.32 calculated as follows:

וס 1 A B с D E F G 1 Present Value of Annuity Payments at the end of each period 2 Present value of annuity is calculated using the formula PVA= P*{[1-(1+r)^-n]/r]} 3 Where P= Periodical payments, n= Number of payments. 4 r= Rate of interest per period in decimals 5 All amounts in $ Given that 7 Periodical payments (P)= 249,112.25 No. of years (N)= 4 8 Rate of interest (% p.a)=R= 6.1 No. of payments a year (t)= 9 Calculations: Formula Cell reference Value 10 Interest rate per period in decimals (r )= R/(100*t) D8/(100*68) 0.061 11 No. of periods (n)= N*t G7*G8 12 (1+r)= 1+G10 1.061 13 (1+r)^-n= G121-G11 0.78911167 [1-(1+r)^-n]= 1-613 0.21088833 15 [1-(1+r)^-n]/r= G14/10 3.45718579 16 Present value of annuity PV= P*{[1-(1+r)^-n]/r]} 07*G15 861227.317 17 Rounded to 861,227.32 4 14