Question

RBC wishes to borrow $2.1 million for 8 years. The company APPE offers to lend the money at j2= 9% if it is amortized semi-annually. Another company ECHO offers it at j2= 7.6% only if the interest is paid semi-annually and the principal is returned at the end of 8 years. If you take ECHO’s offer a sinking fund is established by semi-annual deposits at j2= 3.9%. Which company should AB InBev take the offer from and how much can they save semi-annually with the better option?

Answer 1

To decide the company from which offer should be taken by AB InBev will be decided on the basis of least semi-annual paynents. So, we will compute the semi-annual payments for both the companies and then compare and draw conclusions.

APPE option

Since loan is to be amortised semi-annually, hence r = 9%/2 = 4.5% and n= 8*2 = 16 periods

Semi-annual installment = [P*r*(1+r)^n] / [(1+r)^n]-1

= [2,100,000*0.045*(1+0.045)^16] / [(1+0.045)^16]-1

= [2,100,000*0.045*2.0223] / [2.0223-1]

=191,114 / 1.0223

= $186,932.28

ECHO option

For this option, semi annual payment = Semi-annual interest payment + Sinking fund periodical contribution

Semi-annual interest payment = Loan amount * Interest rate/2

= 2,100,000 * 7.6% / 2

= $79,800

Contribution from sinking fund = [FV/(1+r)^n]*r / [1-(1+r)^-n]

= [2,100,000/(1+0.0195)^16]*0.0195 / [1-(1+0.0195)^-16]

= [2,100,000/1.3620]*0.0195 / 0.2658

= 30,065 / 0.2658

= $113,103.35

Total semi-anmnual payment = Semi-annual interest payment + Contribution from sinking fund

= 79,800 + 113,103.35

= $192,903.35

Since the semi-annual payments is lower in case of APPE option, hence AB InBev should select the offer of APPE.

Savings in semi-annual cost = 192,903.35 - 186,932.28

= $5,971.07