Question

A company can borrow $760000 for 7 years by issuing bonds, on which interest is paid semi-annually at j2 = 11% and the principal is paid off using a sinking fund earning j2= 2%. The other option is to borrow $760000 from a bank and repay the loan over 7 years with equal semi-annual payments at j2 = 12%.

Which option will result in a smaller periodic cost for the company? Bank loan or Sinking fund method

How much will you save each period with this option?

Answer 1

- First, we will calculate the periodic semiannual payments to sinking fund using Future value of ordinary annuity formula:

|(1+r)" - 11 FutureValue = C*

Where, C= Periodic Payments

r = Periodic Interest rate = .02/2 = 0.01

n= no of periods = 7 years *2 semiannual payments = 14

Future Value = $760,000

760,000 = C+ [(1 + 0.01)14 - 11 0,01

760,000 = C*11 (1.1494742132 - 11 0,01

760,000 = C * 14.94742132

Periodic semiannual payments = $ 50844.89

Interest on semi-annual bonds = $760,000*11%*1/2

= $41,800

Total payment with Sinking fund Method = $ 41800 + $50844.89

= $92,644.89

Now, we will calculate semi-annual payments of loan amount borrowed using formula:

= P*r* (1+r) (1+r) - 1

where, P = Loan amount = $760,000

r = Periodic Interest rate = 0.12/2 = 0.06

n= no of periods = 7 years *2 semiannual payments = 14

= 760000 * 0.06 * (1 + 0.06)14 (1+0.06)14 – 1

2.26090396 = 45600 * 2.26090396-1

= $ 81,764.53

Semiannual payments to loan = $ 81,764.53

So, Bank Loan has smaller periodic payment thus have a smaller periodic Cost.

You will save $ 10880.36 ($92644.89-$81764.53) with bank option.

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