Question

LOAN AMORTIZATION. Today is T=0. You borrow $250,000 today at a rate of interest of 8%. You agree to repay the loan over five years. Assuming a 40% tax rate, what are the tax implications, annually, if you repay the loan as a

• Zero amortization schedule
• Full amortization schedule
• Partial amortization schedule ($100,000 extra balloon payment at T=5

Answer 1

a. Zero amortization schedule means that the borrower pays monthly interest only during the period and not the principal portion. He will pay entire prinicpal amount in a lumpsum payment on the date of maturity i.e on the last of the loan term. So every month only interest is paid which will be equal throughout the life of the loan i.e 5 years. In the given case we will pay 20000 p.a (250000 * 8%) every year and will close the loan at the end of Year-5 by paying 250000. As the interest is tax deductible from the EBIT, we will save around 8,000 p.a (20000*40%) in the form tax reduction because of interest. Tax saving for 5 years will be $ 40,000 (i.e 8000 * 5)

b. Full amortization involves payment of equal instalments over the period so that the final balance in the loan by the end of year-5 will be 'zero'.

Formula for calculating Equated Instalments is

where E = Instalments

P = Loan Amount

r = rate of interes

n = no. of periods

So Equated instalments as per the question is = 250000 * 0.08 * [(1+0.08)^5] / [ (1+0.08)^5 - 1)

= 250000 * 0.08 * 1.469328 / 0.469328

= $ 62614 p.a

Amortization schedule will be as calculated below: (Assuming yearly payments at the end of the year)

Year end	Opening Balance	Interest @ 8%	Total Payable	Equated pymts	Interest	Principal	Closing Balance	Tax saving @ 40% on Interest
1	250000	20000	270000	62614	20000	42614	207386	8000
2	207386	16591	223977	62614	16591	46023	161363	6636
3	161363	12909	174272	62614	12909	49705	111658	5164
4	111658	8933	120590	62614	8933	53681	57976	3573
5	57976	4638	62614	62614	4638	57976	0	1855
		63071		313071	63071	250000		25228

c. Partial Amortization

If we pay 45569 every year for 5 years then the closing balance of loan at the end of year 5 will be $ 100,000 which is paid as extra balloon payment on T=5. Amortization schedule is given below

Year end	Opening Balance	Interest @ 8%	Total Payable	Equated pymts	Interest	Principal	Closing Balance	Tax saving @ 40% on Interest
1	250000	20000	270000	45569	20000	25569	224432	8000
2	224432	17955	242386	45569	17955	27614	196818	7182
3	196818	15745	212563	45569	15745	29823	166994	6298
4	166994	13360	180354	45569	13360	32209	134785	5344
5	134785	10783	145568	45569	10783	34786	100000	4313
		77842		227843	77842	150000		31137

Now the Tax reduction for 5 years in the above three cases will be

a. Zero Amortization = $ 40,000

b. Full Amortization = $ 25,228

c. Extra Balloon Payment = $ 31,137