Corporate Finance

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Corporate Finance

Loan outstanding for 1st year = Rs 1000000

Loan outstanding for 2nd year = Rs (1000000 – Loan repaid) = 10L – 151290

= Rs 848710

Interest for 2nd year = 0.14 × 848710 = Rs 118819

Principal component = Annual installment – Interest for 2nd year

= 291190 – 118819 = Rs 172470

All other entries could be worked out similarly.

An Illustration: Making sense out of housing loans

Assume that you are in the process of borrowing Rs 10 lac to construct a house. The repayment period is
15 years. Bank A charges 14 percent annually; bank B charges 14.5 percent. Verify that equated monthly
installment is Rs 13,600 for bank A, and Rs 14,000 for bank B. A reduction of 0.5 percent interest will save
Rs 400 every month, Rs 4,800 a year and Rs 72,000 by the time the loan is cleared. Interest rates on housing
loans are calculated either on a monthly reducing or an annual reducing basis. In the former case, interest is
computed on the reducing outstanding balance on a monthly basis whereas in the latter case, interest is
levied on the annual principal, which reduces annually.
HDFC charges 15.5 percent p.a. on a loan of Rs 10 lac; GIC Housing Finance (HF) charges 16.5 percent.
On the face of it, HDFC is cheaper. However, since GIC HF calculates its interest on a monthly reducing
basis, the EMI for a 5 year loan works out to Rs 24,585, against Rs 25,200 for HDFC which calculates interest
on an annual reducing basis. By the way, calculation of EMIs is similar to calculation of EAIs.

EFFECTIVE AND NOMINAL RATES

In all the examples considered so far, compounding was done annually. This may not be true of all situations.
For instance, a fixed deposit scheme may offer quarterly compounding; a car dealer may quote an interest
rate on a monthly basis. How should we compare interest rates that are quoted for different periods? Let’s
look at a numerical. A car dealer offers two schemes—A and B. Under the first scheme you have to pay an
interest of 12 percent compounded monthly and under the second scheme you have to pay an interest of
12 percent compounded annually. You are required to choose between the two.
The trick is to convert both of them into the same basis. There is a simple formula to do this:

(1 + Annual rate) = (1 + Monthly rate)^12

For the first scheme, the annual rate is 12 percent. So the rate per month is 12/12 = 1 percent.

Substitute in the above equation:

(1 + Annual rate) = (1 + 0.01)^12

Annual rate = 12.68 percent

From the numerical it must be clear that the shorter the compounding period, the higher will be the
interest rate. The rate quoted on an annual basis (12 percent) is the simple annual rate and the rate that
considers more frequent compounding is called effective rate (12.68 percent in the above example).