Page 41 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Personal Financial Planning

Notes 2.12 Loan Amortisation

Loan is an amount raised from outsiders at an interest and repayable at a specified period
(lumpsum) or in installments. The repayment of loan is known as amortisation. A financial
manager may take a loan and he may interested to know the amount of equal instalment to be
paid every year to repay the complete loan amount including interest. Instalment can be calculated
with the following formula:
⎛ ( I1 I ) n ⎞
+
L = P A ⎜ ⎟
n
I
⎝ (1I+ ) − ⎠
1
or
L = P ÷ PVIFA
I A n . I
Where,
L = Loan installment.
I
P = Principal amount.
A
I = Interest rate.
n = Loan repayment period.

PVIFA = PV interest factors at loan repayment period at a specified interest rate.
n . I
Illustration 30
ABC Company took a loan of ` 10,00,000 lakh for an expansion program from IDBI at 7 per cent
interest per year. The amount has to be repaid in 6 equal annual installments. Calculate the per
instalment amount.
Solution:
⎛ 0.06 (1 0.06 ⎞
6
+
)
L =10,00,000 ⎜ 6 ⎟
+
)
I ⎝ (10.06 − 1 ⎠
or
L = 10,00,000 ÷ PVIFA
I 7%. 6y
= 10,00,000 ÷ 4.769 = ` 2,09,687.56
2.12.1 Present Value of Growing Annuity
Growing annuity means the cash flow that grows at a constant rate for a specified period of time.
In others, the cash flow grows at a component rate.
Steps involved in calculation:
1. Calculate the series of cash flows.

2. Convert the series of cash flows into present values at a given discount factor.
3. Add all the present values, of series of cash flows to get total PV of a growing annuity.
Formula ⎛ (1g+ ) n ⎞
⎜ 1 − n ⎟
CIF ⎜ (1I+ ) ⎟
PVG = (1g ⎜ (1g− ⎟
+
A
)
⎜ ⎜ ⎝ ) ⎟ ⎟ ⎠

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