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ABC company just issued 50 Lakhs Rs. 100-par bonds payable carrying 8% coupon rate and maturing in 15 years. The bond indenture requires the company to set up a sinking up to pay off the bond at the maturity date. Semi-annual payments are to be made to the fund which is expected to earn 5% per annum. Find the amount of required periodic contributions.
Solution
The future value required to be accumulated equals 50 Crores (50,00,000 × 100)
Since the payments are semi-annual, the periodic interest rate = 5% ÷ 2 = 2.5%
Number of periods = 2 × 15 = 30
Periodic Contribution to Sinking Fund
PMT(FV) = ( FV / (((1+i)^n - 1) / i) )
PMT = Payment per Time Period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods
= (50,00,00,000 / (((1+0.025)^30 - 1) / 0.025)
= (50,00,00,000 / ((2.097567579 - 1) / 0.025)
= (50,00,00,000 / (1.097567579 / 0.025)
= (50,00,00,000 / 43.90270316)
= 1,13,88,820
So, ABC company must deposit Rs. 1,13,88,820 at the end of each 6 months for 15 years in order to accumulate enough money to pay off the bonds when they are due.
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A company wants to set up a sinking fund for the repayment of a loan of Rs. 10 Crores at the end of four years. It makes equal deposits at the end of each month into a fund that earns interest at 12% per year compounded monthly. Determine the size of each deposit.
Also construct a sinking fund schedule(the first three months only).
Solution :
Loan is 10 Crores to be repaid at the end of 4 years.
Monthly deposits are made.
Interest rate is 12% per year compounded monthly.
This is a Payment for a Future Value type problem.
PAYMENT FOR A FUTURE VALUE EQUATION
PMT(FV) = ( FV / (((1+i)^n - 1) / i) )
PMT = Payment per Time Period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods
FV = Rs. 10,00,00,000
i = 0.12 / 12 = 0.01
n = 12*4 = 48
Intermediate calculations would be:
(1.01)^48 - 1 = 1.612226078 - 1 = 0.612226078
So,
PMT = 10,00,00,000 / (0.612226078/.01) which would become:
PMT = Rs. 16,33,383.54
Also, sinking fund schedule for the first three months are :
End of month 1 = Rs. 16,33,383.54
End of month 2 = Rs. 16,33,383.54 * (1+i) = 16,49,717.378 + p = 32,83,100.92
End of month 3 = Rs. 32,83,100.92 * (1+i) = 33,15,931.929 + p = 49,49,315.47
This may not be so much important for the exam point of view. Still, no harm in getting familiarised.
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