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Case Studies on Sinking Fund
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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 newly constructed building stands on a plot costing Rs. 100000.
The construction cost of building is Rs. 2000000 and the estimated life of building is 66 years.
The investor wants a 5% return on land cost and 8% return on the construction cost.
Calculate the annual rent to be charged if annual repairs cost 0.5% of cost of construction and other outgoings equal 30% of gross rent.
The co-efficient for sinking fund at 3% for 66 years may be taken as 0.005.
Return on land cost = 5% of 100000 = 5000
Return on construction cost = 6% of 2000000 = 120000
Total Income desired = Rs. 125000 (a)
Let gross annual rental be 'r'
Outgoings:
Annual repairs = 0.5% of 2000000 = 10000
Other outgoings = 30% of r or 0.30 r
Amount towards sinking fund = 0.005 x 2000000 = 10000
Hence, net income = r - 0.30 r - 20000 (b)
Equating (a) and (b),
0.70r - 20000 = 125000
0.70r = 125000 - 20000
0.70r = 105000
r = 105000/0.70
= 12500
Hence, rent per month = Rs. 12500
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