a) Joy Mummy Ltd is establishing an endowment fund to finance a scholarship scheme to provide funding for the education of children of its employees. The company plans to make an initial deposit of GH¢500,000 into the fund now. The initial deposit will be invested for three years before any disbursements will be made from the fund. The effective annual rate of return on the fund is expected to be 14% in the first year, 15% in the second year, and 16.5% in the third year.
Required:
Compute the balance of the fund at the end of three years. (4 marks)
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b) Wobete Ltd is offering 5 million units of 15-year bonds with a face value of GH¢100 each. Though the bonds are being offered at a price of GH¢95 each, the bonds will be redeemed at a premium of 10%. The annual coupon rate of the bonds is 15%. Interest is payable at the end of every six months.
A provision in the bond indenture requires that Wobete Ltd establishes a sinking fund to accumulate enough money to pay the total redemption value of the bonds upon maturity.
To comply with this provision, Wobete Ltd plans to set aside an even amount at the end of each quarter over the next 15 years. Each of the even amounts that will be set aside will be invested at an annual interest rate of 12% with quarterly compounding.
Required:
Calculate the even amount that should be put into the sinking fund at the end of each quarter to raise enough money to pay the total redemption value of the bonds. (6 marks)
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As the objective of the sinking fund is to raise enough money to pay the redemption value of the bonds when they mature in 15 years’ time, the future value of the sinking fund (SF) should be equal to the total redemption value of the bonds (Total RV):
The future value of the sinking fund, SFn = GH¢550,000,000
Annual interest, i = 12%
Frequency, m = 4
Term (in years), t = 15
Number of periods, n = Term x Frequency = 15 x 4 = 60
That is, Wobete Ltd will have to deposit GH¢3,373,127.31 into the sinking fund at the end of each quarter.