Corporation having recently issued a $25 million. 10-years bond issue is required to make annual year...

Corporation having recently issued a $25 million. 10-years bond issue is required to make annual year end sinking fund deposits of $ 1,800,000. The deposits are made on the last day of each year and yield a return of 5%.

1. Compute the fund balance at the end of the 10 years.

2. Compute the additional annual deposit amount that should have been made at the end of each of the 10 years to accumulate the $25 million.

Solutions

Expert Solution

(Amount in million $)

(1) 1st yr= 1.8*(1.05)^{9 =} 2.792

2nd yr= 1.8*(1.05)^8
= 2.659

3rd yr= 1.8*(1.05)⁷ = 2.533

4th yr= 1.8*(1.05)⁶ = 2.412

5th yr= 1.8*(1.05)⁵ = 2.297

6th yr = 1.8*(1.05)⁴ = 2.188

7th yr= 1.8*(1.05)³ = 2.084

8th yr= 1.8*(1.05)² = 1.985

9th yr= 1.8*(1.05)¹ = 1.89

10th yr= 1.8 = 1.8

22.640

(2) Additional amount deposit:-

X*(1.05)⁹ + X*(1.05)⁸ + X*(1.05)⁷ + X*(1.05)⁶ + X*(1.05)⁵ + X*(1.05)⁴ + X*(1.05)³ + X*(1.05)² + X*(1.05) + X = 25

11.5779X = 25

X= 25/11.5779 = 2.16

Additional amt= 2.16-1.8 = 0.36

ekkarill92 answered 1 year ago

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