Question

A corporation sold 5,000 issues of 20-year bonds, having a total face value of P5,000,000, for P4,750,000. The bonds bear interest at 10%, payable semiannually.

(a) The company wishes to establish a sinking fund for retiring the bond issue and will make semiannual deposits that will earn 8% compounded semiannually. Compute the annual cost for interest and redemption of these bonds.

Answer 1

Given:
Face value= P 5,000,000
r= 10% and semi-annuallly 10/2 = 5%
i= 8% and semi-annually 8/2= 4%
n= 20 year and semi-annualy n = 20*2 = 40

Interest on Bond per period = Face value * r
= 5,000,000 * 0.10
= 5,00,000

Note: Here interest rate is used 10% because interest is calculated on annual basis.

Periodic on the sinking funds ( A) = Facevalue / [ ( 1+i)ⁿ - 1 / i ]

= 5,000,000 / [ ( 1 + 0.04 )⁴⁰ - 1 / 0.04 ]

= 52,620.50

Note: I've used two decimal places in calculation. Answer may differ from some points.

Annual Expenses = P 52,617.73

Therefore, total annual cost = 2*A + Fr

= 2 * 52,620.50 + 5,00,000

= 1,05,241 + 5,00,000

= 6,05,241

annual cost for interest and redemption of these bonds is P6,05,241