Question

Math of Finance

A company wanted to raise $100, 000 and issued twenty, $5000 bonds paying a 10% coupon rate payable semi-annually for 5 years. It set up a sinking fund to repay the debt at the end of 5 years and made deposits at the end of every six months into the fund. The sinking fund was earning 6.5% compounded semi-annually.

(a) calculate the periodic cost of the debt

(b) calculate the book value of the debt after 3 years

(c) construct a partial sinking fund schedule showing details of the first two and last two payments and the totals of the schedule

Answer 1

(a)Periodic cost of the debt

is the semi-annual interest on the debt

ie. $ 5000*20 *10%/2=

$5,000

(b)Book value of the debt after 3 years

will be the same till repayment at end of 5 yrs.

ie. $ 100000

Using the Future value of ordinary formula,

we can find the semi-annual contribution to the Fund

to be made so as to accumulate $ 100000 (the face value of the bond to be repaid at end of 10 semi-annual periods))

earning interest at the rate of 6.5% p.a./2= 3.25% per semi-annual period,

for 10 semi-annual periods

FVOA=Pmt.*((1+r)^n-1)/r

100000=Pmt.*((1.0325^10-1)/0.0325)

8623.11

c.Sinking fund schedule
No.of contribution to the Fund	Amt./Contn.	Interet/period(3.25%* prev. bal.	Bal.in Fund
1	8623.11	0	8623.11
2	8623.11	280.25	17526.47
3	8623.11	569.61	26719.19
4	8623.11	868.37	36210.68
5	8623.11	1176.85	46010.63
6	8623.11	1495.35	56129.09
7	8623.11	1824.20	66576.39
8	8623.11	2163.73	77363.24
9	8623.11	2514.31	88500.65
10	8623.11	2876.27	100000
Total	86231.10	13768.93