if $100,000 of 12-year, 7% bonds, paying interest annually, were issued at par four years ago,...

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if $100,000 of 12-year, 7% bonds, paying interest annually, were issued at par four years ago,...

if $100,000 of 12-year, 7% bonds, paying interest annually, were issued at par four years ago, and the current market rate of interest for the same type of security is 10%, what is the present value of the liability (rounded to the nearest dollar)?

business accounting

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Answer 1

Answer #1

Present Value of liability = $ 83,995 (refer working note:1)

Working Note:1

Remaining life of bond = 8 years

Interest Rate = 7% annually

Therefore, Annual Interest Payable for 8 years = 100000*7%= $7000 each year

Current market rate of interest for the same type of security = 10%

To calculate Present Value of liability, we consider 10% discount rate, as it will indicate the actual position based on current market rate.

Here,

Redemption value after 8 years from now(A) = $ 100000

Period(n) = 8 years

Discounting rate(i)=10% p.a.

Using annuity,

Present Value=Annual Interest*Annuity Factor(10%,8 years)+Redemption value*discounting factor(10%,8years)

=7000*5.3349+100000*0.4665

=37344.30+46650.00

=83994.30

i.e.Present Value of liability = $ 83,995

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Answer 2

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