Question

In: Finance

A noncallable Treasury bond has a quoted yield of 4.78 percent. It has a 5.75 percent...

A noncallable Treasury bond has a quoted yield of 4.78 percent. It has a 5.75 percent coupon and 13 years to maturity. Assuming $1,000 par value. What is its quoted price?

Expert Solution

Quoted price is $1,092.34

Working:

Price of bond is the present value of cash flows from bond -(a) Coupon Interest and (b) Maturity Value.

Present Value of coupon interest

$ 547.36

Present Value of Par Value

$ 544.98

Price of bond

$ 1,092.34

Working:

Annual coupon interest

=

Face Value x Coupon rate

=

$ 1,000.00

x

5.75%

=

$ 57.50

Cumulative discount factor

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.0478)^-13)/0.0478

i

4.78%

=

9.51924

n

13

Discount factor for 13th period

=

1.0478^-13

=

0.54498

Present Value of coupon interest

=

Coupon Interest x Cumulative discount factor

=

$ 57.50

x

9.51924

=

$ 547.36

Present Value of Par Value

=

Par Value x discount factor

=

$ 1,000.00

x

0.54498

=

$ 544.98

jeff jeffy answered 2 years ago

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