Question

In: Finance

29) Within Year, Inc. has bonds outstanding with a $1,000 par value and a maturity of...

29) Within Year, Inc. has bonds outstanding with a $1,000 par value and a maturity of 30 years. The bonds have an annual coupon rate of 8.0% with quarterly coupon payments. You would expect a quoted annual return of 17.0% if you purchased these bonds. What are the bonds worth to you?

$494.04
$474.17
$2,020.50
$622.47
$1,876.38

Solutions

Expert Solution

$474.17

Working:

Price of bond is the present value of cash flows from bond.
Present Value of coupon interest $     467.40
Present value of Par Value $         6.77
Present Value of cash flows $     474.17
So, price of bond is $ 474.17
Working:
# 1 Semi annnual coupon interest = Face Value * Semi annual coupon rate
= 1000*2%
= $       20.00
# 2 Present value of annuity of 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.0425)^-120)/0.0425 i 17%/4 =      0.0425
= 23.370014 n 30*4 = 120
# 3 Present value of 1 = (1+i)^-n
= (1+0.0425)^-120
= 0.0067744
# 4 Present Value of coupon = Coupon Interest * Present Value of annuity of 1
= $       20.00 * 23.37001
= $     467.40
# 5 Present value of face value = Face Value * Present value of 1
= $ 1,000.00 * 0.006774
= $         6.77

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