In: Finance
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 |
$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 | ||||||||||||