Question

R- G 0,= 1.50×(1.04) = 10.1% = 7 % 1.56 101-boy = 25.57 Suppose you are considering investing in a 5-year, 11% coupon, S1000 face value bond trading for = $1294.73. What is the yield to maturity? You must show work to get full credit. a. 4.32% b. 5.00% c. 5.68% d. 11.00% e. 13.72% Price=1000 coupon = 11%

Answer 1

The correct answer is option a

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The price of the bond, yield to maturity and coupon payment are related according the following equation

м Bond price = { ufret (

$110 $1000 $1294.73 = ) 2(1+r)5*(1+r)s

In the above equation, the value of r is the yield to maturity of the bond. The value of r is found using trial and error.

let r = 4%

The RHS of the equation is calculated as

= $ 110 $\times$ PVIFA _{r=4%, n = 5 years} + $ 1000  $\times$ PVIF _{r=4%, n = 5 years}

PVIFA _{r=4%, n = 5 years} = Present value interest factor of annuity

PVIF _{r=4%, n = 5 years} = Present value interest factor

= $ 110 $\times$ 4.452 + $ 1000 $\times$ .8219 = $ 1,311.62

The price calculated is above the market price

Let r = 5%

The RHS of the equation is calculated as

= $ 110 $\times$ PVIFA _{r=5%, n = 5 years} + $ 1000  $\times$ PVIF _{r=5%, n = 5 years}

= $ 110 $\times$ 4.329 + $ 1000 $\times$ .7835

= $ 1,259.69

The yield to maturity lies between 4 % and 5 %

($ 1,311.62 - $ 1294.3] Yield to maturity = 4% +7 [$ 1,311.62 - $ 1,259.691

Yield to maturity = 4.32 %