Question

I need the answer by using the original calculator. no excel and no advanced calculators please.

aidwev YIELD TO MATURITY AND FUTURE PRICE maturity, and a 7% annual coupon and sells for $985. What is its yield to maturity (YTM)? A bond has a $1,000 par value, 10 years to a. Assume that the yield to maturity remains constant for the next 3 years. What will the price be 3 years from today? b.

Answer 1

a)

Annual coupon payment = 0.07 x $ 1000 = $ 70

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

с м Σ Price + (1 r)(1r)" t 1

In the above equation, the value of r is the yield to maturity.

10 70 $1000 $985 = L+r)10(1+r)10| t-1

The value of r is calculated using trial and error method.

P = $ 70 x PVIFA_{r=? ,n = 10years} + $ 1000 x PVIF_{r=?, n = 10 years}

where PVIFA = present value interest factor of annuity

PVIF = present value interest factor

Let r = 6%

The right hand side of the equation = $ 70 X PVIFA_{r=6%, n = 10 years} + $ 1000 x PVIF_{r=6%, n = 10 years}

= $ 70 x 7.360087 + $ 1000 x 0.558395

= $ 1073.60109 ( higher than $ 985)

Let r = 7%

The right hand side of the equation = $ 70 X PVIFA_{r=7%, n = 10 years} + $ 1000 x PVIF_{r=7%, n = 10 years}

= $ 70 X 7.023582 + $ 1000 x 0.508349

= $ 999.99974 ( higher than $ 985)

Let r = 8%

The right hand side of the equation = $ 70 X PVIFA_{r=8%, n = 10 years} + $ 1000 x PVIF_{r=8%, n = 10 years}

= $ 70 X 6.710081 + $ 1000 x 0.463193

= $ 932.89867 ( less than $ 985)

The yield to maturity lies between 7 % and 8%

[$ 999.99974-$ 985] Yield to maturity= 7% + $ 932.89867] [S 999.99974

Yield to maturity = 7.22%

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b)

The price three years from now is calculated as follow

3 $1000 70 Σ Price (10.0722)3 (10.0722)3 t 1

Price = $ 70 x PVIFA_{r=7.22%, n = 3 years} + $ 1000 x PVIF_{r=7.22%, n = 3 years}

Price = $ 70 x 2.6138 + $ 1000 x 0.81128

Price 3 years from today = $ 994.25