Question

In: Finance

a) On March 1, 2016, Corporation issues a $1,000 par value bond with a 10 percent...

a) On March 1, 2016, Corporation issues a $1,000 par value bond with a 10 percent coupon (paid semi-annually) that matures in exactly two years. If the yield to maturity is 7%, at what price should the bond sale?

b) If the yield to maturity remains at 7%, at what price should the bond sell on May 1, 2016 (2 months after issue)? what is the dirty price on May 1, 2016?

c) Actions by the Fed cause market interest rates go up. If the yield to maturity increases to 8%, at what price should the bond sell on June 1, 2016 (3 months after issue)? what is the dirty price on June 1, 2016?

Solutions

Expert Solution

Par Value of the bond = $1000

Coupon Rate of the bond = 10%

Coupon Interest (Half Yearly) = $1000*10%/2= $50 (Half-yearly)

YTM = 7% (annually), 3.5% (half yearly)

Time to Maturity = 4 semi-annual periods

Price of the bonds = Coupon Interest * PVIFA (3.5%, 4) + Par Value of Bonds * PVIF (3.5%, 4)

Price of the bonds = $50* pvifa (3.5%, 4) + $1000 * pvif (3.5%, 4)

Price of the bonds = $50* 3.6731 + $1000* 0.8714= $1055

Par Value of the bond = $1000

Coupon Rate of the bond = 10%

Coupon Interest (Half Yearly) = $1000*10%/2= $50 (Half-yearly)

YTM = 7% (annually), 3.5% (half yearly)

Time to Maturity = 1 year 10 months or, (3 half year + 4months/6months= 3.66 half years)

Price of the bonds = Coupon Interest * PVIFA (3.5%, 3.66) + Par Value of Bonds * PVIF (3.5%, 3.66)

Price of the bonds = $50* pvifa (3.5%, 3.66) + $1000 * pvif (3.5%, 3.66)

Price of the bonds = $50* 3.3801 + $1000* 0.8817= $1050.71

Dirty Price of the Bond (formula) = Book Value of the bond as on that date * (1+ ytm%/ n years) ^ (t/T)

YTM% = annual yield

N = half years

T = T is the total number of days in the coupon period (180 days)

t = it is the number of days since the last coupon date

Book Value of the bond (1^st May 2016) = $1050.71

YTM% = 7%

N= 2

T = 180 days

t = (31+30) = 61 days

Or, 61/180= 0.34

Dirty Price of the Bond = $1050.71* (1 + 0.07/2)^ 0.34= $1063.70

Par Value of the bond = $1000

Coupon Rate of the bond = 10%

Coupon Interest (Half Yearly) = $1000*10%/2= $50 (Half-yearly)

YTM = 8% (annually), 4% (half yearly)

Time to Maturity = 1 year 9 months or, (3 half year + 3months/6months= 3.50 half years)

Price of the bonds = Coupon Interest * PVIFA (3.5%, 3.50) + Par Value of Bonds * PVIF (3.5%, 3.50)

Price of the bonds = $50* pvifa (3.5%, 3.66) + $1000 * pvif (3.5%, 3.66)

Price of the bonds = $50* 3.2411 + $1000* 0.8866= $1048.655

Dirty Price of the Bond (formula) = Book Value of the bond as on that date * (1+ ytm%/ n years) ^ (t/T)

YTM% = annual yield

N = half years

T = T is the total number of days in the coupon period (180 days)

t = it is the number of days since the last coupon date

Book Value of the bond (1^st May 2016) = $1048.655

YTM% = 7%

N= 2

T = 180 days

t = (31+30+31) = 92 days

Or, 92/180= 0.511

Dirty Price of the Bond = $1048.655* (1 + 0.07/2)^ 0.5111= $1067.256

jeff jeffy answered 1 year ago

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