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Homework answers / question archive / 1) The duration of an 11-year, $1,000 Treasury bond paying a 8 percent coupon and selling at par has been estimated at 7

1) The duration of an 11-year, $1,000 Treasury bond paying a 8 percent coupon and selling at par has been estimated at 7

Finance

1) The duration of an 11-year, $1,000 Treasury bond paying a 8 percent coupon and selling at par has been estimated at 7.9106 years. What is the modified duration of the bond? The bond has semi-annual coupon payments.

2) A stock has a required return of 11%. ROE is 8%. The firm's retention ratio is 0.65. The last period's earnings per share was $15.00.

 What is the firm's PVGO?

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1) Computation of the modified duration:-

The bond is selling at par so the YTM is equal to coupon rate.

YTM = Coupon payment = 8%/2 = 4% (semiannual)

Modified duration = Duration  / (1 + YTM)

= 7.9106 / (1 + 4%)

= 7.606 years

 

2) Computation of the firm's PVGO:-

Growth rate = ROE * Retention ratio

= 8% * 0.65

= 5.20%

Dividend = Earnings * Dividend payout ratio

= $15 * (1 - 0.65)

= $5.25

Stock price = D1 / (Required return - Growth rate)

= $5.25 * (1 + 5.20%) / (11% - 5.20%)

= $5.52 / 5.80%

= $95.22

PVGO = Stock price - (Earnings / Required return)

= $95.22 - ($15 / 11%)

= $95.22 - $136.36

= -$41.14

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