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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 7.9106 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?
Expert Solution
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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