Question

9. Bond T is a 3 year, 8% annual coupon bond with a par value of $1000 and current value of $1000. The discount rate is equal to the coupon rate. What is the duration of Bond T?

10. Using the information in #9 and considering an expected rise of interest rates by 1%, calculate the modified duration for Bond T.

13. Daniels Company’s preferred stock is expected to pay a $1.25 dividend at the end of each year. The required rate of return on this stock is 8.5 %. What is the price of Daniels Company’s preferred stock?

Answer 1

9. Bond T is a 3 year, 8% annual coupon bond with a par value of $1000 and current value of $1000. The discount rate is equal to the coupon rate. What is the duration of Bond T?

Discount rate = coupon rate = 8%

Year (t)	Cash Flow from coupon payments (8% of $1000)	Cash Flow from maturity amount	Total Cash Flow from coupon payments and maturity amount (CF)	Present value (PV) discounted at 8% of yield to maturity	PV *t
1	$80.0		$80.0	$74.07	$74.07
2	$80.0		$80.0	$68.59	$137.17
3	$80.0	$1,000.0	$1,080.0	$857.34	$2,572.02
sum				$1,000.00	$2,783.26
				Bond's Price↑
			Duration = sum of (PV*t)/sum of PVs =	$2,783.26/$1,000	2.78	Years

The duration of Bond T is 2.78 years

10. Using the information in #9 and considering an expected rise of interest rates by 1%, calculate the modified duration for Bond T.

Modified Duration = Macaulay Duration / (1 + YTM/n)

Where,

Macaulay Duration = 2.78 years

Yield to maturity, YTM = 9% per year, after 1% increase

Number of discounting periods in year, n = 1 (for annual coupon payments)

Therefore,

Modified Duration = 2.78 *(1+ 9%)

= 3.03 years

13. Daniels Company’s preferred stock is expected to pay a $1.25 dividend at the end of each year. The required rate of return on this stock is 8.5 %. What is the price of Daniels Company’s preferred stock?

Price of Daniels Company’s preferred stock = Dividend per share / required rate of return of preferred stock

Where,

Dividend per share = $1.25

Required rate of return of preferred stock = 8.5%

Therefore,

Price of Daniels Company’s preferred stock = $1.25 /8.5% = $1.25 /0.085 =$14.71

The price of Daniels Company’s preferred stock is $14.71 per share.