Question

1-1 The yield-to-maturity on a bond is the interest rate you earn on your investment if interest rates do not change. If you actually sell the bond before it matures, your realized return is known as the holding period yield. Suppose that today you buy a 9 percent annual coupon bond for $1,000. The bond has 12 years to maturity. Three years from now, the yield-to-maturity has declined to 7 percent and you decide to sell. What is your holding period yield？

1-2 Apocalyptica Corp. pays a constant $20 dividend on its stock. The company will maintain this dividend for the next 7 years and will then cease paying dividends forever.If the required return on this stock is 9 percent, what is the current share price?

1-3 A bond has a coupon rate of 8 percent, 7 years to maturity, semiannual interest payments, and a YTM of 7 percent. If interest rates suddenly rise by 2 percent, what will be the percentage change in the bond price?

1-4 E-Eyes.com Bank just issued some new preferred stock. The issue will pay a $19 annual dividend in perpetuity, beginning 10 years from now. If the market requires a 7 percent return on this investment, how much does a share of preferred stock cost today

1-5 Antiques R Us is a mature manufacturing firm. The company just paid a $12 dividend, but management expects to reduce the payout by 10 percent per year indefinitely.If you require an 16 percent return on this stock, what will you pay for a share today?

Answer 1

1-1) today price of bond = $ 1000
After 3 years
Price of bond = Interest x PVIFA(YTM%,n) + Redemption value x PVIF(YTM%,n)
Interest = $1000 x 9% = 90 $
YTM = Yield to maturity = 7%
n = no . Of coupon payments = 12-3 = 9
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(7%,9) = [1-(1/(1+7%)^9 / 7%]
=[1-(1/(1+0.07)^9 / 0.07]
=[1-(1/(1.07)^9 / 0.07]
=[1-0.54933 / 0.07]
=0.4561/0.07
=6.5152
PVIF(7%,9) = 1/(1+7%)^9
=1/(1.07)^9
= 0.543934
Value of bond = 90 x 6.5152 + 1000 x 0.543934
= 586.37 + 543.93
= 1130.30 $

holding period yield = Selling price - Buying price/Buying price
= 1130.30 - 1000/1000
= 130.30/1000
=13.03%

1-2) Statement showing price of stock today

Year	Dividend	PVIF @ 9%	PV
1	20	0.9174	18.35
2	20	0.8417	16.83
3	20	0.7722	15.44
4	20	0.7084	14.17
5	20	0.6499	13.00
6	20	0.5963	11.93
7	20	0.5470	10.94
Price of stock today	100.66

Thus price of stock today = 100.66 $

1-3) When YTM = 7%

Price of bond = Interest x PVIFA(YTM%,n) + Redemption value x PVIF(YTM%,n)
Interest = $1000 x 8%/2 = 40 $
YTM = Yield to maturity = 7%/2 = 3.5%
n = no . Of coupon payments = 7 x 2 = 14
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(3.5%,14) = [1-(1/(1+3.5%)^14 / 3.5%]
=[1-(1/(1+0.035)^14 / 0.035]
=[1-(1/(1.035)^14 / 0.035]
=[1-0.61778 / 0.035]
=0.382218/0.035
=10.9205
PVIF(3.5%,14) = 1/(1+3.5%)^14
=1/(1.035)^14
= 0.61778
Value of bond = 40 x 10.92052 + 1000 x 0.61778
= 436.82 + 617.78
= 1054.60 $

When YTM = 9%
Price of bond = Interest x PVIFA(YTM%,n) + Redemption value x PVIF(YTM%,n)
Interest = $1000 x 8%/2 = 40 $
YTM = Yield to maturity = 9%/2 = 4.5%
n = no . Of coupon payments = 7 x 2 = 14
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(4.5%,14) = [1-(1/(1+4.5%)^14 / 4.5%]
=[1-(1/(1+0.045)^14 / 0.045]
=[1-(1/(1.045)^14 / 0.045]
=[1-0.61778 / 0.045]
=0.539972/0.045
=10.2228
PVIF(4.5%,14) = 1/(1+4.5%)^14
=1/(1.045)^14
= 0.53997
Value of bond = 40 x 10.2228 + 1000 x 0.53997
= 408.913 + 539.9728
= 948.89 $

Thus % change in bond price = 948.89 - 1054.60/1054.60

= -105.71/1054.60

= -10.02 %

1-4) let us first find present value of perpetuity at end of 10 years

PV of perpertuity = Dividend/required rate of return

= 19/7%

=271.43 $

Now present value of this perpetuity = PV = FV/(1+r)^n

= FV = 271.43$

n = 10

r = 7%

Thus PV = 271.43/(1+7%)^10

=271.43/(1.07)^10

=271.43/1.9672

=137.98 $

share of preferred stock will cost today = 137.98$