A14, B16, B18

A14. (Stock valuation) Suppose Toyota has nonmaturing (perpetual) preferred stock outstanding

that pays a $1.00 quarterly dividend and has a required return of 12% APR (3% per quarter).

PMT= 1.00, r=0.030

The Stock Worth is.

Stock value = PVA perpetuity = dividend / r = 1.00/0.030 = $33.33

B16. (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock

Exchange. Suppose PhilEl’s bonds have identical coupon rates of 9.125% but that one issue

matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment

was made yesterday.

FV = -1000

a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?

PMT= 1000x 9.125%= -91.25, -45.63 semiannual cupon payment,

semi annual return is 4%

1year

B0 = (45.63) [((1.04)2 -1)/ ((0.04)(1.04)2] + 1000/(1.04)2 = $1,010.42

7year

B0 = (45.63) [((1.04)14 -1)/ ((0.04)(1.04)14] + 1000/(1.04)14 = $1,058.57

15year

B0 = (45.63) [((1.04)30 -1)/ ((0.04)(1.04)30] + 1000/(1.04)30 = $1,096.29

b. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%.

What is the fair price of each bond now?

PMT= 1000x 9.125%, 45.63 semiannual cupon payment,

semi annual return is 3.5%

1year

B0 = (45.63) [((1.035)2 -1)/ ((0.035)(1.0352] + 1000/(1.035)2 = $1,019.86

7year

B0 = (45.63) [((1.035)14 -1)/ ((0.035)(1.035)14] + 1000/(1.035)14 = $1,114.52

15year

B0 = (45.63) [((1.035)30 -1)/ ((0.035)(1.035)30] + 1000/(1.035)30 = $1,193.54

` c. Suppose that the yield to maturity for all of these bonds changed instantaneously again,

this time to 9%. Now what is the fair price of each bond?

PMT= 1000x 9.125%, 45.63 semiannual cupon payment,

semi annual return is 4.5%

1year

B0 = (45.63) [((1.045)2 -1)/ ((0.045)(1.0452] + 1000/(1.045)2 = $1,001.15

7year

B0 = (45.63) [((1.045)14 -1)/ ((0.045)(1.045)14] + 1000/(1.045)14 = $1,006.29

15year

B0 = (45.63) [((1.045)30 -1)/...