5. Kiss the sky has bonds on the market making annual payments , with 13 years to maturity and selling for $1045,at this price the bonds yield 7.5%.what must the coupon rate be on the bonds ?


             P = $1,045 = C (PVIFA7.5%, 13) + $1,000(PVIF7.5%, 36)

Solving for the coupon payment,:

C = $80.54

The coupon payment is the coupon rate times par value. Using this relationship:

Coupon rate = $80.54 / $1,000

 = .0805 or 8.05%

6. Grohl Co. issued 11-year bonds a year ago at a coupon rate of 6.9 percent. The bonds make semiannual payments. If the YTM on these bonds is 7.4 percent, what is the current bond price?


The maturity of the bond is 10 years. The bond was issued one year ago, with 11 years to maturity, so there are 10 years left on the bond. Also, the coupons are semiannual, I use the semiannual interest rate and the number of semiannual periods. The price of the bond is:

P = $34.50(PVIFA3.7%, 20) + $1,000(PVIF3.7%,20)

= $965.10

7. Ngata Corp. issued 12-year bonds 2 years ago at a coupon rate of 8.4 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM?


Finding the YTM of a semiannual coupon bond, the bond price equation is:

P = $1,050 = $42(PVIFAR%, 20) + $1,000(PVIFR%, 20)

Solving the equation directly for R using a spreadsheet, a financial calculator, or trial and error,

R= 3.837%

Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond,

YTM = 2 x 3.837%

= 7.67%

11. An investment offers a 14 percent total return over the coming year. Bill Bernanke thinks the total real return on this investment will be only 9 percent. What does Bill believe the inflation rate will be over the next year?


     The fisher equation

1+R) =1+r)(1+h)

(1 + .14)= (1+.09)(1 + h)


1.14/1.09= 1 +h



23. Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $1,000 and the current date is April 15, 2009. What is the yield to maturity of the bond? What is the current yield?


(Ticker)     Coupon        Maturity           Last Price     Last Yield    EST Vol


IOU (IOU)   7.2             Apr 15, 2023            108.96            ??                 1,827


The bond has 14 years to maturity, so the bond price equation is:

P = $1,089.60 = $36(PVIFAR%, 28) + $1,000(PVIFR%, 28)

Using a spreadsheet, financial calculator, or trial and error we find:

R = 3.116%

This is the semiannual interest rate, so the YTM is

YTM = 2 x 3.116% = 6.23%

The current yield is the annual coupon payment divided by the bond price,

Current yield = $72 / $1,089.60 = .0661 or 6.61%

28. You want to have $1.5 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 11 percent and the inflation rate is 3.8 percent. What real amount must you deposit each year to achieve your goal?


Using the fisher equation

(1+R)= (1+r)(1+h)          






FVA=C {[(1+r)t-1]/r}


C= $7,637.76


5. Keenan Co. is expected to maintain a constant 5.2 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 6.3 percent, what is the required return on the company’s stock?


       R= dividend yield + capital gains yield

= .063 + .052

= .115=11.5%     

12. Bread, Inc., has an odd dividend policy. The company has just paid a dividend of $6 per share and has announced that it will increase the dividend by $4 per share for each of the next 5 years, and then never pay another dividend. If you require an 11 percent return on the company’s stock, how much will you pay for a share today?


         P4 = D4 (1 + g) / (Rg)

 = $() / (1.11)

= $19.09

P0 = $10 / (1.11) + $14.00 / (1.11)2 + $18.00 / (1.11)3 + $22.00 / (1.11)4+$26.00 / (1.11)5

The price of the stock=$ 63.45

15. Eva Corp. is experiencing rapid growth. Dividends are expected to grow at 25 percent per year during the next three years, 15 percent over the following year, and then 8 percent per year indefinitely. The required return on this stock is 13 percent, and the stock currently sells for $76 per share. What is the projected dividend for the coming year?


Finding the dividend next year for a stock experiencing supernormal growth, and rom the information above, stock price, the dividend growth rates, and the required return, all are.

Dividend in Year 3 is the current dividend times the FVIF. The dividend in Year 3 will be:

D3=D0 (125)3

And the dividend in Year 4 will be the dividend in Year 3 times one plus the growth rate, D4=D0 (1.25)3(1.15)

The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4 as the dividend In Year 5, divided by the required return minus the growth rate. The equation for the price of the stock in Year 4 is:

P4 = D4 (1 + g) / (R g)

Substitute the previous dividend in Year 4 into this equation as follows:

P4 = D0 (1 + g1)3(1 + g2)(1 + g3)/ (R g)

P4 = D0 (1.25)3(1.15) (1.08)/ (.13-.08)

Stock price in year 4=48.52D0

The stock price in Year 4 is 48.52 times as large as the dividend today. The stock price today is the PV of the dividends in Years 1, 2, 3, and 4, plus the PV of the Year 4 price.

Po=D0 (1.25)/ (1.13) + D0(1.25)2/1.132 + D0(1.25)3/1.133+ D0(1.25)3(1.15)/1.133 + 48.52D0/1.134

Factor out D0 in the equation, and combine the last two terms. Doing to get

P0=D0 {1.25)/(1.13) +(1.25)2/1.132 + (1.25)3/1.133+[ (1.25)3(1.15) + 48.52]/1.134}

Reducing the equation even further by solving all of the terms in the braces:

$76 = $34.79D0

D0 = $76 / $34.79

D0 = $2.18

This is the dividend today, so the projected dividend for the next year will be:

D1 = $2.18(1.25)


16. Antiques R Us is a mature manufacturing fi rm. The company just paid a $10.46 dividend, but management expects to reduce the payout by 4 percent per year indefinitely. If you require an 11.5 percent return on this stock, what will you pay for a share today?


The constant growth model can be applied even if the dividends are declining by a constant percentage, the price of the stock today will be:

P0 = D0 (1 + g) / (R g)

P0 = $10.46(1 – .04) / [(.115 – (–.04)]

P0 = $64.78

18. Bank just issued some new preferred stock. The issue will pay a $20 annual dividend in perpetuity, beginning 20 years from now. If the market requires a 6.4 percent return on this investment, how much does a share of preferred stock cost today?


The price of a share of preferred stock is the dividend payment divided by the required return. We know the dividend payment in Year 20, so we can find the price of the stock in Year 19, one year before the first dividend payment, :

P19 = $20.00 / .064

P19 = $312.50

The price of the stock today is the PV of the stock price in the future, so the price today will be:

P0 = $312.50 / (1.064)19

P0 = $96.15

20. Thirsty Cactus Corp. just paid a dividend of $1.25 per share. The dividends are expected to grow at 28 percent for the next eight years and then level off to a 6 percent growth rate indefinitely. If the required return is 13 percent, what is the price of the stock today?


 Two-stage dividend growth model is used for this problem,

P0 = [D0 (1 + g1)/(R – g1)] {1 – [(1 + g1)/ (1 + R)] T}+ [(1 + g1)/(1 + R)]T[D0(1 + g2)/(R – g2)]

P0 = [$1.25(1.28)/ (.13 – .28)][1 – (1.28/1.13)8] + [(1.28)/(1.13)]8[$1.25(1.06)/(.13 – .06)]

P0 = $69.55

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