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#3, Problem Lycan, Inc. has 7 percent coupon bonds on the market that have 8 years left to maturity. The bonds make annual payment. If the YTM on these bonds is 9 percent, what is the current bond price? The price any is any bond is the PV of the interest, Plus the PV of the par value. The problem assumes an annual coupon. The price of the bond will be: P=$70({1-[1/(1+0.07)]8}/.09)+$1,000[1/(1+.09)8] P=2302.066 We would like to introduce shorthand notation here. Rather than write ( or type, as the case may be ) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equation as: PVIFAR, t= ({1-1[1/(1+r)]t}/r) Which stands for Present Value Interest Factor of an Annuity? These abbreviation are shorthand notation for the equation in which the interest rate and the number of period are substituted into the equation and solved. We will use this shorthand notation in the remainder of the solution key. The bond price equation for this problem would be: P=$70(PVIFA7%, 8) + $1,000(PVIF7%, 8) P=$889.30 #5, Coupon Rates. Merton Enterprises has bonds on the market making annual payment, with 16 years to maturity, and selling for $963. At this price, the bonds yield 7.5 percent. What must the coupon rate be on Mertons bonds? Here we need to find the coupon the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P=$963= C x(PVIFA7.5%, 16)+$1,000x (PVIF7.5%.16) Solving for the coupon payment, we get: C=$71 The coupon payment is the coupon rate times par value. Using this relationship, we get: Coupon rate=$71/$1,000 Coupon rate=.0710 or 7.10%
#7 on page 196 Night Hawk Co. issued 15-year bonds two years ago at a coupon rate8.4 percent. The bonds make semiannual payments. If these bonds currently sell for 108 percent of par value, what is the YTM? Here, we are finding the YTM of a semi-annual coupon. The bond price equation is: P=$960=$42x (PVIFAR%, 26) +$1,000x (PVIFR%, 26) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and terror, we find: R=4.463% Since the coupon payments are semi-annual, this is the semi-annual interest rate. The YTM is the APR of the bond, so: YTM=24,463% YTM=7.43% Problem #9 on page 197 Calculating real rates of return If treasury bills are currently paying 5.7percent and the inflation rate is 2.9 percent, what is the approximate real rate of interest? The exact real rate? The approximate relationship between nominal interest rates(R), real interest rate(r), and inflation (h), is: R=r+h Approximate r=.057-.029 Approximate r=0.028 or 2.8% The fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is : (1+R)=(1+r)x(1+h) (1+.08)=(1+r)x(1+.047) Exact r = [1+.057)/(1+.029)]-1 Exact r=0.027211 or 2.7%
Problems #1, Stock Values Patience Inc., just paid a dividend 2.35 of per share its stock. The dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely. If investors require an 11 percent return on this stock. What is the current price? What will the price be in three years? In 15 years? The constant dividend growth model is : Pt=Dt(1+g)/(R-g) So, the price of the stock today is : P0=D0(1+g)/(R-g) P0=$2.35(1.045)/(0.11-0.045) P0=$37.78077 The dividend at year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so : P3=D3(1+g)/(R-g) P3=D0(1+g)^4/(R-g) P3=$2.35(1.045)^4/(0.11-0.045) P3=$43.11413 We can do the same thing to find the dividend in year 16, which gives us the price in year 15, so: P15=D15(1+g)/(R-g) P15=D0(1+g)^16/(R-g) P15=$2.35(1.045)^16/(0.11-0.045) P15=$73.11646
#3, Stock Values The next dividend payment by Mosby, Inc., will be $2.45 per share. The dividend are anticipated to maintain a 5.5 growth rate , Forever . If the stock currently sells for $45.50 per share, what is the required return? We need to find the required return of the stock. Using the constant growth model we can solve the equation for R. Doing so. We find : R: (D1/P0)+g R=($2.45/45.5)+0.055 R= 0.108846 or 10.88%
For the company in the previous problem. What is the dividend yield? What is expected capital gain yield? The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield =D1/P0 Dividend yield=$2.45/$45.5 Dividend yield = 0.053846 or 5.38% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield =5.5% #5 on page 225 Stock Valuation. Bruer, Inc., is expected to maintain a constant 5.8 percent growth rate in its dividend, indefinitely. If the company has a dividend yield of 4.3 percent. What is the required return on the stock today? The required return of a stock is made up of two parts : The dividend yield and the capital gains yield. So the required return on this stock is: R= Dividend yield +Capital gains yield R= 0.043+0.058 R=0.101 or 10.1%
Problem #11 on page 226 Valuing preferred Stock
E-Eyes.com has a new issue of preferred stock it calls 20/20 preferred. The stock will pay a $20 dividend per year, but the first dividend will not paid until 20 years from today. If you require a 7 percent return on this stock, how much should you pay today? Here, we have a stock that pays no dividends for 20 years. Once the stock begins paying dividends, it will have the same dividends forever, a preferred stock equation. It is important to remember that the price we find will be the price one year before the first dividend, so: P19=D20/R P19=$20/0.07 P19=$285.7143 The price of the stock today is simply the present value of the stock price in the future. We simply discount the future stock price at the required return . The price of the stock today will be : P0=285.71/1.07^19 P0=$79

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