FIN Quiz 3
A bond yielded 6.62 percent last year. The inflation rate for the same period was 1.54 percent. What was the actual real rate of return?
5.00% r = 1.0662/1.0154 − 1 r = .0500, or 5.00%
Westco Company issued 15-year bonds a year ago at a coupon rate of 5.4 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 4.5 percent, what is the current price of the bond in dollars?
$1,092.74 To find the price of this bond, we need to realize that the maturity of the bond is 14 years. The bond was issued 1 year ago, with 15 years to maturity, so there are 14 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is: P = $27(PVIFA2.25%,28) + $1,000(PVIF2.25%,28) P = $1,092.74 https://www.omnicalculator.com/finance/bond-price
You find a zero coupon bond with a par value of $10,000 and 24 years to maturity. If the yield to maturity on this bond is 4.2 percent, what is the price of the bond? Assume semiannual compounding periods.
$3,687.77 Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. To find the price of a zero coupon bond, we need to find the value of the future cash flows. With a zero coupon bond, the only cash flow is the par value at maturity. We find the present value assuming semiannual compounding to keep the YTM of a zero coupon bond equivalent to the YTM of a coupon bond, so: P = $10,000(PVIF2.10%,48) P = $3,687.77 calculator: N - 24x2 I/Y - 4.2% / 2 PV - solve for PMT - FV - 10,000
Weismann Company issued 11-year bonds a year ago at a coupon rate of 6 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 9 percent, what is the current bond price?
$804.88 To find the price of this bond, we need to realize that 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, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is: P = $30(PVIFA4.5%,20) + $1,000(PVIF4.5%,20) P = $804.88
A preferred stock pays an annual dividend of $7.95 and sells for $48.89 per share. What is the rate of return?
16.26% R = $7.95/$48.89 R = .1626, or 16.26%
A Japanese company has a bond outstanding that sells for 96.318 percent of its ¥100,000 par value. The bond has a coupon rate of 3.4 percent paid annually and matures in 16 years. What is the yield to maturity of this bond?
3.71% Here we need to find the YTM of a bond. The equation for the bond price is: P = ¥96,318 = ¥3,400(PVIFAR%,16) + ¥100,000(PVIFR%,16) Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find: R = YTM = 3.71% calculator: N - 16 I/Y - solve for PV - 96,318 PMT - 3,400 FV - 100,000 https://www.omnicalculator.com/finance/yield-to-maturity
Fegley, Incorporated, has an issue of preferred stock outstanding that pays a $3.80 dividend every year in perpetuity. If this issue currently sells for $93 per share, what is the required return?
4.10% The price of a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. Using this equation, we find the required return of the preferred stock is: R = D/P0 R = $3.80/$93 R = .0409, or 4.09%
The 30-year, 5.5 percent bonds issued by Modern Kitchens pay interest semiannually, mature in four years, and have a $1,000 face value. Currently, the bonds sell for $1,020.66. What is the yield to maturity?
4.92% $1,020.66 = $27.50[(1 − {1/[1 + (r/2)]^4 × 2})/(r/2)] + $1,000/[1 + (r/2)]^4 × 2 calculator: N - 4x2 I/Y - solve for PV - -1020.66 PMT - 27.59 FV - 1000 YTM = 2(2.462%) YTM = 4.92%
Five Star Corporation will pay a dividend of $3.04 per share next year. The company pledges to increase its dividend by 3.75 percent per year indefinitely. If you require a return of 11 percent on your investment, how much will you pay for the company's stock today?
41.93 Using the constant growth model, we find the price of the stock today is: P0 = D1/(R − g) P0 = $3.04/(.11 − .0375) P0 = $41.93
Ashburn Corporation issued 25-year bonds two years ago at a coupon rate of 5.6 percent. The bonds make semiannual payments. If these bonds currently sell for 97 percent of par value, what is the YTM?
5.84% Here we are finding the YTM of a semiannual coupon bond. The bond price equation is: P = $970 = $28(PVIFAR%,46) + $1,000(PVIFR%,46) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 2.919% Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: YTM = 2 × 2.919% YTM = 5.84% calculator: N - 46 I/Y - solve for PV - 970 PMT - 56/2 FV - 1000
Caccamise Company is expected to maintain a constant 3.4 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 5.3 percent, what is the required return on the company's stock?
8.70% The required return of a stock is made up of two parts: The dividend yield and the capital gains yield. So, the required return of this stock is: R = Dividend yield + Capital gains yield R = .053 + .034 R = .0870, or 8.70%
The next dividend payment by Im, Incorporated, will be $1.87 per share. The dividends are anticipated to maintain a growth rate of 4.3 percent forever. If the stock currently sells for $37 per share, what is the required return?
9.35% Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. 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 = ($1.87/$37) + .043 R = .0935, or 9.35%
Which one of following is the rate at which a stock's price is expected to appreciate?
Capital gains yield
Which one of the following types of stock is defined by the fact that it receives no preferential treatment in respect to either dividends or bankruptcy proceedings?
Common
What is the model called that determines the market value of a stock based on its next annual dividend, the dividend growth rate, and the applicable discount rate?
Constant growth model
Valenica Corporation has a capital structure that includes bonds, preferred stock, and common stock. Which one of the following rights is most apt to be granted to the preferred shareholders?
Right to share in company profits prior to other shareholders
Suppose you buy a 7 percent coupon, 20-year bond today when it's first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond?
The price of the bond will fall. Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. This is because the fixed coupon payments determined by the fixed coupon rate are not as valuable when interest rates rise—hence, the price of the bond decreases.
You cannot attend the shareholder's meeting for Alpha United so you authorize another shareholder to vote on your behalf. What is the granting of this authority called?
Voting by proxy
Assume the current market price of a bond exceeds its par value. Which one of these equations applies?
Yield to maturity < Coupon rate
Treasury bills are currently paying 4.6 percent and the inflation rate is 1.9 percent. a.What is the approximate real rate of interest? b. What is the exact real rate?
a. 2.7 b. 2.65 The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation (h) is: R = r + h Approximate r = .046 − .019 Approximate r = .027, or 2.70% The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is: (1 + R) = (1 + r) (1 + h)(1 + .046) = (1 + r)(1 + .019) r = [(1 + .046)/(1 + .019)] − 1 r = .0265, or 2.65% approximate formula: nominal rate - inflation rate. exact rate: https://www.omnicalculator.com/finance/real-rate-of-return
The next dividend payment by Im, Incorporated, will be $1.87 per share. The dividends are anticipated to maintain a growth rate of 4.3 percent forever. The stock currently sells for $37 per share. a. What is the dividend yield? b. What is the expected capital gains yield?
a. 5.05% b. 4.3% The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield = D1/P0 Dividend yield = $1.87/$37 Dividend yield = .0505, or 5.05% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 4.3%
Ana just received the semiannual payment of $35 on a bond she owns. This is called the ______ payment.
coupon
Dilan owns a bond that will pay him $45 each year in interest plus $1,000 as a principal payment at maturity. The $1,000 is referred to as the:
face value
The current yield is defined as the annual interest on a bond divided by the:
market price.
Red, Incorporated, Yellow Corporation, and Blue Company each will pay a dividend of $4.15 next year. The growth rate in dividends for all three companies is 4 percent. The required return for each company's stock is 8 percent, 11 percent, and 14 percent, respectively. What is the stock price for each company?
red - 103.75 yellow - 59.26 blue - 41.40 We can use the constant dividend growth model, which is: Pt = Dt × (1 + g)/(R − g) So the price of each company's stock today is: Red stock price = $4.15/(.08 − .04) = $103.75 Yellow stock price = $4.15/(.11 − .04) = $59.29 Blue stock price = $4.15/(.14 − .04) = $41.50 As the required return increases, the stock price decreases. This is a function of the time value of money: A higher discount rate decreases the present value of cash flows. It is also important to note that relatively small changes in the required return can have a dramatic impact on the stock price.
The bond market requires a return of 6.2 percent on the 15-year bonds issued by Mingwei Manufacturing. The 6.2 percent is referred to as the:
yield to maturity.
Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 7 years to maturity, and a coupon rate of 6 percent paid annually. If the yield to maturity is 11 percent, what is the current price of the bond?
€764.39 The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = €$60({1 − [1/(1 + 0.11)]^7 }/0.11) + €1,000[1/(1 + 0.11)^7] P = €764.39
