Connect Quiz 2

There is a zero coupon bond that sells for $351.98 and has a par value of $1,000. If the bond has 20 years to maturity, what is the yield to maturity? Assume semiannual compounding.

$352.00 = $3/(1 + r)^40 r = .0264, or 2.64% YTM = 2.64% × 2 = 5.29%

Maxxie purchased a tract of land for $28,500. Today, the same land is worth $46,400. How many years have passed if the price of the land has increased at an annual rate of 6.9 percent?

$46,400 = $28,500(1.069)^t t = 7.30 years

You purchased a bond at a price of $700. In 20 years when the bond matures, the bond will be worth $5,000. It is exactly 12 years after you purchased the bond and you can sell the bond today for $3,550. If you hold the bond until it matures, what annual rate of return will you earn from today?

$5,000 = $3,550 × (1 + r)^8 r = ($5,000/$3,550)^1/8 r = .044, or 4.4%

You expect to receive $4,200 upon your graduation and will invest your windfall at an interest rate of .65 percent compounded quarterly until the account is worth $5,575. How many years do you have to wait until you reach your target account value?

$5,575 = $4,200(1.0065)^t t = 43.71 quarters Years to wait = 43.71/4 = 10.93 years

Thom owes $5,600 on his credit card. The credit card carries an APR of 17.6 percent compounded monthly. If Thom makes monthly payments of $185 per month, how long will it take for him to pay off the credit card assuming that he makes no additional charges?

$5,600 = $185{[1 − 1/(1 + .176/12)^t]/.176/12} t = 40.31 months

You purchase a bond with an invoice price of $1,065. The bond has a coupon rate of 5.81 percent, it makes semiannual payments, and there are 2 months to the next coupon payment. The par value is $1,000. What is the clean price of the bond?

Coupon payment = .0581($1,000)/2 = $29.05 Accrued interest = $29.05[(6 − 2)/6] = $19.37 Clean price = $1,065 + 19.37 = $1,084.37

CDB stock is currently priced at $67. The company will pay a dividend of $4.97 next year and investors require a return of 11.3 percent on similar stocks. What is the dividend growth rate on this stock?

Dividend yield = $4.97/$67 = 7.42% Dividend growth rate = 11.30% − 7.42% = 3.88%

Shares of common stock of the Samson Co. offer an expected total return of 12.00 percent. The dividend is increasing at a constant 6.70 percent per year. The dividend yield must be:

Dividend yield = 12.00% - 6.70% = 5.30%

Ghost Riders Co. has an EPS of $1.59 that is expected to grow at 7.9 percent per year. If the PE ratio is 18.55 times, what is the projected stock price in 6 years?

EPS6 = $1.59(1.079)^6 = $2.51 P6 = $2.51(18.55) = $46.54

A bond with a coupon rate of 5.76 percent and semiannual coupon payments matures in 23 years. The YTM is 6.82 percent. What is the effective annual yield?

Effective rate = (1 + .0682/2)^2 − 1 = 6.94%

Assuming an interest rate of 6.3 percent, what is the value of the following cash flows five years from today? Year Cash Flow 1 3540 2 4655 3 5630 4 6910

FV = $3,540(1.063)^4 + $4,655(1.063)^3 + $5,630(1.063)^2 + $6,910(1.063) = $23,818.42

Your sister just deposited $6,500 into an investment account. She believes that she will earn an annual return of 9 percent for the next 8 years. You believe that you will only be able to earn an annual return of 8.4 percent over the same period. How much more must you deposit today in order to have the same amount as your sister in 8 years?

FV = $6,500 × 1.090^8 = $12,951.66 PV = $12,951.66/1.084^8 = $6,793.46 Difference = $6,793.46 − 6,500 = $293.46

Santa Klaus Toys just paid a dividend of $2.30 per share. The required return is 9.6 percent and the perpetual dividend growth rate is 3.2 percent. What price should this stock sell for five years from today?

P = [$2.30(1 + .032)^6]/(.096 − .032) P = $43.41

There are zero coupon bonds outstanding that have a YTM of 6.21 percent and mature in 15 years. The bonds have a par value of $10,000. If we assume semiannual compounding, what is the price of the bonds?

PV = $10,000/(1 + .0621/2)^30 PV = $3,995.84

Jenny Enterprises has just entered a lease agreement for a new manufacturing facility. Under the terms of the agreement, the company agreed to pay rent of $16,500 per month for the next 6 years with the first payment due today. If the APR is 7.44 percent compounded monthly, what is the value of the payments today?

PV = $16,500(1.0062)[(1 −1/1.0062^72) / .0062] = $961,834.78

You just won the $62.5 million Ultimate Lotto jackpot. Your winnings will be paid as $2,500,000 per year for the next 25 years. If the appropriate interest rate is 5.8 percent, what is the value of your windfall?

PV = $2,500,000[(1 −1/1.058^25)/.058] = $32,574,855.64

You need to have $30,250 in 17 in years. You can earn an annual interest rate of 4 percent for the first 5 years, 4.6 percent for the next 4 years, and 5.3 percent for the final 8 years. How much do you have to deposit today?

PV = $30,250/1.053^8 = $20,012.36 PV = $20,012.36/1.046^4 = $16,717.51 PV = $16,717.51/1.040^5 = $13,740.58

Kasey Corp. has a bond outstanding with a coupon rate of 5.6 percent and semiannual payments. The bond has a yield to maturity of 6.1 percent, a par value of $1,000, and matures in 15 years. What is the quoted price of the bond?

PV = $56{[1 − (1/1.0305^30)]/.0305} + $1,000/1.0305^30 = $1,496.60/10 = 149.66

A prominent alumnus of your university has just donated $3,300,000 to fund a scholarship that will distribute $119,000 per year forever beginning in one year. For this to be true, what rate of return is expected on the donation?

R = $119,000/$3,300,000 = .0361, or 3.61%

You want a seat on the board of directors of Four Keys, Inc. The company has 260,000 shares of stock outstanding and the stock sells for $67 per share. There are currently 5 seats up for election. The company uses straight voting. How many shares do you need to guarantee that you will be elected to the board?

Shares necessary = 260,000/2 + 1 = 130,001 shares