4. Practice problem set with answers-updated-module-2 PDF

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HandoutforFM‐1course

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Module 2-practice problems 01

Problem

New price =806.96

Consider a bond with: $1000 face value, semiannual coupon payments @5% per annum , time to maturity =5 years. Its yield to maturity is 6.3% . Suppose because of decreasing liquidity in the system the govt. increases all interest rates because of which the yield to maturity of the bond increased to 10%( from 6.3%)

% change = -14.61% Sensitivity = -3.947

What is the % change in the bond’s price? What is the sensitivity of the price change w.r.t change in YTM ?

02

Consider a five-year, $1000 bond with 5% coupon rate and semiannual coupons with 10% YTM. Find the CGY and the CuY of the bond at the end of 1 period (i.e one semiannual period) ? At the end of 2 periods?

3%,2%

03

You are given two bonds identical in every way except for their coupons and of course their prices. The first bond has a 10% coupon rate and sells for $935.08. The seco % coupon rate. The maturity period for the bonds is 12 yrs. What do you think it would sell for?

1064.92

04

The Sue Fleming Corporation has two different bonds currently outstanding. Bond A has a face value of $40,000 and matures in 20 years. The bond makes no payments for the first six years and then pays $2,000 semiannually for the subsequent eight years, and finally pays $2,500 semiannually for the last six years. Bond B also has a face value of $40,000and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required rate of return is 12 percent compounded semiannually, what is the current price of Bond A? of Bond B?

18,033.86

05

Six years ago, the Singleton company issued 20-year bonds at par with a 14% annual coupon rate on their $1000 par value. The bonds had a 9% call premium, with 6 years of call protection. Today (at the end of 6 years) Singleton called the bonds. Compute the realized rate of return for an investor who purchased

3888.89

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14.98% APR.

=RATE(12,-70,1000,-1090,0,0.1)

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the bonds when they were issued and held them when they were called. Assume semiannual coupon payment.

06

Bond X is noncallable and has 20 years to maturity, a 9% annual coupon, and a $1000 par value. Your required return on Bond X is 10%; and if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 8.5%. How much should you be willing to pay for the bond X today? (Hint : You will need to know how much the bond will be worth at the end of 5 years )

•

$987.87

07

You are considering a 10-year, $1000 par value bond. Its coupon rate is 9% and interest is paid semiannually. If you require an effective annual interest rate (not a nominal rate) of 8.16%, how much should you be willing to pay for the bond?

•

$1,067.95

08

The YTM on a bond is the interest rate you earn on your investment if the interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the Holding Period Yield (HPY)

9.43%

Suppose that today you buy an 8 percent annual coupon bond for $ 1,105. The bond has 10 years to maturity. What rate of return do you expect to earn on your investment? Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What will your bond sell for? What is the HPY on your investment?

09

Bond P is a premium bond with 9% coupon. Bond D is a 5 percent coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have 5 years to maturity. What is the current yield of bond P? For bond D? If interest rate remains unchanged what is the expected capital gains yield over the next year for bond P? For bond D? Explain your answers and the inter relationships among the various types of yields.

P: Current yield= 8.32%, Capital gains yield = –1.32% D: Current yield =5.44%, Capital gains yield = +1.55%

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10

The St Anger Corporation needs to raise $25 million to finance its expansion into new markets. The company will sell new shares of equity via a general cash offering to raise the needed funds. If the offer price is $35 per share and the company’s underwriters charge an 8% spread, how many shares need to be sold?

11

A firm is thinking of raising Rs. 5 crore . It has 5 lakh shares outstanding and the current market price of a share is Rs. 170.The subscription price of the new share will be Rs. 125 per share. − − − −

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Ans : 776,398

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400,000, 1.25 , Rs. 150, R= 20

How many shares would be sold? How many rights are needed to purchase one new share ? What is the value of one right? Show the impact on a shareholder’s wealth who holds required rights to buy one new share if a) he exercises rights b) sells his rights and c) does not exercise rights

12

XYZ co has announced a rights offer. The company has announced that it will take four rights to buy a new share in the offering at a subscription price of $40.At the close of business the day before the ex rights day, the company’s stock sells for $80 per share. The next morning it is noticed that the stock sells for $72 per share and the rights sell for $6 each. Are the stocks and the rights correctly priced on the ex rights day? If not, then describe a transaction in which you could use these prices to create an immediate profit.

No

13

Atlas Corporation wants to raise $4.1 million via a rights offering. The company currently has 490,000 shares of common stock outstanding that sell for $40 per share. Its underwriter has set a subscription price of $36 per share and will charge the company a 4% spread. Over and above that the other components of floatation costs amount to another 2% of the subscription price. If you currently own 5000 shares of stock in the company and decide not to participate in the rights offering, how much money can you get by selling your rights?

3964.88

14

A company’s dividend is expected to grow @20% for the next five years. After that, the growth rate is

66.64

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expected to be 4% forever. If the required return is 10%, what is the value of the stock. The dividend just paid was $2.

15

Great Pumpkin farms just paid a dividend of $3.50 on its stock. The growth rate in dividends is expected to be a constant 5% per year indefinitely. Investors require a 16% return on the stock for the first 3 years, a 14% return on the stock for the next 3 years and an 11% return thereafter. What should be the current share price?

$50.75

16

Metallica Bearings Inc. is a young startup company. No dividends will be paid on the stock over the next nine years because the firm needs to plough back its earnings to fuel growth. The company will pay a $10 per share dividend in year 10 and will increase the dividend by 6% per year thereafter. If the required return on the stock is 13%, what is the current share price?

$47.55

17

Spears Inc. has an odd dividend policy. The company $51.13 has just paid a dividend of $7 per share and announced that it will increase the dividend by $4 per share for each of the next four years, and then never pay another dividend. If you require an 11% return on the company’s stock, how much will you pay for a share today? What do you think should be price of the share four years after?

18

Consider a stock Z which have a required rate of Z: Div yield =5.6%, Cap Gains return of 18% and a most recent dividend of $4.50 yield=12.4% per share. Stock Z is a growth stock that will increase its dividend by 20% for the next two years and then maintain a constant 12% growth rate thereafter. What is the dividend yield for the stock? What is the expected capital gains yield?

19

Storico Co. just paid a dividend of $2.75 per share. The company will increase its dividend by 20% next year and will then reduce its dividend growth rate by 5% per year until it reaches the industry average of 5% dividend growth, after which the company will keep a constant growth rate forever. If the required rate on Storico stock is 13%, what will a share sell for today?

P0 = $46.76

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North Great Timber company will pay a dividend of $1.50 a share next year. After this, earnings and dividends are expected to grow at a 9% annual rate indefinitely. Investors currently require a rate of return of 13%. The company is considering several business strategies and wishes to determine the effect of these strategies on the market price per share of its stock. A. Continuing the present strategy will result in the expected growth rate and required rate of return stated above. B. Expanding timber holdings and sales will increase the expected dividend growth rate to 11% but will increase the risk of the company. As a result, the rate of return required by the investors will increase to 16%. C. Integrating into retail stores will increase the dividend growth rate to 10% and increase the required rate of return to 14%. What should be the best strategy for the company’s management?

21

7.47% Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per year in recent years. The same growth rate is expected to last for another 2 years, then decline to gn =6%. a. If D0=$1.60 and re=10%, what should be TTC’s stock worth today? What are its expected dividend and capital gains yield at this time? b. Now assume that TTC’s period of supernormal growth is to last for 5 years rather than 2 years. How would this affect the price, dividend yield and capital gains yield now?

22

A three month CD is issued on 6 September 2019, and matures on 6 December 2019 ( Maturity 91 days). The CD requires a deposit of Rs.20,000,000 by the investor and assures an interest rate of 5.45% to be paid at maturity along with the principal. What is the yield realized by an investor who purchased on 6th Sep and sold on 11th October,2019 if the yield for short 60 -day paper is 5.60% on 11th October,2019? (Day count = actual/365)

5.21%

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23

Suppose the direct quote for sterling in New York is 1.1110‑5. $/£ .What is the direct quote for dollars in London(£/$) ?

0.8997, 0.9001

24

Mississippi Mud Pies, Inc. needs to buy 1,000,000 Swiss francs (CHF) to pay its Swiss chocolate supplier. Its banker in Switzerland quotes bid–ask rates of CHF1.3990–1.4000/USD. What will be the dollar cost of the CHF1,000,000?

714,796$

25

Suppose the quote on British pounds is $1.624-31.

$9957.08

a. If you converted $10,000 to British pounds and then back to dollars, how many dollars would you end up with?

$232000

b. Suppose you are the dealer and could buy pounds at the bid rate and sell them at the ask rate. How many dollars would you have to transact in order to earn $1,000 on a round-trip transaction (buying pounds for dollars and then selling the pounds for dollars)? 26

Suppose Dow Chemical (US company) receives quotes of $0.009369-71 for the yen and $0.03675-6 for the Taiwan dollar (NT$). How many U.S. dollars will Dow Chemical receive from the sale of ¥50 million?

468450, 9371000, 13,601,741

What is the U.S. dollar cost to Dow Chemical of buying ¥1 billion? How many NT$ will Dow Chemical receive for U.S.$500,000?

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