COMM 121 – INTRODUCTION TO FINANCE
FALL 2004 MIDTERM, TIME PERMITTED 2 HRS
Aids Allowed: Financial and/or Scientific Calculator and one-sided, letter-sized reference sheet
This exam contains 11 pages
Student Number: SOLUTIONS
Please circle your section: A B C D
Notes to students:
Ø Answer all 5 questions in the space provided on the question sheet.
Ø You have two hours to complete this exam.
Ø You may use a financial and/or scientific calculator and are permitted a one-sided, letter-sized reference sheet. No other aids are allowed.
Ø Show your work clearly for questions 2 – 5.
Ø If you are unclear as to the meaning of a question please state explicitly any assumptions that you are making.
Ø There is a blank page at the end of the exam which you can use as scrap paper. This page will not be marked.
Good luck!
Question / Marks EarnedQuestion 1 / /20
Question 2 / /22
Question 3 / /18
Question 4 / /16
Question 5 / /9
Total marks
//85
Question 1: Multiple Choice questions (20 marks – 2 marks per question)
Select the response that BEST answers the following questions. Circle your choice.
1. An investor is looking at a 10-year corporate bond currently on the market for $1,150. The bond pays semiannual coupons of $35 each. The investor has a three-year holding period and expects the bond to have a market value of $1,100 three years from today. The coupon rate on the bond is about:
a) 1.6%
b) 3.5%
c) 5%
d) 7%
Solution: d
2. The nominal interest rate compounded monthly which is equivalent to a stated rate of 20% with semiannual compounding is about:
a) 10%
b) 4.9%
c) 22.3%
d) 19.2%
Solution: d
3. The written agreement between a corporation and the bondholder’s representative is called:
a) the call provision
b) the collateral maintenance agreement (CMA)
c) the indenture
d) the prospectus
Solution: c
4. A $100,000 mortgage loan is arranged at a rate equivalent to 6% compounded semi-annually. The loan payments are calculated using a 25 year amortization period. The monthly mortgage loan payment would be:
a) $639.76
b) $4261.83
c) $644.30
d) $782.67
Solution: a
5. A particular debt is being amortized over ten years at monthly payments of $450 each (principal and interest) and the interest rate being charged is 12% compounded monthly. The amount of principal still owing just after the 40th payment would be:
a) $36,000
b) $24,700
c) $14,776
d) cannot be determined with the data given
Solution: b
6. From the corporate perspective callable bonds may have value over non-callable bonds because:
a) the corporation has the option to control market interest rates
b) call prices vary inversely with the interest rate
c) the corporation has the option to call the bond if interest rates fall
d) the corporation has the option to call the bond if interest rates rise
Solution: c
7. A 60 year old woman approached an insurance company to purchase an annuity which will supplement her pension. The company offered the woman two options to choose from. Option 1 – A monthly annuity of $600 for life (the first payment to occur one month from today); Option 2 – A monthly annuity of $650 for 20 years (the first payment to occur one month from today). How long must the woman live before the life-long annuity is the more beneficial option if the current stated interest rate is a stated rate of 12% compounded monthly?
a) To about age 80
b) To about age 87
c) Option 2 would always be better than Option 1
d) She must live to be at least 90.
Solution: d
8. An individual has income of $35,000 in period 0 and $40,000 in period 1. An investment opportunity that costs $10,000 in period 0 is worth $11,000 in period 1. What is the maximum possible consumption in period 0 if the individual consumes $50,000 in period 1 when the market rate of interest is 8%.
a) $25,926
b) $26,667
c) $44,000
d) $44,720
Solution: a
9. Under the ______method, the underwriter buys the securities for less than the offering price and accepts the risk of not selling the issue, while under the ______method, the underwriter does not purchase the shares but merely acts as an agent.
a) best efforts; firm commitment
b) firm commitment; best efforts
c) seasoned; unseasoned
d) general cash offer; best efforts
Solution: b
10. If you own 1000 shares of stock and you can cast only 1000 votes for a particular director then the stock features,
a) cumulative voting
b) absolute priority voting
c) sequential voting
d) majority voting
Solution: d
Question 2 (22 marks)
a) DPC Corp. currently pays a dividend of $2 per share and the dividend is expected to grow at a 0 percent annual rate for three years, then at a 10 percent rate for the next three years, after which it is expected to grow at a 5 percent rate forever. What value would you place on this stock if an 18% rate of return were required? (8 marks)
b) Yoma Inc. is attempting to raise $5,000,000 in new equity with a rights offering. The subscription price will be $40 per share. The stock currently sells for $50 per share and there are 250,000 shares outstanding. How many rights are needed to buy a new share? Briefly explain why some companies prefer to issue shares through rights offerings. (6 marks)
If the company wants to raise $5,000,000 and the subscription price is $40 per share then the company should issue $5,000,000/$40 = 125,000 new shares. We know that each share receives one right so there are 250,000 rights outstanding. To ensure that we have 125,000 new shares issued the company should require that 2 rights be required for each new share (250,000/125,000 = 2).
Companies may issue shares through a rights issue if they wish to ensure that shareholders maintain their ownership positions. For instance, a majority shareholder may want to ensure that they are still able to hold over 50% of the shares even when new issues occur. A rights issue ensures that investors can continue to hold the same proportion of shares if they choose to exercise all of their rights.
c) Show that a firm with earnings of $10,000 a year in perpetuity would be better off paying all earnings in dividends rather than making a one time investment of 25% of its earnings immediately. The investment would earn 14% in perpetuity with the first cash flow occurring in one year’s time. Assume the discount rate for the firm is 15%. To illustrate which option is better, find the share price under both of the scenarios assuming that 5000 shares are outstanding. (8 marks)
The first scenario essentially finds the share price assuming that the firm acts as a cash cow. This implies that the earnings per share are $10,000/5000 = $2 and therefore the dividend would also be $2 per share. Under these conditions the price is $2/.15 = $13.33.
Under the second scenario, we combine the value of the firm if it did not invest with the PV of the growth opportunity. The opportunity requires an investment of $10,000 * 0.25 = $2,500. It returns 2500 * 0.14 = $350 in one year’s time and continues to return this amount in perpetuity. Therefore the PV of the opportunity is: -2500 +350/.15 = -166.67. On a per share basis this is -0.033 so that the share price will in fact decrease from the cash cow value if the investment is undertaken.
P = $13.33 – 0.033 = $13.296
Alternatively we will accept a response that assumes the firm can only pay a dividend of 75% of earnings in year one (or $1.50 per share) and then begins to pay total dividends of $10,000 + $350 (or $2.07 per share) in years 2 on. This new dividend reflects the investment in the project. The price in this case is:
Question 3 (18 marks)
You observe the following spot rates in the market:
Years to Maturity / Spot Rate1 / 5.0%
2 / 5.4%
3 / 5.9%
a) Calculate the 1 year forward rates over each of the next two years (ie from year 1 to year 2 and from year 2 to year 3). (4 marks)
Use the following formula to find f2 and f3:
b) Assume that there exists a 3 year bond with a coupon rate of 7.8%. The bond pays coupons semi-annually, has a par value equal to $1000 and has a yield to maturity equivalent to the three-year spot rate from the table above.
§ Is the bond trading at a premium or discount? How can you tell without finding its actual price? (2 marks)
§ What is the price of the bond? (4 marks)
We know that the bond will trade at a premium since the coupon rate exceeds the current spot rate of 5.9%.
To find the exact price we first find the semi-annual interest rate of 5.9/2 and the semi-annual coupon of $39.
c) Given that the one year spot rate is 5% and the two year spot rate is 5.4%, what can you deduce about investor’s expectations of next year’s one-year spot rate if the expectations hypothesis is correct? ( 2 marks)
If the two year spot rate exceeds the one year spot rate and the expectations hypothesis holds, investors assume that interest rates in the second year will be greater than the current one year interest rate. We can see this from the following equation:
(1+ k2)2 = (1+k1)(1+f2) where f2 must be greater than k1 if k2 is greater than k1. Since the expectations hypothesis holds, f2 is equal to the expected future spot rate. Therefore, investors believe that the future rate will be greater than the current rate.
d) If the expectations hypothesis is correct, what do you expect the price of a three year, $1000 face value bond that pays annual coupons of $50 to be in one year’s time (ie what is the price at the end of year 1)? (6 marks)
To find the price of the bond in one year’s time, we discount the future cash flows by the expected future spot rates. These spot rates are equivalent to the forward rates found in part a.
Note: the wording to this question would have been slightly clearer if the bracketed sentence read: ie what is the price at the end of the first year. As a result, we will accept prices found at the beginning of year 2 which would be equal to 1050/(1+E(k3))
Question 4 (16 marks)
An investor estimates the following parameters for the coming year.
___Equities___
State of High Gold
Economy Prob. T-Bills Tech Mines
Recession 0.3 8.0% -22.0% 28.0%
Average 0.4 8.0 20.0 0.0
Boom 0.3 8.0 50.0 -20.0
(a) Calculate the expected return on each investment alternative. Based solely on expected returns, which alternative would you pick? (3 marks)
T-Bill: (.3)(8.0) + (.4)(8.0) + (.3)(8.0) = 8.0%
Hi-Tech: (.3)(-22.0) + (.4)(20.0) + (3.)(50.0) = 16.4%
Gold Mines: (.3)(28.0) + (.4)(0.0) + (.3)(-20.0) = 2.4%
Pick Hi-Tech.
(b) Calculate the standard deviation of possible rates of return for each of these alternatives. (5 marks) More space is available on the next page.
T-Bill:
{(.3)(8.0-8.0)2 + (.4)(8.0-8.0)2 + (.3)(8.0-8.0)2}1/2 = 0
Hi-Tech:
{(.3)(-22.0-16.4)2 + (.4)(20.0-16.4)2 + (.3)(50.0-16.4)2}1/2 =
28.04%
Gold Mines:
{(.3)(28.0-2.4)2 + (.4)(0.0-2.4)2 + (.3)(-20.0-2.4)2}1/2 =
18.69%
(c) Form an equally weighted portfolio of High Tech and Gold Mines. What are the expected return and standard deviation of return of this portfolio? (5 marks)
kp = (.5)(16.4) + (.5)(2.4) = 9.4%
σp = {(0.5)2(28.04)2 + (0.5)2(18.69)2 + 2(0.5)(0.5)covht,gm}1/2
where covht,gm = (0.3)(-22.0-16.4)(28-2.4) + (0.4)(20.0-16.4)(0.0-2.4) + (0.3)(50.0-16.4)(-20.0-2.4) = -524.16
σp = 4.67%
(d) Are there benefits to diversifying your holdings across High Tech and Gold Mines stock? Explain (3 marks)
k σ
Hi-Tech 16.4% 28.04%
Gold Mines 2.4% 18.69%
Portfolio 9.4% 4.67%
The portfolio has less risk than the weighted average risk of the individual stocks in the portfolio, while the return is a weighted average of the individual assets’ returns. Hence, you have diversified by forming the portfolio. There are benefits to diversifying as long as the correlation is less than 1.
Question 5 (9 marks)
Your uncle plans to retire in 10 years, and at that time he wants to have a bank balance of $100,000. Interest rates will remain constant at 10%.
(a) How much would he have to save each year to realize his plan? Assume equal amounts are saved at the end of each year. (3 marks)
Future value = PMT(FVAk,n)
$100,000 = PMT {(1.1)10 – 1)/0.1} = PMT (15.94)
PMT = $6,273.53
(b) How would your answer change if your uncle were to make each deposit to his account at the beginning of the year rather than at the end of the year? Find the new amount that he would have to save each year under these conditions. (3 marks)
PMT = $6,273.53/1.1 = $5,703.21
Alternatively, you could use the future value of an annuity formula to solve for the payment amount if payments occur at the beginning of the period. As a final option, you could solve for the payment using a financial calculator in BGN mode.
(c) After he retires, your uncle wants to withdraw equal amounts each year for a further ten years. Interest rates are still 10%, and the withdrawals will be at the end of each year. How much can he withdraw each period, if the account is to have a zero balance at the end of the ten years? (3 marks)
PV = PMT (PVAk,n)
$100,000 = PMT {(1-(1/(1.1)10)/0.1}
$100,000 = PMT (6.145)
PMT = $16,273.39
SCRAP PAPER – Work on this page will not be marked.
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