Midterm Test: Answers
Melbourne Business School
Term 1 2006
Part 1: Multiple Choice Questions. Please choose the best one. Do not need to write down
your reasoning process. (36 points total, 4 points each).
1. The Gordon’s formula of share price P0 = D1/(r g) assumes:
a. The dividends are growing rate at a constant rate g forever.
b. r> g
c. g is never negative.
d. Both a and b.
e. Both a and c.
2. Capital equipment costing $100,000 today has zero salvage value at the end of 5 years. If
straight-line depreciation (i.e. 20% of the equipment cost per annum) is used, what is the
book value of the equipment at the end of three years?
Table 1: The following cash flow projection applies to Questions 3 to 5, Part 1.
Time T =0 T= 1 T=2 T=3 T= 4 T =5
Cash flow -250,000 100,000 100,000 50,000 25,000 20,500
3. What is the payback period of the project? (See Table 1)
a. one year
b. two years
c. three years
d. four years
4. What is the net present value of the project at a 12% discount rate? (See Table 1)
e. None of the above
5. What is the internal rate of return for the project? (See table 1)
d. there exist two IRRs. I don’t know which one to report
e. there is no IRR
B. Note: I deduct two points if your answer is 8.00%.
6. Suppose you invested $10,000 for ten years at a nominal rate of 7% per year. If
the annual rate of inflation was 3%, what was the real value of your investment at
the end of the ten years?
7. Consider a 10-year bond with a face value of $1,000, a coupon rate of 10 percent
(with annual coupon payments), and a yield of 12 percent. The price of the bond is:
8. Air conditioning for a college dormitory will cost $1.5 million to install and
$200,000 per year to operate. The system should last 25 years. The cost of capital is 5%,
and the college pays no taxes. What is the equivalent annual cost?
a. $ 60,000
e. none of the above.
C. The PV of total cost of using the system for 25 years is
200000 1 EAC 1
PV 1 25
4,318,789 4,318,789 1 EAC 306,429
0.05 1.05 0.05 1.0525
9. Company B's dividends are expected to grow at a constant rate of g. The current
price is P0 = $40 and dividend D0 = $2. The discount rate r = .10. What is the
capital gains yield of this stock?
e. cannot say without additional information.
A. Based on the constant-growth model: P0 = D1/(r-g), where D1 = D0*(1+g).
Thus, 40 = 2*(1+g)/(0.10 – g) solving for g = 4.76%.
Part 2: Answering the following problems. (64 points total)
1: Short Answer Questions (18 points, 6 points each)
a. Under what circumstances is it not wise to apply the IRR rule in evaluating projects?
Answer: Non-conventional projects are those which will have negative cash flows after
some positive ones in the future. It is not wise to apply the IRR rule to non-
conventional projects because you may find multiple IRRs or zero IRR. Also for
mutually exclusive projects, a project with a smaller scale may give you a higher
IRR, but in dollar terms, it actually has a lower NPV. Using IRR in choosing
among mutually exclusive projects could give you the wrong answer.
b. If the 3-year spot rate is 9% per annum, the 2-year spot rate is 8% per annum, and the
1-year spot rate is 6.5%, what is the forward rate of interest f3? Please explain the
practical meaning of the rate f3.
Answer: (1+f3) = 1.093/1.082 = 1.1103 f3 = 11.03%, which is the forward interest rate you can
lock it in now (at t = 0) if you deposit a certain amount of money at t=2 for one year.
c. “You consider buying a house in the next few years. You have some savings to invest
at the moment. For you, a five-year bond (sold at par) paying 8% coupon is preferred to
a twenty-year bond (sold at par) paying 8% coupon, other things being equal.” True or
Answer: True. Both bonds will give you the same yield-to-maturity at 8% (because if a
bond is sold at par, then the YTM is equal to the coupon rate). However, a long-term
bond will be more sensitive to the interest rate changes, therefore, have a higher interest
rate risk. You need to pay a down-payment for your house in the next few years.
Therefore, you may need to sell your bonds in the market when you need to pay the
down-payment. With a lower interest rate risk, you would like to choose a safer 5 year
2. (8 points) The share price of ore giants Rio Tinto and BHP Billiton took a dive
on 09 March 2006 on reports China had imposed price caps on iron ore imports in a bid
to fend off new price increases. No one could confirm the rumours, which appear to have
originated from a Chinese industry association, but that didn't stop investors bailing out.
Rio shares lost $1.65 to $67.95, while BHP dropped 40c to $23.60. China is the world's
biggest consumer of iron ore. The iron ore price rose 71.5 per cent last year.
Is the share price drop a rational reaction to the news? What would happen to the
share prices of Rio Tinto and BHP if the price caps are confirmed to be true?
(Note: there are no calculations required. Answer the questions in words only.)
Answer: (1) The share price is determined by the discounted expected future dividends
(using free-cash flows or PVGO is OK here.) You need to establish the link between the
price of iron ore and the future dividend payments of BHP Billiton and Rio Tinto.
(2) In general, the price reduction for the products sold is not necessarily linked to
reduced future earnings. Many companies routinely reduce the price of their products to
increase the volume of their sales, which in turn, may actually increase the earnings.
Some companies may cut costs to maintain the same earnings when there is a cap or
reduction in prices for their products. The rationality lies in the market’s belief that by
capping (therefore reducing) the price of iron ore, the increased demand for iron ore
imports from China (and other places as well) will not be big enough to actually increase
the earnings of BHP and Rio Tinto. Therefore, there exists a positive relationship
between the price of iron ore and the earnings in this case. The expected future dividend
payments are also reduced. In this way, the cap on the price of ore will reduce the
expected future dividends.
(3) Because at this stage, they are unconfirmed, which means that the probability of the
price caps is not 100%? Once the price caps are confirmed to be true, it would be possible
that the share prices would fall further, other things being equal. There are some follow-
up reports in the Financial Times about this issue.
3. (10 points) A CEO just signed a five year contract with the following provisions:
- $500,000 signing bonus.
- $1,250,000 salary per year for five years.
- 5 years of deferred payments of $400,000 per year (these payments begin in year
- plus several bonus provisions that total as much as $1,500,000 per year for the
five years of the contract.
Assuming that he has a 70% probability of receiving the bonuses each year.
Assume the discount rate of 8%, and ignore taxes. For simplicity, assume that the
salaries, etc. will be paid at the end of each year. What is the present value of this
The cash flows are: (in ‘000)
T=0 1 2 3 4 5 6 7 8 9 10
500 2,300 2,300 2,300 2,300 2,300 400 400 400 400 400
NPV (at 8%) = $10,770,182. Of course, you can use the short-cut formula of annuities to get the
answer as well.
4. (12 points) You believe that in the next four years the AusPhone Company will
pay a dividend of 10 cents, 15 cents, and 25 cents per share on its common stock
respectively. Thereafter you expect dividends to grow at a rate of 5% a year in
perpetuity. The discount rate is 13.4%.
a. How much should you be prepared to pay for the stock now? (6 points)
b. Suppose all of your current assumptions are still valid next year. What is the
stock price next year? If you sell it next year, what is the rate of return on your
investment? (6 points)
0.1 0.15 0.25 0.25 *1.05 1
Answer: a: P0 * 2.52
1.134 1.134 2
1.134 3 0.134 0.05 1.134 3
0.15 0.25 0.25 *1.05 1
b: P0 * 2.76
1.134 1.134 2 0.134 0.05 1.134 2
The rate of return = (2.76 + 0.1 -2.52)/2.52 = 13.49%. Don’t forget the dividend
payment at t = 1.
5. (16 points) In Japan, they have 100 year mortgages, or the so-called
"generational" mortgages that the children are required to pay off. To buy a flat,
Yoshihisa Nakashima borrowed $400,000 from a bank fourteen years ago and
pays a fixed annual percentage rate of 4.8% per annum. The debt will be repaid
by monthly installments over 100 years. The current market price for the flat is
about $200,000. (This is based on a true story).
a. Calculate the monthly payment. (4 points)
b. Nakashima is now 50 years old and in good health. He is expected to live
another 36 years. When he dies at the age of 86, what is the expected amount of
debt his children will inherit? (5 points)
c. Nakashima does not want leave a large amount of debt to his children when he
dies. He plans to pay an additional $600 per month to the bank from now on.
Then how long will it take him to pay off the debt? (7 points)
Answer: You can use the spreadsheet. However, you it doesn’t take too much
time to do it using the short-cut formulas.
a. Using the monthly interest rate of 4.8%/12 = 0.4%, apply the annuity formula,
400000 1 100*12
, C $1,613.41/ month
b. When he dies at the age of 86, he still has 50 years to pay his debt. The amount he
still owes to the bank is equal to:
PV 1 , PV $366,585.60
c. At this moment, he owes:
PV ' 1 86*12
, PV ' $396,798.70
If he pays $600 per month more, then, he has to pay another T months to retire the
2213.41 1 1
396798.70 1 , 1 0.71708
0.004 1.004T 1.004T
1 log 3.5346
0.2829 1.004T 3.5346 T 316.3
1.004T log 1.004
Or, roughly, he has another 26 years 4 months to pay. But at least, he won’t leave
any debt to his children.
(A final thought: In Japan, the inheritance tax rate is 70%. Does this have
anything to do with the 100-year mortgage loans?)