MGMT 2000 Exam with Solutions

QUESTION 1 [8 points]

A particular type of printer ribbon is produced by only two companies, Alamo Ribbon Company and South Jersey Products. Suppose Alamo produces 65% of the ribbons and South Jersey produces 35%. Eight percent of the ribbons produced by Alamo are defective and 12% of the South Jersey ribbons are defective.

a) A customer purchases a new ribbon. What is the probability that Alamo produced the ribbon? [2 points]
b) The ribbon is tested, and it is defective. Now what is the probability that Alamo produced the ribbon? [2 points]
c) Which company would you choose to become your ribbon supplier and why? What other factors must you consider when making this decision? [4 points]

Answer:
a) 65%
b) p(A|D) = p(A,D) / p(D) = (.65)(.08) / [(.65)(.08) +(.35)(.12)] = .553
c) I would have to know the price of both types of ribbons and any costs (time, damages etc.) associated with identifying a particular ribbon as defective. If the price were the same for both and costs of identifying defectives were negligible, I would choose Alamo since it has the greatest market share (and may therefore be more reliable) and the lowest defect rate.


QUESTION 2 [10 points]

You decide to purchase new furniture for your apartment. The cash price for the furniture is $1500 (option A). You have the option to select an instalment plan of $84/month for 24 months (option B).

a) Draw a cash flow diagram for each option. [2 points]
b) What is the interest per month that you are charged? [4 points]
c) What are the nominal and effective rates per year? (If you were unable to solve part b), assume an interest rate of 1.5% per month for your calculations here and for part d).) [2 points]
d) Which option would you select and why? [2 points]

Answer:
a) Option A Option B
0 1 24
-$84
-$1500

b) PV = U * [(1+i)n-1]
[i(1+i)n]
at I=2%, PV(B-A) = 1500 + 84 ((1.02)24-1)/[(.02)(1.02)24) = -88.77
at I=3%, PV(B-A) = 1500 + 84 ((1.03)24-1)/[(.03)(1.03)24) = 77.41

IRR = r1 + (r2-r1) |NPV1| .
|NPV1| + |NPV2|
= 2 + (3-2) (88.77) / (88.77+77.41) = 2.53%

c) nominal = 12(2.53) = 30.36%
effective = (1.0253)12 –1 = 34.96%
or, using the 1.5% rate:
nominal = 12(1.5) = 18%
effective = (1.015)12 –1 = 19.56%

d) I would pay the $1500 up front. The furniture store is implicitly offering me a loan at over 30% interest. I can get a bank loan for considerably less.

QUESTION 3 [11 points]

You want to invest $10,000 in the stock market by buying shares in one of 3 companies. Shares in Company A, though risky could yield a 50% return on investment during the next year. If the stock market conditions are not favourable (a “bear” market), the stock may lose 20% of its value. If the market is neutral, the value of Company A stock will not change. Company B provides safe investments with 15% return in a “bull” market, 10% in a neutral market, and only 5% in a “bear” market. Company C is a counter-cyclical investment. It provides 10% in a “bear” market and loses 5% in a “bull” market. Its value does not change in a neutral market. All the publications you have consulted are predicting a 60% chance for a bull market, a 10% chance for a neutral market, and a 30% chance for a bear market.

a) You began to draw a decision tree to solve the problem but were called away by the sound of reindeer landing on your roof. Complete the attached tree, filling in the shaded areas. [5 points]



Bull 0.6
15000

Company A Neutral 0.1
10000

Bear 0.3
8000


Bull 0.6


Company B Neutral 0.1

11150
Bear 0.3



Bull 0.6


Company C Neutral 0.1


Bear 0.3




b) Which stock would you invest in? [1 point]
c) Compute the value of perfect information. [3 points]
d) Perfect information about the future performance of the stock market is impossible to obtain. Knowing that, why would you compute the value of perfect information? [2 points]

Answer:
a)

Bull 0.6
15000

Company A Neutral 0.1
10000
12400
Bear 0.3
8000


Bull 0.6
11500

Company B Neutral 0.1
11000
12400 11150
Bear 0.3
10500


Bull 0.6
9500

Company C Neutral 0.1
10000
10000
Bear 0.3
11000

b) company A
c) EVw/PI = .6*15000+.1*11000+.3*11000 = 13400
VOPI = 13400-12400 = 1000
d) The value of perfect information gives us an upper bound on the amount we would be willing to pay for any kind of information. We can use this value as a filter to eliminate from consideration any offers of information at a price greater than the value of perfect information.

QUESTION 6 [9 points]

Schulich tracks the number of students graduating in each term.

Year Term Graduates Moving Average
2000 Fall 23
2001 Winter 48 75.33333
2001 Summer 155 74.66667
2001 Fall 21 70
2002 Winter 34 76
2002 Summer 173 75
2002 Fall 18 69.33333
2003 Winter 17 60.33333
2003 Summer 146 65
2003 Fall 32 69
2004 Winter 29 68
2004 Summer 143

a) Use the above data to compute seasonal indices. [5 points]
b) Over how many observations was the moving average taken? [1 point]
c) Explain the meaning of the seasonal index for Fall. [2 points]
d) What Excel feature is helpful in organizing data to compute seasonal indices? [1 point]

Answer:
a)
Moving Average
F W S
75.33333 0.637168 0.637168 2.075893
74.66667 2.075893 0.3 0.447368 2.306667
70 0.3 0.259615 0.281768 2.246154
76 0.447368 0.463768 0.426471
75 2.306667
69.33333 0.259615 0.341128 0.448194 2.209571 2.998893
60.33333 0.281768
65 2.246154 0.341254 0.448359 2.210387
69 0.463768
68 0.426471

b) 3
c) The number of graduates in the fall term is 34% of what you would expect in a typical term if there were no seasonal variation.
d) pivot table
QUESTON 7 [7 points]

At the latest firemen’s union meeting, the membership expressed concern that their wages were not keeping up with the pace of inflation. The following regression model was created to investigate the growth in firemen’s average wages in thousands of dollars:
ln(Wage) = 10.69 + 0.039 (Time)
where Time = 1 in the year 1990.

a) Forecast firemen’s average wages for 2006. [1 point]
b) Compute the growth rate. [2 points]
c) Inflation has been in the 2-3% range in the last decade. Are the firemen justified in their concerns? Why or why not? [2 points]
d) Sketch a rough graph of firemen’s wages over time. [2 points]

Answer:

a) ln (Wage) = 10.69 + 0.039(17) = 11.353
Wage = 85,220.73
b) e0.039 - 1 = 3.98%
c) No. On average, their wages are growing at slightly more than the rate of inflation. (However, individual firemen’s wages may be increasing at a faster or slower rate, so some may have reason for their complaints while others would not.)
d) Wage($)







Time

QUESTION 8 [8 points]

The Finance Department at Treasure Island Toys is evaluating its cost structure. One of the things the company would like to evaluate is the appropriateness of its allocation of expenses between fixed and variable costs. The Finance Department produced the following graph using financial results for the company and industry statistics for the last 10 years:

a) Is this an effective graph for comparing the company’s cost allocation to industry standards? Why or why not? [3 points]
b) Does the company have high or low variable costs relative to the industry? [1 point]
c) Last year, the company’s sales were $500,000 and profits were 5% of income. Unfortunately this has been a slow year, and sales are forecast to drop to $400,000. What will be the effect on the company’s profit? Does the company appear to have made a good choice with respect to its degree of operating leverage under the current circumstances? [4 points]

Answer:
a) It is effective. It shows the degree of operating leverage for the company over time, which allows us to see any trends. It also shows the values relative to industry totals for easy comparison. It is easy to see that DOL has been increasing for the company while industry values remained steady; the company’s DOL is now appreciably higher than industry average. The graph is clear and easy to follow. One improvement could be to put actual years rather than a time index for the horizontal axis.
b) The company has a higher proportion of variable costs than the industry.
c) % change in sales = (400-500)/500 = -0.2
DOL = % change in profit/%change in sales ~= 2.5
Therefore % change in profit must be about –0.5
Profit(last year) = 500,000*.05 = 25,000
Profit (this year) = 25,000 (.5) = 12,500
The company’s profit will drop to $12500.
Because the company is more highly leveraged, the effect on profit is greater than it would have been if the company followed industry standard. Being more leveraged is hurting the company in this instance as its profit will drop more than it would have if DOL had been lower.
QUESTION 9 [7 points]
True/False
Determine whether the statement is true or false and circle the corresponding word.

a) An  of 0.1 weights the most recent observation more heavily than an  of 0.2. True False
b) Ieff compounded monthly is greater than ieff compounded quarterly for the same APR. True False
c)
d) Fred and Jane each invest $100 today. Fred earns 6% per year for the first 2 years and 8% per year for the second 2 years. Jane earns 8% per year for the first 2 years and 6% per year for the second 2 years. At the end of 4 years, Fred and Jane will have the same amount of money. True False
e) Fred and Jane each invest $100 at the beginning of each year for a period of 4 years. Fred earns 6% per year for the first 2 years and 8% per year for the second 2 years. Jane earns 8% per year for the first 2 years and 6% per year for the second 2 years. At the end of 4 years, Fred and Jane will have the same amount of money. True False
f) Quarterly seasonality can be captured in a regression model using 3 dummy independent variables. True False
g) When forecasting sales with seasonality, we use the model Deseasonalized Sales = a + b (Time) because it predicts the trend alone, while the model Sales = a+b (Time) would predict both the trend and seasonality. True False




QUESTION 10 [6 points]
Select the correct answer(s). Points will be granted for correct choices but will be deducted for incorrect choices.

1) The coefficient of determination (r2) tells us
a) that the coefficient of correlation is larger than 1
b) whether R has any significance
c) that we should not partition the total variation
d) the proportion of total variation in y that is explained by x

2) What Excel function can be used to do the equivalent of: IF(J4>H3,J4,H3)
a) MAX
b) MIN
c) GOALSEEK
d) COUNT

3) An investment is acceptable if its IRR
a) is exactly equal to its net present value (NPV)
b) is exactly equal to zero
c) is less than the required return
d) exceeds the required return

4) Net present value:
a) is equal to the initial investment in a project
b) compares project cost to the present value of the project benefits
c) is equal to zero when the discount rate used is less than the IRR
d) is simplified by the fact that future cash flows are easy to estimate
e) requires a firm to set an arbitrary cut-off point for determining whether an investment is acceptable

5) What are the disadvantages of the payback period method:
a) ignores the time value of money
b) biased against long-term projects
c) biased toward liquidity