Commercial fishermen in Alaska go into the Bering Sea to catch all they can of a
particular species (salmon, herring, etc.) during a restricted season of a few weeks.
The schools of fish move about in a way that is very difficult to predict, so the fishing in a
particular spot might be excellent one day and terrible the next.
The day-to-day records of catch size were used to discover that the probability of a good
fishing day being followed by another good day is 0.5, by a medium day 0.3, and by a poor
day 0.2.
A medium day is most likely to be followed by another medium day, with a probability of 0.4,
and equally likely to be followed by a good or bad day.
A bad day has a 0.1 probability of being followed by a good day, 0.4 of being followed by a
medium day, and 0.5 probability of being followed by another bad day.
a) (10 points) If the fishing day is bad on Monday, what is the probability that it will be
medium on Thursday?
b) (10 points) Suppose the fishing day will be good w.p. 0.25, medium w.p. 0.30 and bad
with 0.45 on the current day, which is a Tuesday. How do you think fishermen came up
with these probabilities for the current day? Argue.
c) (10 points) Given the probabilities in part b, calculate the probability of having a bad
fishing day after three days.
d) (10 points) What is the probability of four consecutive good fishing days until it gets
worse.
e) (10 points) If the fishing day is medium initially, for how many days on the average will it
remain medium? What is the distribution of this number of days?

Devon Limited is a company that has issued corporate bonds with a par value of $100 and a coupon rate of 11%. The Total Statement of Financial Position value of bonds is $50million. The company’s bonds are currently trading at a price of $103. Interest is payable annually in arrears. The maturity date is in four years time. The company has a target capital structure of 25% debt, 15% redeemable preference shares, 10% non-redeemable preference shares, and 50% in ordinary equity financing. Retained earnings and contributed capital amount to $100million. The company has two types of preference shares in issue. There are 0.2 million non-redeemable preference shares which are issued at $100 per share and there are 0.3 million redeemable shares which were also issued at $100 and are redeemable at $100 per share. The maturity date of redeemable shares is in four years’ time. Preference dividends are payable annually in arrears for both issues. Non-redeemable preference shares are currently priced at $107 and the redeemable preference shares are currently priced at $104. The coupon rates are 9% for each issue and coupon payments were recently paid.The company’s beta is 1.20 and the risk free rate is 8%. The market premium is expected to be 5.5%. The corporation tax rate is 28%.

Required:

(a)What is Devon’s after tax cost of debt?

(b)What is the cost of the two types of preference shares?

(c)What is the cost of equity?

(d)What is the company’s weighted average cost of capital?

Managers of an Auto Products company are considering the national launch of a new car cleaning product. For simplicity, the potential average sales of the product during its lifetime are classified as being either high, medium, or low, and the net present value of the product under each of these conditions is estimated to be 80M, 15M, and -40M Tl respectively. The company’s marketing manager estimates that there is a 0.3 probability that average sales will be high, a 0.4 probability that they will be medium. It can be assumed that company’s objective is to maximize the net present value.

1. On the basis of the marketing manager’s prior probabilities, determine:

1. whether the product should be launched;

2. expected value of perfect information.

2. The managers have another option. Rather than going immediately for a full national launch, they could first test market the product. This would obviously delay the national launch, and this delay, together with other outlays would lead to costs having a net present value of 3M TL. The test marketing would give an indication as to the likely success of the national launch, and therealibility of each possible indications that could result are shown by the conditional probabilities are given below (e.g. İf the market for the product is such that high sales could be achieved, there is a probability of 0.15 that the test marketing would in fact indicate medium sales):

Determine whether the company should test market the product.

Problem 7-5

1. William Company’s balance sheet at the end of 2019 (beginning of 2020) reported Accounts Receivable of $314,200 and Allowance for Doubtful Accounts of $4,710 (credit balance).
2. The company’s total sales during 2020 were $3,340,000. Of these, $501,000 were cash sales the rest were credit sales.
3. The company also wrote off an account for $4,152.
4. By the end of the year, the company had collected $2,516,680 of the credit sales.

Requirements

1. Create T-accounts for Accounts Receivables and the Allowance for Doubtful Accounts. Post the information from Item 1.
2. Prepare journal entries for Items 2, 3, & 4.
3. Post the journal entries. Calculate William Company’s balances for Accounts Receivable and the Allowance for Doubtful Accounts at the end of 2020, before the adjusting entry is made.
   1. What is the net realizable value at this point?
4. For each of the following separate scenarios, prepare the adjusting entry for bad debt.
   1. Williams Company estimates that 0.3% of credit sales will be uncollectible.
   2. Based on an aging of receivable, Williams Company estimates that $9,500 of the accounts will be uncollectible.
   3. Instead of the write-off being for $4,152, as stated in Item 3, the write-off was $5,152. Recalculate the balances in the Allowance for Doubtful Accounts and Accounts Receivable. Based on an aging of receivable, Williams Company estimates that $9,500 of the accounts will be uncollectible.
5. Based on the journal entry for each of the 3 scenarios in d., calculate the net realizable value that will be reported on the Balance Sheet. Also provide the amount of Bad Debt Expense that will appear on the Income Statement in the Operating Expenses section.

EXPECTED RETURNS

Stocks A and B have the following probability distributions of expected future returns:

A.Calculate the expected rate of return, r_B, for Stock B (r_A = 10.10%.) Do not round intermediate calculations. Round your answer to two decimal places.
%

B.Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 22.00%.) Do not round intermediate calculations. Round your answer to two decimal places.
%

C. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

Is it possible that most investors might regard Stock B as being less risky than Stock A?

1. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
2. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
3. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
4. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
5. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.

(a) Calculate overall duration of all the assets.

(b) Calculate overall duration of all the liabilities.

(c) Calculate the leverage adjusted DGAP.

(d) Calculate overall change in values for all the assets for a 3% increase in interest rate.

(e) Calculate overall change in values for all the liabilities for a 3% increase in interest rate.

(f) Using the results from (d) and (e), compute the change in equity value for a 3% increase in interest rate.

(g) The director of Michael Bank wants to immunize the balance sheet completely by setting a new value of duration of all the assets. However, if it is impossible to change the duration of all the liabilities, and the top management does not want to change the total values of assets and liabilities. In that case, calculate a new value of duration of all the assets for the director so that immunization can be carried out.

A Pharmaceutical company produces three drugs: A, B, and C. It can sell up to 500 kg of each drug at the following prices (per kg):

Drug Sales price

A $10

B $15

C $25

The company can purchase the raw material at $7 per kg. Each kg of raw material can be used to produce either one kg of Drug A or one kg of Drug B. Assume cost of these operations is negligible. For a cost of $4 per kg processed, Drug A can be converted to 0.7 kg of Drug B and 0.3 kg of Drug C. For a cost of $5 per kg processed, Drug B can be converted to 0.9 kg of Drug C. Formulate this problem as a spreadsheet model and use Solver to determine the number of kgs of the raw material to purchase to make Drug A and Drug B, and the number of kgs of Drugs A and B to further process in order to maximize profit from selling the drugs subject to producing more than using each drug and max sales constraints.

Hint: Each operation in this problem has one input and one or more outputs, whereas each operation in the Production Process problem in Session 10 had one output but 1 or more inputs.   So in this problem, instead of "Production of 1 unit of" on the top, put the "Usage of 1 unit of" on the top, and put kgs of each drug to be produced on the left.   Consider the raw material to make Drug A different from that to make Drug B (call them RM1 and RM2). Instead of labour, there is cost.

Stocks A and B have the following probability distributions of expected future returns:

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 15.20%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 24.39%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. Is it possible that most investors might regard Stock B as being less risky than Stock A?

   1. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   2. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   3. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   4. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.

Question 5

a) (1) X~Normal(mean=4, standard deviation=3), (2) Y~Normal(mean=6, standard deviation = 4), and (3) X and Y are independent, then, P(X+Y>13) equals (in 4 decimal places)

Answers options: a) 0.7257, b) 0.3341, c) 0.2743, d) 0.6759, e) none of these

b) Let X~Gamma(4, 1.2). Which of the following is possible R code for computing the probability that X < 2.6?

Answers options: a) dgam(2.6, 4, 1.2), b) pgamma(4, 1.2, 2.6), c) dgamma(2.6, 4, 1.2), d) pgamma(2.6, 4, 1.2), e) None of these

c) If X~Exponential(lambda=2.8), which of the following code computes P(X>2) correctly?

answers options: a) 1-dexp (2, rate=2.8), b) pexp(2, rate=2.8), c) 1-pexp(2, rate=2.8), d) dexp(2, rate=2.8)

d) If X has an Exponential distribution with mean 2.5, which of the following code computes P(X<3) correctly?  

Answers options: a) pexp(3, rate=2.5), b) dexp(3, rate=2.5), c) pexp(3, rate=0.4), d) dexp(3, rate=0.4), e) None of these

e) If X1, X2, ..., X100 are independent and identically distributed as Uniform (0,1), the probability that the average of these 100 random variables is less than 0.3 equals   , approximately? ( ). Answers options: a) 0.4586, b) 0.5414, c) 0.6406, d) 0.3594, e) None of these

a. About % of the area under the curve of the standard normal distribution is outside the interval z=[−0.3,0.3]z=[-0.3,0.3] (or beyond 0.3 standard deviations of the mean).

b. Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(−b<z<b)=0.6404P(-b<z<b)=0.6404, find b.

b=

c. Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z=−1.6z=-1.6 and z=1.6z=1.6 standard deviations of the mean (or within 1.6 standard deviations of the mean). What percent of the data points will fall in that range?

Answer:  percent (Enter a number between 0 and 100, not 0 and 1 and round to 2 decimal places)

d. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.6 years, and standard deviation of 3.1 years.

If you randomly purchase one item, what is the probability it will last longer than 20 years?

e. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 224-cm and a standard deviation of 1.8-cm. For shipment, 27 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is between 223.6-cm and 224.2-cm.
P(223.6-cm < M < 224.2-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.