Work on the question below

11. (a) Briefly explain the significance of the firm's cost of capital. What

are the factors determining that cost of capital, and how can that

cost be estimated?

(b) Given that debt finance is generally cheaper than equity finance,

explain why the firm is unlikely to use solely debt finance to fund

expansion.

(c) A commodity broker is contemplating the acquisition of a new

computer-driven management information system (MIS). The

hardware for this would cost an initial 4 million, whilst software

and staff training would cost 1 million for each of the first two

years operation, and 200 000 per year thereafter. After six

years, the system would be due for replacement. However

scrapping the current (manual) system would save staff costs of

1.5 million each year.

To finance the new investment the broker would use a combination of debt and equity capital in the ratio 1:3. The broker can

borrow at an interest rate of 10%, whilst interest paid can be set

against the corporation tax liability (currently taxed at 30%).

The broker is a listed company with a current share price of

3.00, and current dividend of 15 pence. Over the period the

share price is expected to grow at an annual rate of 6%.

Use the above information to evaluate investment in the new

MIS, finding the net present value and internal rate of return on

that investment.

What other factors should the decision-maker take into account?

3. The Hot-Bake shop sells only bread made that day. Each loaf

produced has a variable cost of 30p and sells for SOp. Any bread

unsold at the end of each day is thrown away.

At the start of each day, the manager must decide how many loaves

to produce. The table below records sales over the past month:

Daily sales Frequency

1000 6

1200 10

1400 10

1600 4

(a) Fixed costs are estimated at X per day. Find the breakeven

number of loaves produced and sold, and the number if expected

daily profit was 50.

(b) Find the number of loaves produced to minimise expected

opportunity loss.

(c) Bread is produced by a fully automated machine which mixes the

dough, divides it into 1 lb units, fills each baking tin and passes

them through an oven. Out of each batch, some are rejected for

being underweight or burnt.

The proportion rejected has the probability distribution given

below:

Proportion rejected

0.05

0.10

0.15

Probability

0.25

0.60

0.15

(i) Find the number of loaves produced if the expected number of saleable loaves equals your answer to question (b).

(ii) The services of a maintenance engineer would set the

rejection rate equal to 0.05, but would cost 11 per day.

Advise the manager on whether to engage the engineer or

not, if the desired daily production is 1300.

(d) Comment on the assumptions underlying your answers, and

discuss the relevance of other decision criteria.

4. 'Profit is the maximum value a company can distribute during the

year and still expect to be worth as much at the end of the year as it

was at the beginning.' Discuss this statement, and comment on its

value in measuring profit for decision-making

Problem 5 A river has the following observed annual flood peaks at a gaging station for the period from 1982 to 1995. Determine the 2-year, 10-year, and 100-year flood discharges based on the log- normal distribution. The frequency factors for different exceedance probabilities for the log- normal distribution are shown in the following table. Annual Flood Peak Discharge Year Year (cfs) (cfs) 1982 8000 1989 9400 1983 8800 1990 14200 1984 7400 1991 7600 1985 6700 1992 5800 1986 11100 1993 14300 1987 12200 1994 11600 1988 5700 1995 10400 Frequency Factors versus Exceedance Probabilities for the Log-normal Distribution P K P K P K 0.0001 3.719 0.100 1.282 0.600 -0.253 0.0005 3.291 0.150 1.036 0.650 -0.385 0.001 3.090 0.200 0.842 0.700 -0.524 0.002 2.880 0.250 0.674 0.750 -0.674 0.003 2.760 0.300 0.524 0.800 -0.842 0.004 2.650 0.350 0.385 0.850 -1.036 0.005 2.576 0.400 0.253 0.900 -1.282 0.010 2.326 0.450 0.126 0.950 -1.465 0.025 1.960 0.500 0.000 0.975 -1.960 0.050 1.845 0.550 -0.126 0.990 -2.326Let X1, X2, . Xn represent the i.i.d. random samples from a log-normal distribution with pa- rameter u and o. We know that the MLE for the two parameters are . ' =1EL (InX - #) = 12[InX - (12, InX.)]? Please derive . The bias and variance of a (6 pts). . The bias of o (4 pts).The statistical parameters of the logarithms (base 10) of the largest discharge values of a river during 50 years of record are as follows: X = 2.3670, S = 0.4771, g= -0.45 (i) Estimate 5, 10, 20, 50, and 100 year flood peaks using frequency factor formula (Quantile Estimation) for following: (a) Log-Normal distribution (b) Log Pearson type 3 distribution (ii) Which distribution explains the frequency of the flood peaks better, why?The Log-normal Distribution. In atmospheric science, the Log-normal distribution is often used to characterize particle size distributions. In one study, the distribution of silicone nanoparticle size (in nm) was found to be approximately Log-normal with Log-mean 0 = 3.91 and Log-sd w = 0.47. Suppose the desired range of particle sizes is (40nm, 110nm). What percentage of silicone nanoparticles do you expect to fall within this range