Detailed answers only.
The senior partner in a local amounteoey rm is oonoeraed about the error rate amongst assessments issued by her ofce. A careful check over the past few years enables her to estimate that the error rate has the following probability distribution: Errormte Probability 0.05 (115 t]. it] (135 1115 0.25 {LIB [115 Eaeh error oosts 40 because of the labour time involved in reassess ment. Her rm is just entering the assessment 'season', and is expeeted to perform 5m assessments over the next few months. One way to reduce the error rate is to send all staff to a oneday training eonrse at the local urtiversity- 'Preeision in AsseSsmettt'. The university claims this would ensure an error rate of 0115. but she considers that an error rate of I110 would he equally.T likely The oourse tee is Hill for all her staff, whilst lost prot from one das' a work missed would be 500 Adi-use her on whether to send staff on the eonrse or not. A careful check of that day's output shows that in ten assessments, two oontained errors. Use this information to update the error rate probability distribution and hence determine whether your advice needs amendment. 9. (a) Briey analyse the effect of an increase in interest rates on the investment portfolio of a prot maximising holding company. {it} The University is contemplating building a netsr squash court, adjacent to its new hall of residence. To secure local support tor its planning application1 the University has offered to open the court to local players at student rates for the rst ve years. After ve years, the University can charge what it likes for the courts. Consequently, the University estimates that net revenue from the court will be ill!\" for each of the rst ve years, rising by lti'ih (cornpounded) in each of the sixth to tenth years. In the eleventh and twelfth years rising maintenance costs will com- pletely offset rising fees so that net revenue stays at tenth year level. At the end of the twelfth year, the site is due for redevelopment. The cost of btdldiug the squash court is estimated to be 60.13. To nance the court' the University must draw from its re serves. currently earning 12% in Local Authority Bonds. Selling sufcient bonds wotdd involve legal and administrative costs of 321]. Advise the University on the viability of the project. What other factors should the University take into account? to. A rm has an annual demand of 5 units for a good whose purchase cost is 5*: per unit. Each order costs {a to place. and the cost of holding stock is bit: of the average value of stock per annum. Determine the optimal order quantity. A local rm uses 2000 units of a particular component each year. The component has a purchase price of Wunit. while the cost of holding stock is estimated at 211% of the average stock value. If the cost of placing each order is 12.50, nd the optimal number of orders placed each year. Suppose the component supplier offers a discount of 2% on the purchase price if orders are placed in units of liltlll. Is the discount worth accepting? Suppose that instead of a single gure you had been given a probability distribution for the number of units used each year. Indicate the effect on stock policy. \f3. {a} {b} Shaw that an increase in the unit value efetnek will lead to a less than proportionate fall in the optimum mount of stock held. What asaumptiuus underlie your answer? A rm faces a uniform annual demand of ltIII] units. The purchase cost at" stock is Eli] per unit, whilst the nest of ordering stack is 20, and the east 0! holding attack is 14% of the average stack value. Find the Emuemie Order Quantity and the Mini- mum Acquisitiun Cost. I-ImmI are your amwer: affected by: {i} the feet it takes two weeks between [eeing an order and stuck. arriving: (ii) the offer of a 1% discount eff the purchase met if stock is ordered in lorry loads of 1? DUB units. 3. The Hot-Bake-shop sells and}.I bread made that day. Each loaf produced has a variable cost of 30p and sells for 501:. 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 ruler Frequency 1000 IS 1201] 1t] 1411'! 1!] 1600 4 {a} Fixed costs are estimated at H per dav. Find the breakeven number of loaves produced and sold, and the number if expected daily prot was 50. {b} Find the number of loaves produced to minimise expected opportunity loss. (e) Bread is produced by a full].r automated machine which miles the dough, divides it into 1 lb units. lills each halting tin and passes them through an oven. Out of each batch, same are rejected for being underweight or burnt. The proportion rejected has the probabilityr distribution given below: Pic-portion rejected Probability 0.05 {L15 [LII] (161} 1.15 1.15 {i} Find the number of ioaves. produced if the expected num- ber of saleable loaves equals your answer to question {b} {ii} The services of a maintenance engineer arould set the rejection rate equal to $.05. but would east 11 per day. Advise the manager on whether to engage the engineer at not, if the desired dain production is 13m. \f9. An engineering firm about to undertake a production run of 2000 items must decide whether to overhaul the production machinery. Because the machinery is quite old, the cost of an overhaul is uncertain. However, after the overhaul the failure rate for the machinery is certain to be 0.01. Without the overhaul, the machinery has a failure rate with the probability distribution given below. Each defective item costs the firm f6 in hand finishing. Failure rate Probability 0.01 0.5 0.02 0.2 0.03 0.1 0.04 0.1 0.05 0.1 Examination questions and answer notes 341 (a) Find the expected cost of overhaul that would make the risk- neutral decision-maker indifferent between overhauling or not. (b) The decision-maker decides to seek further information. Contact with the machinery supplier suggests an overhaul is equally likely to cost either f175 or f225, depending on the problems encoun tered. Moreover a sample run of 10 items is produced, resulting in 2 defectives. Use this new information to re-assess the overhauling decision. (c) How would the decision be influenced by: (i) the firm's precarious financial position; (ii) the knowledge that the machinery is to be scrapped after the next production run.11. (I) {b} [Cl Briey explain the signicance of the rm's cost of capital. What are the factors determining that cost of capital. and how can that cost be estimated? Given that debt nance is generally cheaper than equity nance, explain why the rm is unlikely to use solely debt nance to fund expansion. A commodity broker is contemplating the acquisition of a new emuputer-driven management information system {M15}. The hardware for this would cost an initial 4 million, whiht software and staff training would cost 1 million for each of the rst two years operation, and more per year thereafter. After six years, the system would be due for replacement. However scrapping the current {manual} system would save staff coats of 1.5 million each year. TC! nance the liE-'W investment 111$ broker WCIt \"SE a Militia- tion of debt and equity capital in the ratio 1:3. The broker can borrow at an interest rate of 10%. whilst interest paid can he set against the corporation tax liability {currently taxed at seas}. The broker is a listed company with a current share price of ill]. 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 M15. nding the net present value and internal rate of return on that investment. What other factors should the decision-maker take into account
