ANSWER SHEET HELP 1346: QUANTITATIVE METHODS - company has Rs 6,00,000 to invest, and a total of three investments are available to it. If xj rupees (in lakhs) are invested j, then a net present value

Tuesday, 17 January 2017

QUANTITATIVE METHODS - company has Rs 6,00,000 to invest, and a total of three investments are available to it. If xj rupees (in lakhs) are invested j, then a net present value

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QUANTITATIVE METHODS

Note : Attempt only 8 Questions

A company is deciding to choose between two mutually exclusive projects A and B. Project A requires an initial investment of Rs. 3,00,000 and is expected to generate cash flow of Rs. 1,50,000 per annum for the 3 years of its life. Project B, on the other hand, requires 3,40,000, has a life of 6 years and would generate Rs., 1,00,000 every year. Which proposal should be accepted?

A repairman is to be hired by a company to repair machines that break down following a Poisson process, with an average rate of four per hour. The cost of non-productive machine time is Rs 90 per hour. The company has the option of choosing either a fast or a slow repairman. The fast repairman charges Rs 70 per hour and will repair machines at an average rate of 7 per hour, while the slow repairman charges Rs 50 per hour and will repair machines at an average rate of 6 per hour. Which repairman should be hired?

A company has Rs 6,00,000 to invest, and a total of three investments are available to it. If x_j rupees (in lakhs) are invested j, then a net present value (in lakhs of rupees) of v_j(x_j) is obtained, where v_j(x_j)’s are given below:

V₁(x₁) = 7 x₁ + 2

V₂(x₂) = 3 x₂+ 7

V₃(x₃) = 4 x₃ + 5

The amount placed in each investment has to be in multiples of Rs 1 lakh only. How should the company invest Rs 6,00,000 in order to maximise the net present value obtained from the investments?

An investor has Rs 10,000 to invest and she has an opportunity to invest the amount in either of two investments A or B, at the beginning of each of the following three years. The investment A results either in a total loss of the amount invested with probability 0.2. The conditions allow at the most one investment each year and she can invest only Rs 10,000 each time and any additional funds accumulated are left idle. Using dynamic programming, find the investment policy that maximizes the expected amount of money will have after three years.

A company manufacturers around 150 mopeds. The daily production varies from 146 to 154 depending upon the availability of raw materials and other working conditions.

Production per day	Probability
146	0.04
147	0.09
148	0.12
149	0.14
150	0.11
151	0.10
152	0.20
153	0.12
154	0.08

The finished mopeds are transported in a specially arranged lorry accommodating only 150 mopeds. Using following random numbers 80,81,76,74,64,43,18,26,10,12,65,68,69,61,57, stimulate the process to find out:

(i) What will be the average number of mopeds waiting in the factory?

(ii) What will be the average number of empty spaces on the lorry?

The XYZ company is considering whether or not to invest Rs 1,20,000 in an investment proposal to add a new product to its existing range. The management forecasts that the new plant will generate incremental net cash flows, each of which is assumed to be normally distributed random variable with following parameters.

Year	Expected Value (Rs)	Standard Deviation (Rs)
1	44,000	5,800
2	40,000	5,600
3	40,000	6,000
4	35,000	5,000
5	30,000	4,000

Using the discount rate of 10 % determine:

(a) the mean of the present value distribution and its standard deviation,

(b) the probability that the investment shall have a negative NPV,

(c) whether the project should be undertaken if the management has laid down that no project be undertaken unless it has at least 70 % chance of giving an NPV at least equal to Rs 25,000.

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