Question

Bathrooms R Us Limited (BRUL) is a manufacturer of bathroom appliances. BRUL has decided to increase the capacity of its Wellington factory to accommodate increased customer demand in the lower North Island and South Island. As part of this expansion, BRUL is considering proposals from four equipment suppliers that will assist in the production of a new style of bath. The equipment from each of the suppliers is different however all of them meet BRUL's specifications for the production of the new bath.

The selling price of the new bath is expected to be $1,150.

Details of each of the four proposals are contained in the following table:

	Supplier
	A	B	C	D
Cost of equipment	$1,650,000	$800,000	$1,025,000	$1,100,000
Installation costs	$75,000	$50,000	$25,000	$150,000
Salvage value1	$70,000	$50,000	$40,000	$100,000
Depreciation2	45%	40%	40%	40%
Variable cost per unit	55% of selling price	80% of selling price	75% of selling price	60% of selling price
Fixed costs per annum	$375,000	$175,000	$275,000	$300,000
Net working capital requirement3	15% of next year's sales	20% of next year's sales	18% of next year's sales	10% of next year's sales

Notes:

1. The salvage value is at the end of year 5.

2. The equipment will be depreciated using the diminishing value (also known as reducing balance) depreciation method at the Inland Revenue Department (IRD) approved maximum rates in the table (note: the equipment from Supplier A is depreciated at a higher rate due to its specialised technology).

3. The company expects that net working capital will be a percentage of the sales in the following year. For example. if BRUL selects Suppliers A's equipment it will need an initial investment, before Year 1 begins, in working capital of 0.15 x 2,400 x $1,150 = $414,000

The following table presents sales forecasts for the new bath. It is expected that the popularity of this bath will decline during years 4 and 5 and that BRUL will stop producing and selling this product at the end of year 5.

Year	Unit Sales
1	2,400
2	3,200
3	4,000
4	2,300
5	500
After year 5	0

Other information includes:

- The company has a policy of accepting projects where there are a Discounted Payback Period of three (3) years or less.

- The company's discount rate for projects of this nature is 15% based on current funding.

- The company's tax rate is 28%.

Required:

a) Prepare a summary table that includes the following for each of the four suppliers:

i) The Discounted Payback Period (DPP)

ii) The Net Present Value (NPV)

iii) The Internal Rate of Return (IRR)

iv) Profitability Index (PI)

b) Based on your summary table in part a) above rand each of the suppliers' equipment from 'most preferred' to 'least preferred' using four criteria

c) Evaluate the calculations in part a) above and your ranking in part b) above and provide a recommendation on which of the supplier's equipment should be accepted.

Answer 1

To solve this question just input those variables which are to be used in logistic regression, as the question talks about using two variables only that is total loans and leases to total assets & total expenses/ total assets, so we will not input total cap/assets as an input variable in our excel, here we go

As one can see, we have taken only two variables , total exp/assets and total lns & leases/ assets in calculation, follwing steps have been followed to construct the above table

1. Assume logit= b0+ b1* independent variable1+ b2* independent variable 2 , take values of b0=0.1, b1=0.1, b2=0.1, note that these values of b0, b1 and b2 are just taken for calculation, one could assume any values here for bo , b1 and b2

2. Calculate exponential of logit in the next column by using exp (value in previous column)

3. Calculate probability by using formula, probability= exp (logit)/ { 1+ exp(logit)} in the next column

4. In next column, calculate log likelihood by using formula : financial condition value (i.e. 1 or 0) * LN( probability calculated in previous column) + (1- financial condition value)* LN( 1- probability calculated in previous column)

5. take the total of the column values of log likelihood

6. use solver function in excel to change this total by putting max value of 0 and changing the variable cells containing assumed values of b0, b1 and b2 , by clicking on solve, you will get actual values of b0, b1 and b2

which comes out to be b0=-14.72, b1=89.83, b2= 8.37

therefore you will get logit as

-14.72+ 89.83* Total exp/assets+8.37*Total lns & lsses/ assets

With values given in the question as total exp/ assets= 0.11 and total loans & leases/ assets= 0.6 , we get

logit as -14.72+ 89.83* 0.11+ 8.37*0.6= 0.1833

exp (logit) = 1.20

Probability= 0.546

Loglikelihood= 1*LN(0.546)+0*LN(1-0.546)= LN(0.546)= -0.605