Question

Mr. John Backster, a retired executive, desires to invest a portion of his assets in rental property. He has narrowed his choices to two apartment complexes, Windy Acres and Hillcrest Apartments. The anticipated annual cash inflows from each are as follows: Windy Acres Hillcrest Apartments Yearly Aftertax Cash Inflow Probability Yearly Aftertax Cash Inflow Probability 30,000 0.2 35,000 0.2 35,000 0.2 40,000 0.4 50,000 0.2 50,000 0.2 65,000 0.2 60,000 0.2 70,000 0.2 Mr. Backster is likely to hold the apartment complex of his choice for about 25 years and will use this period for decision-making purposes. Either apartment can be purchased for $175,000. Mr. Backster uses a risk-adjusted discount rate approach when evaluating investments. His scale is related to the coefficient of variation (for other types of investments, he also considers other measures). Coefficient of Variation Discount Rate 0–0.35 7% 0.35–0.40 12 (cost of capital) 0.40–0.50 15 Over 0.50 not considered

a. Compute the risk-adjusted net present value for Windy Acres and Hillcrest Apartments. (Do not round intermediate calculations. Round the final answers to nearest whole dollar.) (If you're using the TVM funtions of a calculator to answer the question, then you can ignore this note. If you're using the PV tables at the back of the book to answer this question, round "PV Factor" to 3 decimal places.) Net present value Windy Acres $ Hillcrest Apartments $ b-1. Which investment should Mr. Backster accept if the two investments are mutually exclusive? Hillcrest Windy Acres Both None b-2. Which investment should Mr. Backster accept If the investments are not mutually exclusive and no capital rationing is involved? Windy Acres Hillcrest Apartments Both None

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