Question

This exercise studies the relationship between monitoring costs and the cost of broken con- tracts. Consider a 200 AUD investment in a local bakery for one year. Without monitoring, the baker might be lazy and the probability of a failure of the bakery and no repayment is 20%. With monitoring, the baker is working hard and the probability of a failure of the bakery and no repayment is 10%. Without a failure the repayment is 250 AUD.

The cost of monitoring is 13. The interest rate for one year is 5%

a) Should the investor monitor the bakery?

b) Does the investment in the bakery (given optimal choice in a)) have a positive NPV?

Now the investment is split into two different individuals investing in the local bakery, each of the 100 AUD. There is no exchange of information.

c) Should one investor monitor the bakery?
d) Does the investment in the bakery (given optimal choice in c)) have a positive NPV? e) Interpret your findings in the context of the lecture content.

Answer 1

Part a)

Let us find the expected value of investment

Expected future value without monitoring

= probability of failure*value of investment + probability of no failure*repayment amount

20%*0 + 80%*250

= $200

Expected future value with monitoring

= 10%*0 +90%*250 - 13 (monitoring cost)

= $212

As the expected future value with monitoring is higher, so the investor should monitor

Part b

NPV in case of optimal choice, i.e. with monitoring will be

NPV = [ ((1-failure probability)*repayment amount) / (1+interest rate)] -Investment amount -monitoring cost

= [ (0.9*250) / (1+0.05) ] -200 -13

=$1.29

So it does have a positive NPV.

Part c

(Amount of repayment is not given in this case so we are assuming the repayment amount will be $125 i.e. half of 250 as investment has also been halved)

Let us find the expected value of investment in this case also

Expected future value without monitoring

= 0.2*0+0.8*125

=100

Expected future value with monitoring

= 0.1*0 + 0.9*125 - 13

= 99.5

As the expected value with monitoring is less than without monitoring, the investor should not monitor as it is not optimal.

Part d.

NPV for optimal choice (i.e. No monitoring in this case)

= [ ((1-failure probability)*repayment amount) / (1+interest rate)] -Investment amount

= [ (0.8*125) / (1+0.05) ] -100

= $ -4.76

So the investment does not have a positive NPV in this case

As the NPV is negative, this investment (of $100) should not be made by the investor.