Question

It is the end of your final year of study as a student in the Master of Finance program and you are trying to determine what you are going to do over the remaining 35 years of your working life. You are trying to decide whether you should remain at university and do your PhD in finance or alternatively leave university and become a consultant.

You anticipate that it will take you 5 years to complete your PhD during which time you will earn a real net cash flow of $25,000 p.a. At the end of these 5 years you must decide whether to remain at the university as an academic or take up a career as a consultant.  There is a 10% chance that you will enjoy great success as an academic earning a salary of  $85,000 p.a., a 50% chance that you will have a moderately successful career earning a salary of $65,000 p.a. and a 40% chance that you will have an unsuccessful academic career earning a salary of only $45,000 p.a. If you decide to become a consultant then it will initially cost you $100,000 to set up your business and there is an 80% chance of generating $60,000 p.a. and a 20% chance of generating $120,000 p.a..

If you decide not do a PhD and instead become a consultant immediately, there is a 60% chance that you will earn $70,000 p.a. and a 40% chance that you will earn $50,000 p.a. over the remainder of your working life.

Assume that all cash flows (other than those specified otherwise) occur at year-end, are expressed in real terms (that is in terms of purchasing power today) and that the real opportunity cost of capital is 10%.

You are to assume that for personal (as opposed to financial) reasons, you have decided to do a PhD. Using the decision tree approach, estimate the value of the option associated with not having to stay in academia after you acquire your PhD.

Answer 1

Estimated value of the option associated with not having to stay in academia after acquiring PhD=Net Value lost(forgone) by choosing not to be employed in academics-- for which we need to arrive at the respective probability * the associated incomes
	100%
	50%	50%
Doing PhD		Becoming a consultant immediately
After 5 yrs.		(50%*60%*70000)+(50%*40%*50000)
50%	50%
Academics	Consultant
((10%*85000)+(50%*65000)+(40%*45000))	-100000+((80%*60000)+(20%*120000))
+ 25000 for all 5 yrs.	+ 25000 for all 5 yrs.
Value of the option of academics =
(25000*3.79079)+PV of Yr. 6 end to yr. 40 end of c/f of (50%*50%*((10%*85000)+(50%*65000)+(40%*45000)))*5.98826
183096.59
Reduced by
Value of choosing to be a consultant=
(25000*3.79079)+PV of Yr. 6 end to yr. 40 end of c/f of ((-100000+((80%*60000)+(20%*120000)))*5.98826)=
-72901.53
So,
Net Value lost(forgone) by choosing not to be employed in academics=
183096.59-(-72901.53)=
255998.12
ie.
255998
OR $ 256000
Note: PV Factors used:
P/A, i=10%,n=5 yrs.(1-1.1^-5)/0.1=3.79079
P/A,i=10%,n=40 yr.(1-1.1^-40)/0.1=9.77905
P/A ,i=10% for yrs.( 40-5)----9.79905-3.79079=5.98826