Question

Q1. Imagine that we’d like to invest in a small startup company. We have secret information (given to us from a legal source, like statistics, so that we aren’t insider trading or anything like that…) that the startup will have 4,000 dollars of profits for its first 5 years, then 20,000 dollars of profits for the next 10 years, and then 50,000 dollars of profits for the 10 years after that.

After year 25, the company will go under and pay 0 profits.

The company would like you to buy 50% of its shares, which means that you will receive 50% of all of the future profits.

If you discount the future at ?=0.05r=0.05, how much would you be willing to pay?

Q2.

In economics, when an individual has knowledge, skills, or education that provides them with a source of future income, we call it human capital. When a student graduating from high school is considering whether to continue with post-secondary education, they may consider that it gives them higher-paying jobs in the future, but requires that they commence work only after graduation.

Consider the simplified example where a student has perfectly forecastable employment and is given two choices:

1. Begin working immediately and make 40,000 dollars a year until they retire 40 years later.
2. Pay 5,000 dollars a year for the next 4 years to attend university and then get a job paying 50,000 dollars a year until they retire 40 years after making the college attendance decision.

Should the student enroll in school if the discount rate is ?=0.05?

Answer 1

Ans 1.
Let us find the PV of the Net Incomes receivable and take 50% of that
as value payable
We consider PVIF for annuities as [1-(1+r)^-n]/r
where r=discount rate , n = no of periods
r=5%	a	b
Period	Profit	PVIF Factor	PV of Profit=a*b
First 5 years	4,000	4.3290	17,316.00
Next 10 years	20,000	7.7220	154,440.00
Next 10 years	50,000	7.7220	386,100.00
Total PV of Profits			557,856.00

50% share of PV of future profits =50%*$557856=	$          278,928.00
So Value that should be payable is $278,928

Ans 2.
Let us find the net PV of both the options .
option 1.
PVIF Factor for 40 years @5=(1-1.05^-40)/5%=	17.1591
So PV of $40,000 receivable for 40 yrs =40000*17.1591=	$                686,364
Option 2.
Let us find the PV of Cost of $5000 for 4 years
PVIF factor for 4 yrs @5% =3.546
PV of Cost of $5000 for 4 yrs =5000*3.546=	$             17,730.00
Then we find the PV (after 4 yrs ) of $50,000 receivable for 36 years
PVIF factor for 36 years @5%= (1-1.05^-36)/5%=	16.5469
PV (after 4 yrs) of $50000 receivable for 36 yrs=36000*16.5469=	$                827,343
So PV of 827343 now=827343/1.05^4=	$                680,657
PV of Net receivable =680657-17730=	$                662,927
So the PV of income from joining job immediately is higher.
Therefore, the student should not enroll for school.