Question

a. Dr. Fatima has been working on an advanced technology in laser eye surgery. The technology is expected to be available to the medical industry six years from today and will generate annual income of $600,000 six years from now and it will grow at 4 percent perpetually starting that year. What is the present value of the technology if interest rate is 12 percent?

1. $600,000.00
2. $7,500,000.00
3. $6,000,000.00
4. $5,000,000.00
5. $4,255,701.42

b. You are saving for the college education of your three children. They are two years apart in age; one will begin college in 6 years, another at year 8 and another at year 10. You estimate your children’s college expenses to be $30,000 per year per child, paid at the beginning of each college year (first payment for first child is at year 6 and so on). The annual interest rate is 5 percent. How much money must you deposit in an account each year to fund your children’s education? You will begin payments one year from today. You will make your last deposit when your oldest child enters college. Also assume that each child will take 4 years to graduate from college.

1. $304,904.07
2. $50,817.35
3. $46.789.20
4. $44,826.22
5. $38,897.22

Answer 1

Req a:
Price of annutiy at the end of 6 year:
Cashflow sfor 7t year			624000
	(600000+4%)
Divide: Net rate of return (12-4)%			8%
Price of annutiy at the end of 6 year:			7800000
Present value:
Year-6	Cashflows	PVf	Present value
Annuity	600000	0.506631	303978.6
Price	7800000	0.506631	3951722
	Present value		4255700
Answer is $ 4255701.42
Req b:
Let the Annual deposits for 6 years be X:
Year	Cashflows	PVF @ 5%	Present value
1	x	0.952381	0.95238x
2	x	0.9070295	0.90703x
3	x	0.8638376	0.863838x
4	x	0.8227025	0.822703x
5	x	0.7835262	0.783526x
6	x-30000	0.7462154	0.746216x -22386.46		Here first child enters)
7	-30000	0.7106813	-21320.4
8	-60000	0.6768394	-40610.4		(Here second child also enters)
9	-60000	0.6446089	-38676.5
10	-60000	0.6139133	-36834.8		(here third child enter and first completed study)
11	-60000	0.5846793	-35080.8
12	-30000	0.5568374	-16705.1		(here second child completed study)
13	-30000	0.5303214	-15909.6
Present value of inflows			5.07569x - 227524
Now, the equation must be equal to zero
5.07569x - 227524 = 0
x= 44826.22
Annual deposits: $ 44826.22
Answer is $44826.22