Question

7. One of your neighbors, Mr. and Mrs. Schekel, ( an elderly couple that always bring cookies when they visit ) has been very interested in hearing about your experiences at university. They would like to send their granddaughter to your university in 8 years’ time. You estimate that tuition will be $45,000 the first year , and the tuition will grow at 1.26% annually. They estimate it will take her 5 years to complete her undergraduate and MBA degrees, provided she attends summer school . they would also like to bestow a gift of $15,000 to her upon her graduation from the MBA program. How much must your clients deposit today, assuming an intrest rate of 6% in order to send their granddaughter to your university and provide her with the graduation present ?

Show time line . use uneven cash flow method

8. The schkels also have another granddaughter of whom they are very proud. They are considering offering her the following :

a. $40,000 today or

b. $45,000 towards a house down payment when she marries 2 years from now when her fiance finishes medical school. Assuming an intrest rate of 5% , which offer should the granddaughter accept ?

9. Another neighbor, Mr Ruble, is considering depositing $1,500 at the end of each year for five years in a saving account that pays 3.5% per year . you recommend that he deposit the funds at the beginning of each year. Calculate and demonstrate the change in value that will accrue to Mr.Ruble. Explain why there is a change in value .

Answer 1

Ans #7

Timeline for the above event is given as follows:

PVIF = Present value interest factor = 1 ÷ (1 + r) ^ n

Where

r = Interest rate = 6% i.e 0.06

n = Year

Hance

Year	8	9	10	11	12	13
=	1÷(1 +0.06)^8	1÷(1 +0.06)^9	1÷(1 +0.06)^10	1÷(1 +0.06)^11	1÷(1 +0.06)^12	1÷(1 +0.06)^13
=	0.627412	0.591898	0.558395	0.526788	0.496969	0.468839

The amount to be deposited today will be computed by finding out the present value of future cash outflow which can be computed as follows

Year	Cash flow Description	Amount ($) (A)	PVIF (6%) (B)	Present value of Cash Flow ($) (A×B)	Remarks
8	Tuition Fee	45000	0.627412	28234	It is assumed that the Tuition fee is payable upfront. Hence 1st-year fee has to be paid at the beginning of 9th year, which we can also say that at the end of the 8th year and so on.
9	Tuition Fee	45567	0.591898	26971	The tuition fee for the year has been increased by 1.26% as compared to the previous year.
10	Tuition Fee	46141	0.558395	25765	The tuition fee for the year has been increased by 1.26% as compared to the previous year.
11	Tuition Fee	46723	0.526788	24613	The tuition fee for the year has been increased by 1.26% as compared to the previous year.
12	Tuition Fee	47311	0.496969	23512	The tuition fee for the year has been increased by 1.26% as compared to the previous year.
13	Gift on Graduation	15000	0.468839	7033	Since the Graduation will be completed at the end of the 13th year Gift of $15000 has to be paid at the end of the 13th year.
Present Value of Total Cash Flow				136127

Hence, Mr. and Mrs. Schekel should deposit $136,127 today to meet the future expenditure in order to send their granddaughter to your university and provide her with the graduation present.

Ans #8

We have to evaluate 2 proposals from the point of view of the Schekel's granddaughter i.e

a. Getting $40,000 today

b. Getting $45000 after 2 year

Above proposal can be evaluated by finding out the present value of $45000 which she will get after 2 years. Which can be computed as follows

Present value of future cash flow = Future cash flow × PVIF

Given

Future Cash inflow = $45000

PVIF = Present value interest factor = 1 ÷ (1 + r) ^ n

Where

r = Interest rate = 5% i.e 0.05

n = Year = 2

Hence PVIF = 1 ÷ (1 + 0.05) ^ 2

= 0.907029

Hence

Present value of future cash flow = 45000 × 0.907029

= $40,816 (Rounded off)

Hence It is recommended that Schekel's granddaughter should accept the 2nd proposal i.e getting $45,000 towards a house down payment when she marries 2 years from now when her fiance finishes medical school since it has more present value as compared to the 1st proposal.