Question

1. MINI CASE ANALYSIS on THE TIME VALUE OF MONEY     

Quilici Family: Greg and Debra Quilici own a four bedroom home in an affluent neighborhood just north of San Francisco, California. Greg is a partner in the family owned commercial painting business. The family is Composed of Greg (father), Debra (mother), and 5 year old son Brady.Greg is a partner in the family owned commercial painting business.Debra is a housewife

After visiting Lawrence Krause, a family financial planner, Greg and Debra became concerned of their spending, and that they are not putting enough money for their son’s future education needs as well as their own retirementThey have a Koegh plan (retirement plan for self-employed individuals and small businesses in the US), but they did not account for Brady’s education.

Greg earns $95,000 per year, Greg is an alumnus of Stanford University (Tuition = $40,000 per year). Debra graduated from University of North Carolina at Chapel Hill (Tuition = $4,500 per year). The couple wants to send Brady to either school when he turns 18, with a slight preference towards Stanford. The problem, however, is that with the rate at which tuition is increasing the Quilicis are not sure they can raise enough money.

They expect the following things to happen.

• Tuition fees is expected to increase at an annual rate of 6%
• Living expenses are estimated to be $7000 per year for both schools (expecting to grow 3.5% per year)
• The couple can deposit their money into a growth oriented mutual fund at Neuberger and Berman Management, Inc. (historically earning 12% per annum)

The couple wishes to have a pre-determined monthly amount automatically paid from their bank account. When Brady starts college they will slowly liquidate the account by making an annual payment to Brady to cover tuition and living expenses at the beginning of each year for the four years he will be in college.

From the Case above

1. Identify the variables for each university (Tution Fees, Living Expenses, Interest rate, No of years) (1 Mark for each variable = 4 Marks for Each University, Total for two universities = 8 Marks)

2. How much will the tuition and living expenses be per year when Brady is ready to attend Stanford University?

3. How much will the tuition and living expenses be per year when Brady is ready to attend University of North Carolina at Chapel Hill?

4. Once Brady starts college what will his total expenses (future) be in each of his four years for Stanford University?.

5. Once Brady starts college what will his total expenses (future) be in each of his four years for University of North Carolina at Chapel Hill?.

6. Based on your analysis which university shoulf Greg and Deba choose for their son?

Answer 1

a).

Variables	Tuition fees	Living expenses	Interest rate	No. of years
Stanford	40000	7000	12%	13
North Carolina	4500	7000	12%	13

b). Stanford university tuition fees when Brady is 18 years = (1+ current tuition fees)^number of years left

= (1+ 40,000)^13 = 85,317.13

Stanford living expenses when Brady is 18 years = (1+current living expenses)^number of years left

= (1+7,000)^13 = 10,947.69

c). N. Carolina university tuition fees when Brady is 18 years = (1+ current tuition fees)^number of years left

= (1+ 4,500)^13 = 9,598.18

Stanford living expenses when Brady is 18 years = (1+current living expenses)^number of years left

= (1+7,000)^13 = 10,947.69

d). For a 4-year course, we have

Total tuition fees for Stanford = 373,229.68

Total living expenses for Stanford = 46,143.90

e). For North Carolina, we have

Total tuition fees for North Carolina = 41,988.34

Total living expenses for North Carolina = 46,143.90

f). PV of a growing annuity due is

where

Pmt = first payment at the beginning; i = interest rate; g = growth rate; n = number of years

First, we calculate the PV of tuition fees and living expenses for both universities when Brady begins college:

PV of tuition fees for Stanford = [85,317.13/(12%-6%)]*[1 - ((1+6%)/(1+12%))^4]*(1+12%) = 314,811.45

PV of living expenses for Stanford = [10,947.69/(12%-6%)]*[1 - ((1+6%)/(1+12%))^4]*(1+12%) = 40,395.86

Total PV for Stanford = 314,811.45 + 40,395.86 = 355,207.31

PV of tuition fees for North Carolina = [9,598.18/(12%-6%)]*[1 - ((1+6%)/(1+12%))^4]*(1+12%) = 35,416.29

PV of living expenses for Stanford = [10,947.69/(12%-6%)]*[1 - ((1+6%)/(1+12%))^4]*(1+12%) = 40,395.86

Total PV for North Carolina = 35,416.29 + 40,395.86 = 75,812.15

Now, we calculate how much they need to save per annum for 13 years to get to these PVs:

PMT for Stanford: FV = 355,207.31; N = 13; rate = 12%, solve for PMT. Per annum amount = 12,672.80

PMT for North Carolina: FV = 75,812.15; N = 13; rate = 12%, solve for PMT. Per annum amount = 2,704.76

Note: The question does not specify whether the saving is to be made at the beginning or end of the year. Here, we have assumed end of the year for calculations. If it is beginning of the year, then Type = 1 will have to be input in the financial calculator for the PMT value and it will be different from the ones calculated above.

As a percentage of Greg's annual income, annual savings for Stanford will be 12,672.80/95,000 = 13.34%

Annual savings for North Carolina will be 2,704.76/95,000 = 2.85%

Saving almost 13.5% p.a. for education needs does not seem very feasible unless expenditure is severly curtailed. Going only by the givne financials, North Carolina is a better option than Stanford.