# Principles of Finance

Any topic (writer’s choice)

FIN 3100                         Principles of Finance                  Summer 2014

Case #2
Basic Concepts: The Time Value of Money
30 points possible

Part 1:  Kate Myers (10 points)

After graduating from Utah Valley State University with a degree in Finance, Kate Myers took a position as a stock broker with Fidelity Investments in American Fork. Although she had several college loans to make payments on, her goal was to set aside funds for the next six years in order to make a down payment on a house. After considering various neighborhoods Kate chose Pleasant Grove as her desired future residence. Based on median house price data, she learned that a comfortable three bedroom, two bath house currently costs about \$259,000. To avoid paying Private Mortgage Insurance (PMI), Kate wants to make a down payment of 20%.

Because it will be six years before Kate buys a house, the \$259,000 price will surely not be the same in the future. To estimate the future home price she considered historic price appreciation in Pleasant Grove. In the past, homes appreciated by about 3% per annum. Kate was satisfied with this estimate of price growth.

Fidelity provides several opportunities for Kate to invest her savings. She feels that a balanced account containing stocks, bonds, and government securities would realistically achieve an annual return of 8%.

Complete the following analysis and write a professional letter to Kate explaining the analysis and findings. Please include a description of the relevant assumptions and any explanatory comments that make the results easier to understand.

•    Taking into consideration the fact that the price of \$259,000 home will grow at 3% per year, what will be the future price of a similar home in Pleasant Grove in six years? What amount will Kate have to accumulate as a down payment if she decides to buy a house in Pleasant Grove?

•    Based on your analysis above, how much will have to be deposited into the Fidelity account (which earns 8% per year) at the end of each month to accumulate the required down payment?

•    If Kate decides to make end of year deposits (rather than monthly deposits) how much would these deposits be? Why is this amount greater than twelve times the monthly payment?

•    If homes in Pleasant Grove appreciate 5% per annum over the next six years instead of the assumed 3%, how much would Kate have to deposit at the end of each month to make the down payment? What if the appreciation was only 2%?

•    Kate is worried that the Fidelity fund earning 8% might be too risky. Redo question number 2 assuming a less risky investment that earns 4%. Also, redo number 2 assuming more risky investment of growth stocks that have an expected return of 13%?

Part 2:  The Pearson Family (20 points)

Matt and Debra Pearson own a four bedroom home in an upscale neighborhood in Orem, Utah. Matt is a partner in the family owned commercial painting business. Debra stays home with their child, Brady, who is age 5. Until recently the Pearson’s have felt very comfortable with their financial position.

After visiting with Larry Sorenson, a financial planner, the couple became concerned that they were spending too much and not putting enough funds aside for both their child’s future educational needs and their own retirement. Matt earns \$95,000 per year, but with the rising costs of education, their past contributions have left them short of their financial goals.

To estimate the amount of money the Pearson’s need to begin putting away for future security some general information was obtained by their financial planner. The couple felt that the amount of money they currently contribute for retirement through the company’s SEP IRA retirement plan would be sufficient for their retirement needs. What they had not accounted for was Brady’s education.

Matt is an alumni of Stanford University, a private school with tuition and book expenses of approximately \$16,000 per year. Debra graduated from Utah Valley University. The expense for tuition and books there is estimated at about \$7,500 per year. When Brady turns 18, the couple wishes to send him to one of these two exceptional universities. They have a slight preference for Utah Valley University. The problem, however, is that with the rate at which tuition is increasing the Pearson’s are not sure they can save enough money and they have decided they do not want to borrow to pay for Brady’s education.

To assist in the calculations assume the tuition at both universities will increase at an annual rate of 7% from now until Brady starts college. Living expenses are currently estimated at \$8,500 per year at both schools. This expense is expected to grow at only 3% per year. Further assume that Pearson’s can deposit their money into a growth oriented mutual fund at the Salt Lake City based mutual fund company, Wasatch Advisors which has historically earned 11% per annum.

The couple wishes to save by having a pre-determined amount automatically withdrawn form their bank account at the end each month. They plan to contribute from now until Brady starts college. When Brady starts college they will stop making contributions. They want to have enough in their account to cover all four years at the time Brady starts college. The plan to make an annual withdrawal from the account to cover both tuition and living expenses for Brady at the beginning of each year for the four years he will be in college.

Complete the following analysis and write a professional letter to the Pearson’s explaining (1) the analysis you performed (2) why you performed it, and (3) the results and conclusions. Please include a description of the relevant assumptions and any explanatory comments that make the results easier to understand.

•    What will be the tuition expense, living expense, and total expense for each of the four years that Brady will attend college? Provide the information for each University.

•    What amount will be needed in the account when Brady starts his freshman year if he attends Stanford? What amount if he attends UVU?

•    How much money will Matt and Debra have to deposit at the end of each month to allow Brady to attend Stanford? How much money will have to be deposited per month to allow Brady to attend Utah Valley University? Assume that Matt and Debra stop making deposits when Brady starts college.

•    The Pearson’s are concerned that given the current market performance the mutual fund will only earn 9% per year. If the return is only 9% how much will have to be deposited per month for Brady to have sufficient funds to attend each school?

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