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The Time Value of Money

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.