Financial Planning: Time Value of Money Case Study & Solutions

This case study delves into the financial planning scenario of Ambrose Studebaker, focusing on the application of time value of money principles. It addresses Studebaker's financial goals, particularly retirement savings and his child's education expenses. The analysis examines Morton's proposal of investing in a life insurance policy, questioning its viability compared to alternative investments with higher yields. It also explores the implications of repositioning home equity through a mortgage, calculating annual mortgage payments for both 30-year and 20-year terms. Furthermore, the case study involves determining the loan balance at specific points in time, specifically years 19 and 20, under a 9% mortgage. The solutions provided utilize present value and future value calculations to assess investment returns and mortgage obligations, offering a comprehensive understanding of financial planning strategies and time value of money concepts.

FINANCIAL PLANNING- TIME VALUE OF MONEY
Financial Planning
Time Value of Money – Case 1

2ReferencesReferences
FINANCIAL PLANNING- TIME VALUE OF MONEY
Q1 On what financial goals dose Studebaker seem to be focusing? Is it the correct goal?
Explain.
Studebaker is currently focusing on the financial goal of additional savings for future use
after 20 years when he would like to retire, and also to meet the expected higher education
expenses of his child who would be 20 years old by that time.
However, while considering Morton’s proposal of investing in 6% yield life insurance policy,
he is ignoring time value of money or the opportunity cost of investing his money market
funds in a higher 7% investment of similar risk and switching over to a costlier mortgage.
Q2 Morton notes that the $550,000 invested in the single-premium life insurance
policy would grow to $1,763,925 in 20 years for a return of 6 percent a year.
Explain how this return was calculated.
The future value of a single cash flow of $550,000 for 20 years with 6%
compounded annually would earn a simple interest of $33,000 on principal amount
($550,000(1.06)) and an interest on interest component from year 2 (DeFusco, et al.,
2015) . For example, for year 2, interest on interest component is $1,980
($33,000*0.06)
In 20 years, the FV= PV(1+r) n = $550,000(1.06) 20 =$1,763,925
Q3 In order to reposition the equity in his home, Studebaker would have to take
out a 30-year, $705,000 mortgage at 9 percent. Explain how the yearly mortgage
payments on this loan were obtained. If the loan is for only 20 years, what
would be the annual repayment?

3ReferencesReferences
FINANCIAL PLANNING- TIME VALUE OF MONEY
For a 30-year $705,000 mortgage at 9%, an equivalent series of equal annual cash
flows (ordinary annuity) can be computed through Present value interest factor of
annuity formula (Kagan, 2019) .
PV= A*((1-(1+r) -n
)/r)
Or $705,000= A*((1-(1.09) -30
)/0.09)
Solving for A will give $68,622
Considering a 20-year loan repayment term, annual repayment value would be
$77,230
$705,000= A*((1-(1.09) -20
)/0.09)
Solving for A will give $77,230
Q4 For the 9 percent mortgage in Exhibit 4, find the loan balance at the end of
years 19 and 20.
For the 9% $705,000 mortgage, Loan balance at end of year 19 considering loan
repayment term of 30 years would be (DeFusco, et al., 2015) :
Balance at year 19= Balance at year 18*(1+r)- Annuity
Or Loan Balance Year19= $491,384*(1.09)-$68,622=$466,986
Similarly, Loan Balance Year 20=$466,986(1.09)-$68,622=$440,393

4ReferencesReferences
FINANCIAL PLANNING- TIME VALUE OF MONEY
References
DeFusco, R. A. et al., 2015. Quantitative Investment Analysis. Hoboken: John Wiley & Sons.
Kagan, J., 2019. Present Value Interest Factor Of Annuity (PVIFA). [Online]
Available at: https://www.investopedia.com/terms/p/pvifa.asp
[Accessed 13th May 2019].