1/15/2015
FUTURE VALUE
$100 lump sum at the end of year 2.
I% = 10%
Ordinary annuity of $100 per year for three years.
I% = 10%
Time period 0 1 2 3
Cash Flow 0 100 100 100
FV at year end 331.00 $331.00 using the FV function
Uneven cash flow stream.
I% = 10%
Time period 0 1 2 3
FV at year end
Retirement Analysis:
Annual retirement payment $145,000
Return on investments 10%
Years to retirement 30
# of yrs to receive payment 20
Step #1: Determine PV of 20-yr. annuity on day of retirement $1,234,466.74
Chapter 29. Mini Case
Susan Greene is a financial planner. Her job is to suggest and implement
investment and savings plans for clients, some of whom are of modest means
a. Draw time lines (1) for a $100 lump sum due at the end of Year 2 and (2) for a 3-year
$100 annuity. Explain how each investment of $100 grows to its future value after 3 years if
the interest rate is 10 percent
Time period 0 1 2 3
FV at year end 110
BOND VALUATION ANALYSIS
KEY INPUT KEY OUTPUT
Coupon rate 10.00% Bond Value $1,000.00
VALUE OF 10-YEAR, 10% COUPON BOND IF REQUIRED RATE OF RETURN REMAINS
AT 13% OR 7% AS BOND APPROACHES MATURITY
# of Yrs Int. Rate Int. Rate Int. Rate Select 10-Yr Bond Graph tab below
Until Remains at Remains at Remains at the worksheet to see the graph of
Maturity 13.00% 7.00% 10.00% this data table.
10 $837.21 $1,210.71 $1,000.00
9 846.05 1,195.46 $1,000.00
8 856.04 1,179.14 $1,000.00
7 867.32 1,161.68 $1,000.00
6 880.07 1,143.00 $1,000.00
5 894.48 1,123.01 $1,000.00
4 910.77 1,101.62 $1,000.00
3 929.17 1,078.73 $1,000.00
2 949.96 1,054.24 $1,000.00
1 973.45 1,028.04 $1,000.00
0 1,000.00 1,000.00 $1,000.00
RISK AND RETURN ANALYSIS
Portfolio Mix:
% High Tech 50.0%
% Collections 50.0%
State of Treas. High Mkt. Port.
the Economy Prob. Bills Tech Collections USR Port. HT/Coll.
Below avg 0.20 8.0% -2.0% 14.7% -10.0% 1.0% 6.4%
Above avg 0.20 8.0% 35.0% -10.0% 45.0% 29.0% 12.5%
`
Expected return 8.0% 17.4% 1.7% 13.8% 15.0% 9.6%
Standard deviation 0.0% 20.0% 13.4% 18.8% 15.3% 3.3%
Coef of variation 0.0 1.2 7.7 1.4 1.0 0.3
Beta coefficient 0.00 1.30 -0.87 0.89 1.00 0.22
Par value (FV) $1,000
Required return 10.00%
Yrs remaining to maturity 10
BETA CALCULATIONS USING FORMULA (EX ANTE DISTRIBUTIONS)
T-Bills
Standard deviation T-bills: 0.0%
Standard deviation Market: 15.3%
Correlation coefficient: 0.0%
Beta coefficient: 0.0%
High Tech
U.S. Rubber
Standard deviation U.S. Rubber 18.8%
Standard deviation Market: 15.3%
Correlation coefficient: 0.73
Beta coefficient: 0.89
Portfolio High Tech/Collections
Standard deviation Portfolio: 3.3%
Standard deviation Market: 15.3%
Correlation coefficient: 0.99
Beta coefficient: 0.22
SECURITY MARKET LINE
Risk-free Rate: 8% See graph of SML by selecting the SML tab
Market Return: 15% below the worksheet.
Beta: 1.00
SML Equation: 15.0%
Expected Returns
Beta Req. Return High Tech Collections
15.00%
-1.00 1.00%
-0.87 1.94% 1.7%
-0.75 2.75%
-0.50 4.50%
-0.25 6.25%
Standard deviation High Tech: 20.0%
Standard deviation Market: 15.3%
Correlation coefficient: 0.99
Beta coefficient: 1.30
Collections
Standard deviation Collections: 13.4%
Standard deviation Market: 15.3%
Correlation coefficient: -0.99
Beta coefficient: -0.87
STOCK VALUATION ANALYSIS
CAPM
Beta (b) 1.2 Stock’s required return 13.00%
Risk-free rate (kRF)7%
Required return on market (kM)12%
Constant and Zero Growth Stock: Dividend Stream:
Supernormal Growth Stock:
Current price (P0)$54.11
Div growth rates:
Year 1 30.00%
Year 2 30.00%
Year 3 30.00%
Year 4 and after 6.00%
Required rate of return 13.00%
Last dividend (D0)$2.00
Dividend Projections During
Supernormal Growth Period:
Year 1 $2.60
Year 2 3.38
Year 3 4.39
Value of Stock After
Supernormal Growth: $66.54
Last dividend paid (D0)$2.00 D1$2.12
Current stock price, P0$30.29
Expected return, given P013.00%
1,300
1,500
10-Year, 10% Annual Coupon Bond Values Over Time
If Interest Rate Remains Constant
k = 7%
20.00%
25.00%
Security Market Line (SML)
High Tech
SML