Formulas and Calculations Flashcards
All relative calculations for the CPWA© exam
Holding Period Return formula?
HPR= (P1 - P0 +D1) / P0
P0 = initial investment
P1 = FMV at end of holding period
D1 = Div. paid
Geometric Average formula?
A geometric mean is found by multiplying the different stock prices and then taking the nth root, where n equals the number of stocks.
Ex. two stocks priced at $10 and $20
Arithmetic avg is $15
Geometric avg. is $14.14 (use Yx on financial calculator)
Internal Rate of Return / Dollar-Weighted Return formula?
An investor buys one share of stock for $50 at the beginning of the first year and buys another share for $55 at the end of the first year. The investor earns $1 in dividends in the first year and $2 in the second year. What is the IRR if the shares are sold at the end of the second year for $65 each?
There are two cash outflows: $50 at time period t = 0 and $55 at time period t = 1. There are also two cash inflows: $1 at time period t = 1 and $132 ($2 dividends plus $130 proceeds) at time period t = 2. The next step is to group net cash flow by time. The t = 0 net cash flow is −50, and t = 1 net cash flow is −54 (−$55 + 1), and the t = 2 net cash flow is $132 ($130 + $2). The net cash flows can be entered on the calculator to solve the IRR. The IRR is 17.21 percent. This is also called the dollar weighted rate of return because it weighs the amount of all dollars flowing into and out of a portfolio during each time period.
Time-Weighted Return (TWR) formula?
An investor buys one share of stock for $50 at the beginning of the first year and buys another share for $55 at the end of the first year. The investor earns $1 in dividends in the first year and $2 in the second year. What is the TWR if the shares are sold at the end of the second year for $65 each?
The first year is ($55 − $50 + $1) ÷$50 = 12%
The return for the second year is ($130 − $110 + $2) ÷$110 = 20%
The time weighted rate of return (geometric average) is
((1.12)(1.20)) 1/2 − 1 = 15.9%
Nominal risk-free rate?
= [(1 + real risk-free rate) / 1 + inflation rate)] - 1
Required Rate of Return formula?
Capitalized Earnings formula?
Valuation = earnings / (discount rate - growth rate)
Calculate Present Value (PV) formula?
PV = FV / (1 + r)n
FV = future value of investment at the end of n years
r = interest rate during each compounding period
n = number of compounding periods
EXAMPLE:
Calculate the present value of $15,000 to be received in 5 years using an annual interest rate of 10%. Solution:
15,000 FV, 10 R, 5 N, calculate PV → $9,313 (ignore the sign)
Calculate Future Value (FV) formula?
FV = PV (1 + r)n
PV = Present value or value of investment today
r = interest rate during each compounding period
n = number of compounding periods
EXAMPLE:
Calculate the future value of $15,000 invested for 5 years using an annual interest rate of 10%. Solution: −15,000
PV, 10 I, 5 N, calculate FV → $24,157
Calculate the future value of an ordinary annuity that will pay $1,000 per year for each of the next 15 years while earning a 10% rate of return.
Solution: 15 N, 10 I, 1000 PMT, CPT FV → $31,772
Calculate the present value of an annuity of $1,000 received annually beginning today and continuing for 15 years earning a 10% rate of return.
Solution: Your calculator should be set at beginning mode; 15 N, 10 I, 1000 PMT, CPT PV → $8,366
Calculate the NPV of a project with an initial cost of $25,000 that produces the following cash flows: year 1, +5,000; year 2, +5000; year 3, +12,000; year 4, −3000; year 5, +4000. The cost of capital is 5%.
Solution: −25,000[CF0]; 5,000 [CFj]; 5,000 [CFj]; 12,000 [CFj]; −3,000 [CFj]; 4,000 [CFj]; 5 [i]; CPT NPV → −$4,670
Calculate the IRR of a project that has an initial outflow of 25,000 and will generate the following cash flows: year 1, 7,000; year 2, −5,000; year 3, 9,000; year 4, 7,000; year 5, 15,000.
Solution: −25,000 [CF0]; 7,000 [CFj]; −5,000 [CFj]; 9,000 [CFj]; 7,000 [CFj]; 15,000 [CFj]; CPT IRR → 7.64%
Calculate the nominal risk free rate if the real rate is 5 percent and the expected inflation rate is 3 percent:
Nominal risk free rate = (1 + real risk free rate) (1 + inflation rate) − 1
(1.05) x (1.03) - 1 = 8.15%
Typically estimated by adding the real rate to the inflation premium (5 +3 = 8)
Serial Payments:
Assume Jeff wants to start a business in 5 years. He needs to have $150,000 (today’s dollars) in 5 years to finance his business. Inflation is expected to average 3%, and Jeff can earn a 7% annual compounded rate on his investments. In order to determine what serial payment he should invest at the end of the first year, he uses the following formula:
What is Jeff’s payment in the second year?
Solution: 150,000 FV; 5 N; 0 PV; [(1.07 ÷ 1.03) − 1] × 100 [i]; CPT PMT = 27,758.62
27,758.62 [x] 1.03 → 28,591.38
Second year:
Solution: 28,591 x 1.03 = 29,449.12
Ex. Third year; 29,449.12 x 1.03 =
Note: Serial payments are not fixed payments like annuities; the first serial payment will be lass than an annuity payment, but the last serial payment will be more than an annuity payment.
