Determinants of Interest Rates r = nominal rate of return
r = r* + IP + DRP + LP + MRP r* = real rate of return
r = 8%, r* = 4%, IP = ?, given that DRP = 0%, LP= 0%, MRP = 0%
8% = 4% + IP + 0% + 0% + 0% = 2%
Marginal vs Average Tax Rate
Income = $35,000 Income = $120,000
Marginal Tax Rate = ? 15% Marginal tax rate = 39%
Tax Liability = ? (0.15)(35,000) = $5,250 Tax Liability = 22,250 + 20,000(0.39)
Average Tax Rate = ? (5,250 / 35,000) = 15% = 22,250 + 7,800 = 30,050
*table should be available Average Tax Rate = (30,050/120,000) = 25.04%
Future Value
FVN =PV* (1 + (r/M))N+M FV = 250,000 ( 1 + (0.06/4)(4)(4)
PV = $250,000 = 250,000 (1 + 0.015)(16)
N = 4 years = 250,000 (1.015)(16)
r = 6% = $317,246.39
Quarterly Compounding M = 4
FV = ?
Present Value
PV =FVN / ((1 + (r/M))N+M)PV = 100,000 / (1 + (0.07)2)
r = 7% = 100,000 / (1.07)2 = $87,343.87
N = 2
FV = 100,000
DuPont Equation
ROE = ROA x Equity Multiplier ROA = (Net Income / Total Assets)
ROE = (Net Income / Sales) x (Sales / Total Assets) ROA = Profit Margin x Total Asset Turnover
x (Total Assets / Common Equity) ROA = (Net Income / Sales) x (Sales / Total
Assets)
Equity Multiplier ≥ 1 (TOTAL ASSETS / TOTAL EQUITY) = (1000/500) = 2
=1 if no debt
ROE = ROA 10% = 5% (0)
CAGR
CAGR = (End Value / Beg Value)(1/# of years) – 1 CAGR = (5500 /4000)(1/8) - 1
Suppose that WPCarey enrollment of 5500 =(1.375)(1/8) - 1
students in 2018. Compared with historical = 1.0406 -1 = 4.06%
data, finding in 2010 the enrollment
= $4000 students. What is the annual
growth rate of student body?
APR vs EAR
(1 + EAR) = (1 + (APR/M))M(1 + EAR) = (1 + (0.1/365)365
APR = 10% 1 + EAR = (1.00273973)365
Daily Compounding M =365 1 + EAR = (1.1052)
EAR = 10.52%
