CFA1 Quans

Quantitative methods
Time value of money
Effective annual rate (EAR)
Effective annual rate (EAR) = (1+stated annual rate/frequency, m) ^ m-1
Annuities
Ordinary annuities: cash flow at the end of each period, normal one;
Annuities due: cash flow at the beginning of each period, first payment =t0; Calculator setting: [2nd][BGN]-[2ND][SET]; same procedure for setback to END;
Payment at beginning of next three years, N=4, always +1 using annuities due
It is a BGN question, if first payment is today!
When calculate PV, make FV=0; when calculate FV, make PV=0 (0 must be input as well)
Perpetuity: PV=PMT/(I/Y)
Loan payment
Borrow 10,000 at 10%, semiannual, 10years. CLT outstanding loan after two year payment?
Use calculator get PMT=802.43
Payment 1: Interest: 10,000*0.05=500; Principal: 802.43-500=302.43
Payment 2: Interest: (10,000-302.43)*0.05=484.88; Principal: 802.43-484.88=317.55
Remaining balance: 10,000-302.43-317.55=9,380.02
Rate of compound growth
Sales for last five years: 4.5, 5.7, 5.3, 6.9, 7.1, CPT compound annual growth rate?
FV=7.1, PV=-4.5, N=4, PMT=0, CPT-I/Y (5 years growth represent 4 years growth)
Continuously compounded rate
Effective annual rate=eR*t-1, where t is holding period
Calculator: ln(1+HPR)=Rcc
Discounted Cash Flow Applications
Cash flow for perpetuity case
CPT NPV: cash flow/discount rate-CF0
CPT IRR: Cash flow/IRR=CF0
Money-weighted return and time-weighted return
Same question: buy stock $100 at t=0, buy another same stock $120 and receive $2 dividend at t=1, sell two stocks for $130/each and receive $2 dividend/each at t=3
For money weighted: apply the concept of IRR
Deposit 100 at t=0, and deposit 118 (120-2) at t=1, and receive 264 at t=2
Use calculator: CF0=-100, CF1=-118, CF2=264, CPT→IRR
For time-weighted (preferred, because not affected by timing of cash inflow and outflow):
Calculate return for each holding period:
Holding period 1: beginning value=100; dividend paid=2; ending value=120
Holding period 2: beginning value=240;