Rate of return to Investment
Rate of Return to Investment
The Concept of investment For a one period investment, the ror can be evaluated each year R t+1 For investments that generate returns in many periods, there are two ways of describing the rate of return ROR in year t-yield/investment Often ask what is rate of return to an investment project?
The Concept of Investment • For a one period investment, the ROR can be evaluated each year. • For investments that generate returns in many periods, there are two ways of describing the rate of return. – ROR in year t = yield/investment. – Often ask: What is rate of return to an investment project? t t 1 t t p p R p + − =
The Example of Consol A consol (or perpetuity) that pays $100 annually can be bought and sold at the market for $1000 Want to compare the investment in the bond ($1000)with alternative investment opportunities(e.g, bank deposit) 0: What is the interest rater(or effective rield) consistent with this price?
The Example of Consol • A consol (or perpetuity) that pays $100 annually can be bought and sold at the market for $1000. • Want to compare the investment in the bond ($1000) with alternative investment opportunities (e.g., bank deposit). • Q: What is the interest rate R (or effective yield) consistent with this price?
Effective Yield of a bond A: Ther that equates the bond price with the present value of the bond Present value of the bond is 100 100 100 100 100 PV= (1+R)(1+R)(1+R)(1+ R Letting bond price equal to the Pv, 100 1000 R →R=100/1000=10
Effective Yield of a Bond • A: The R that equates the bond price with the present value of the bond. • Present value of the bond is • Letting bond price equal to the PV, • R=100/1000=10% 100 1000 R = 234 100 100 100 100 100 ... (1 ) (1 ) (1 ) (1 ) PV R R R R R = + + + + = + + + +
Generalize to all investment Effective yield(or rate of return)is the r that makes the present value of investment returns equal to the present value of the cost Our example: cost=1000 in period 1 return=100 each year starting from period 2 Education example is a little more complex
Generalize to All Investment • Effective yield (or rate of return) is the R that makes the present value of investment returns equal to the present value of the cost. • Our example: cost=1000 in period 1; return=100 each year starting from period 2. • Education example is a little more complex