Question

You are considering an investment that will pay you $3,000 for the next five years. That is, there will be five cash flows of $3,000, but the cash flows are paid at the beginning of the year. • Your opportunity cost of capital (r ) is 7.75%  Using the present value formula calculate the present value of each of the cash flows by 1. Discounting cash flows using annual compounding 2. Discounting cash flows using monthly compounding 3. Discounting cash flows using continuous compounding • How much would you be willing to pay for the investment using each of the three different compounding scenarios? That is, what is the present value of the cash flows from the investment using each of the three different compounding scenarios? Do not use excel or a calculator to solve

Answer 1

1

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 3000*((1-(1+ 7.75/100)^-5)/(7.75/100))*(1+7.75/100)

PV = 12991.93

2

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+7.75/(12*100))^12-1)*100

Effective Annual Rate% = 8.0313

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 3000*((1-(1+ 8.0313/100)^-5)/(8.0313/100))*(1+8.0313/100)

PV = 12929.46

3

EAR =[ e^(Annual percentage rate) -1]*100

Effective Annual Rate=(e^(7.75/100)-1)*100

Effective Annual Rate% = 8.0582

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 3000*((1-(1+ 8.0582/100)^-5)/(8.0582/100))*(1+8.0582/100)

PV = 12923.52